I realise that Toriyama forgets some things and I realise that he introduced Power Levels so that he could prove that knowing them didn't mean anything, but I dont believe that means he didn't take account of Power Levels throughout the rest of Dragonball Z. I believe all it means is that characters can hide or focus their Ki to make themselves appear weaker or artificially strong. The best example of this is when Power Levels with numerical values were first introduced - when Raditz arrived.

After removing their weighted clothing, Piccolo's Power Level raised from 322 to 408 and Goku's from 334 to 416 [DB #199]. They weren't hiding their power at this time, much like the farmer with a Power Level of 5, but Goku made a Kamehameha with a PL of 924 and Piccolo a Special Beam Cannon with a PL of 1,330 [DB #201]. They were able to do this by concentrating their Ki and building it up. This is exactly like the difference between a battery and a capacitor. A battery is how Raditz works. It has a maximum voltage output and a max amp output, and he cannot go higher than that because he never learned to. Goku and Piccolo can also work like a battery and fire Ki blasts of full power instantly, but they can also act like capacitors and use their Ki to build the power from the battery into something greater and more powerful to be released in a short time.

So it's not that Power Levels are irrelevant, they've been referenced since early in Dragonball but they weren't given an actual number until Dragonball Z [DB #195]. To me, the point Toriyama was trying to make with DBZ is that knowing a number doesn't matter when you can manipulate your Ki, but that doesn't mean those max powers dont exist and a number can't be put to them.

In the Dragonball manga there are 2 different measures of Ki or Power Level. The first system is that used by Frieza's men, first seen used by Raditz to measure the PL of a normal human at 5. This system goes up to Future Trunks appearing in front of Frieza when one of his foot-soldiers measures his PL at 5. So here's the list of all stated Power Levels through this method:

• Farmer - 5 - DB#195
• Piccolo - 322 - DB#195
• Gohan - 710 - DB#199
• Goku - 334 - DB#199
• Piccolo - 408 - DB#199 (less weighted clothes)
• Goku - 416 - DB#199 (less weighted clothes)
• Gohan - 1,307 - DB#203
• Master Roshi - 139 - DB#209
• Krillin - 206 - DB#209
• Tien - 250 - DB#209
• Yamcha - 177 - DB#209
• Piccolo - 329 - DB#209
• Gohan - 981 - DB#214
• Piccolo - 1,220 - DB#214 (less weighted clothes)
• Krillin - 1,083 - DB#214
• Saibamen - 1,200 - DB#215 (rivals Raditz power)
• Goku - 5,000 - DB#222 (suppressed)
• Goku - over 8,000 - DB#224
• Goku Kaioken x3 - over 21,000 (stated) - DB#230 (over 24,000 actual)
• Gohan - 1,500 - DB#248
• Krillin - 1,500 - DB#248
• Vegeta - 24,000 - DB#249
• Vegeta - 18,000 - DB#249 (same as Cui when they last met)
• Cui - 18,000 - DB#249 (same as Vegeta when they last met)
• Namekians - 1,000 - DB#253 (suppressed)
• Namekians - 3,000 - DB#253
• Gohan - over 10,000 - DB#274
• Krillin - over 10,000 - DB#274
• Vegeta - 30,000 - DB#275
• Goku - 5,000 - DB#279 (suppressed)
• Goku - 60,000 - DB#284 (suppressed)
• Captain Ginyu - 60,000 - DB#284 (suppressed)
• Goku Kaioken - 180,000 - DB#285
• Captain Ginyu - 120,000 - DB#285
• Nail - 42,000 - DB#286
• Frieza 1st Form - 530,000 - DB#286
• Frieza 2nd Form - over 1,000,000 - DB#296
• Future Trunks - 5 - DB#331

The second form of measurement of Power Levels comes in the Buu arc, where Super Saiyan Goku is measured by Babidi's meter as "3000 Kilis" [DB #452] and Yakon is said to be 800 Kilis. In the anime Dabura says he can take on fighters equal to "4000 Kilis" [DBZ Ep 223].

Given the gaps, there will have to be something in the middle to help us out.

DAIZENSHUU

There are also official numbers released through the Daizenshuu, but one of the figures released through the Daizenshuu is that Raditz had a Power Level of 1,500, though many translations of the manga say that the Saibamen (PL 1200) were each as strong as Raditz. But even if that wasn't said, Piccolo fires a beam last measured at PL 1,330 through Raditz that at 1,500 he should've been able to take - were it not for Gohan weakening him [DB #203]. When Gohan did weaken Raditz by head-butting his chest, Gohan has a power level of 1,307:

It's important that Raditz says "The brat has more power than you!" because if Raditz really was only the same strength, you'd imagine him saying "The brat even has more power than me!" confidently knowing Gohan's PL was back down to "1" at this point. So Raditz power level must surely be above 1,307. That and the original Japanese manga doesn't say that the Saibamen are equal to Raditz, it says they rival or are comparable to Raditz.

So the Daizenshuu could appear to be reliable in many or most circumstances, and Akira Toriyama did oversee their production, so they do have legitimacy. Importantly, it's the Daizenshuu that give us Frieza's 4th Form Max at 120,000,000, and Frieza's power Level is a significant link between the Power Level section of Dragonball and the rest of the series, although appearing to have been pulled out of a hat and baring no relation to Frieza's original Power Level, so it's worth keeping an eye on.

Some people here will have read what I've written about Piccolo destroying the moon a bunch of times and for those that have, I sympathise, but I believe I have - over time - refined my ideas to a point I'm happy with.

DEBUNK 1

It has been argued that Piccolo would not have been Power Level 408 when he destroyed the Moon [DB #208] because Master Roshi destroyed the Moon and his power level is 139. The assumption being made is that when Master Roshi destroys the Moon with a "Maximum Power Kamehameha" [DB #51] he was twice as strong as before, so the real Power Level needed to destroy the Moon would be 278. However Yamcha believes that would kill Goku, and the Oozaru Ape form increase the Power Level by 10x. Even if Goku's Power Level was only 50 at the time, his Oozaru would be 500.

Add to this the events of the Resurrection F saga in Dragonball Super in the movie, manga [RoF #3] and anime [DBS Ep 21], Master Roshi uses his Buff mode - just like when he destroyed the Moon - and takes on several of Frieza's men, who are known to generally be of Power Level around 1,000.

It's more likely that Master Roshi's buff mode is a 10x multiplier like the Oozaru, than just a doubler, therefore Master Roshi's power in Buff could be far too high to measure the Moons destruction by. The weakest person to ever destroy the moon was Piccolo. The truth is Master Roshi is too much of a question mark to rely on.

PICCOLO'S FEAT

When Piccolo fights Raditz the very first time and hopelessly loses [DB #195] he has a weighted PL of 322 though his true unweighted power was 408. Freiza states that taking off the weighted clothing will only make Piccolo faster, not stronger, so even though Raditz's scouter says 322, his ki blast power without a power-up would still be 408. Not powering up is important because that's how Piccolo fired his Ki blast. When he destroys the Moon [DB #208], Piccolo's weighted PL is 329, higher than the 322 when facing Raditz, so he's gotten stronger.

Now either the weighted clothes take a proportion of Piccolo's apparent PL away (408 - 322 = 86 which is 21% of full power) in which case his true PL would be 417, or there is a specific gap the weights make, which would be 86 and his new PL would be 415. I'm more inclined to believe that it's a proportional difference, otherwise Piccolo wouldn't bother removing it against Frieza as the Power Levels would be so great that the difference would be negligible. So Piccolo destroyed the Moon with a Power Level of not more than 417.

But could he use full power that quickly?

DEBUNK 2

It has been argued that because Piccolo didn't power up, he didn't use his full power, but that's not necessarily true. When Vegeta's power has increased from 18,000 to 24,000 after healing after his fight with Goku on Earth, he fights Dodoria. The Daizenshuu suggest his Power Level is 22,000. This is backed up by Dodoria's reaction to the news that Vegeta had eclipsed 22,000, so it's likely to be accurate:

Vegeta kills an aware Dodoria with a single Ki blast without powering up, and Vegeta's expression is no different to Piccolo's - they are both using effort. For this to happen, Vegeta needs to have raised his power to over 22,000 quickly since Dodoria is trying to escape. But only a little over 22,000 wouldn't be enough to wipe him out in one blast. It would need significantly more, but without powering up, Vegeta only has 24,000 to give, and so it seems reasonable that a character should be able to use a full power Ki blast without powering up, but not a specifically high powered ki blast like a Kamehameha, Special Beam Cannon or Gallic Gun without powering up. And therefore it's reasonable to say that Piccolo indeed could have used his full power that quickly in a Ki blast.

Whether or not he did is a different issue, he may have used less, but the effort on his face and the urgency of the situation suggest he would have used everything he could muster in that moment. Up to this point Piccolo has never seen anyone destroy anything remotely close to the size of the Moon before in Dragonball, so there's no reason to think he wouldn't put his all into it just like Master Roshi did.

CONCLUSION

It's my opinion that Piccolo was perfectly capable of using his full power in a Ki blast without powering up, but not more as he didn't concentrate his attack, and I believe that Power Level to be 417.

I dont think, however, that Piccolo using a Power Level of 417 would be readily accepted by the community -even though I believe in it- but it must be acknowledged that his power had risen since the Raditz fight, so I will use the 415 Power Level in the interests of not high-balling, when using this number later on.

It's also worth noting that when Piccolo destroyed the Moon, he vaporised it, meaning that he could probably have destroyed the Moon with less power without vaporising, but it's impossible to know how much less, and since Roshi's feat never gave a clue to his power level or how the moon was destroyed, there's little point in debate.

So I will say that it took a power of 415 to vaporise the Moon. I will though, provide figures based on this and the 408 figure as I'm also sure that the community will also be reluctant to acknowledge the extent of Piccolo's growth and apply it.

There are many ways to apply energy to matter in such high quantities that sufficient bonds within the matter will be broken and atoms and particles will become individual and unlinked to others, i.e. vaporisation. In DBZ they use Ki energy, in the real world this can be achieved with heat, electricity, high energy electromagnetic radiation such as gamma rays and ultra high velocity collision.

The application of the energy may be different but the level of energy required to apply to bonds in order to break them is the same. One large real world explosive that has temperatures high enough to vaporise large amounts of matter is the nuclear bomb.

WHAT SIZE OF NUKE TO DESTROY THE MOON?

All nuclear blasts are different are extremely hard to predict accurately because not all of the nuclear material in a nuke will be used in the process and the amount that is used in seemingly identical amounts of nuclear material can produce different blast energy yields, but there is a range of predictable destruction that relates to the kiloton yield of the weapon itself.

The radius r (in feet) of the cavity is proportional to the cube root of the yield y (in kilotons), r = 55 * y^​(1/​3). For an example, an 8 kiloton explosion will create a cavity with radius of 110 feet (33.53m) which is the Melt Cavity (vaporised) and Crush Zone.

Assuming this equation is consistent and nukes are more consistent, this means that if you know the radius of an amount of rock you want to vaporise, you can use this equation and this table to discover how much of a yield is required by the nuke. The Moons radius is 1,737 km, or 1,737,000m which is what the Melt Cavity must be. Putting the radius of the Moon in the middle of the Melt Cavity range, this means a total theoretical cavity of somewhere in the region of 7,599,375m (24,932,333 ft) which includes the Melt Cavity and the Crush Zone.

Rearranging the equation to make 'y' the subject, I'll use the equation to see how many kilotons of yield are required to vaporise the moon.

• y = r^3 / 55^3
• y = 24,932,333^3 / 166375
• y = 93,153,824,053,382,218 kilotons or 93.154 exatons

However, these equations use a constant that is based on the density of rock (2600kg/m^3), but the Moon has a mean density (3340kg/m^3) that is 1.2845x greater than that of general rock. Accounting for this the size of the nuke required to vaporise the Moon would be 119.667 exatons yield.

HOW ABOUT THE EARTH?

The Earth has a radius of 6,371 km, or 6,371,000m. Using that as the Melt Cavity would give a total theoretical cavity including Melt Cavity and Crush Zone of 27,873,125m (91,447,260 ft). Using this, the kiloton yield for a nuke to vaporise the Earth would be:

• y = r^3 / 55^3
• y = 91,447,260^3 / 166375
• y = 4,596,465,700,869,358,312 kilotons or 4,596 exatons

Again though the mean density of Earth is not 2.6 tonnes per cubic meter, it's 5.51 or 5510kg/m^3. Accounting for this, the size of the nuke needed to vaporise the Earth would be 9.741 zettatons yield.

OTHER CELESTIAL BODIES?

The 9.741 zettatons of the Earth is 81.4x bigger than that required for the Moon (119.667 exatons yield), which is also the difference between the Earth's mass and the that of the Moon (5.972 × 10^24 kg / 7.348 × 10^22 kg = 81.3) - the difference of 0.1 can be accounted for in the rounding up of the radii of the Moon and Earth.

What these numbers show is that the amount of energy required to vaporise the Moon and the Earth when accounting for the difference in density is equal to the difference in mass, which makes sense since Mass is a measure of how much matter is present and it's matter we're vaporising. Therefore, to know how much Ki is required to destroy a Celestial Body can be related to the Moon, it's mass and how high a Power Level was required to destroy it.

Using the Moon and Piccolo's Power Level(s) as a basis, and knowing that the level of energy needed to destroy a specific amount of mass, its possible to calculate the Ki required to vaporise other Celestial Bodies within our Solar System.

The Sun itself accounts for 99.86% of the mass of the entire Solar System, so assuming a character knew a technique to do it, it would take a Power Level of 11,243,608,382 or 11,053,957,156 to destroy the Solar System. These, I believe Toriyama would round off to 11,245,000,000 and 11,055,000,000 respectively.

If the Daizenshuu is correct, and remember its writing was overseen by Akira Toriyama though isn't always accurate, Max Power 4th Form Frieza had a Power Level of 120,000,000. But was Frieza's Power Level really that high? I could imagine someone working on the Daizenshuu asking Toriyama what Frieza's max power was, saying "I was thinking around 120,000,000" and Toriyama saying "Sounds about right".

But how do you get to 120,000,000?

FRIEZA'S 1st & 2nd FORMS

Well, none of the transformations in the manga are given a specific multiplier. The anime on the other hand states that Oozaru Great Ape is 10x stronger than base, but even that is about all for the anime. The closest in the manga is when Frieza goes from 530,000 to over 1 million.

If Frieza's power doubled in this transformation, it would be 1,060,000, which would enough to surpass 1 million, but not by so much that would make Frieza need to describe it in another way, especially since the only person Frieza told his original strength to was Nail, so there'd be little point in telling Vegeta his power had doubled as a frame of reference, but Vegeta understand the number 1 million as a Power Level very well. So it seems likely that this transformation doubles his strength.

FRIEZA'S 3rd FORM

Now we dont know how much power Frieza's next transformation but in his 2nd Form Piccolo is a match for him, in fact Vegeta notes that Piccolo is actually better than Frieza [DB #301], though the fight is close, so not by much. When Frieza transforms again into his 3rd form, his power increases greatly, but not so much a newly healed Gohan can't give him a little trouble. At this point, from the action it's likely that Both Piccolo's and Gohan's powers are over 1 million with Piccolo maybe being 1.1 million. And Frieza manages their combined efforts without giving too much ground.

If we think back to when Piccolo (408) was fighting Raditz (1500) with Goku (416), their powers amounted to little under a third of Raditz but combined they managed to defeat him. Were Raditz only around a Power Level of 800, they would have been able to defeat him without Goku sacrificing his life. So given that Frieza felt the need to transform into his forth form without being too pushed, it seems likely that he felt a combined effort by Piccolo and Gohan along with Vegeta and Krillin throwing Destructo Discs may have been too much for him. Going by the Piccolo/Goku/Raditz fight it would seem that Freiza's 3rd Form would be around 3x higher than his 2nd or a Power Level of 3,180,000 at this point.

FRIEZA'S FINAL FORM

We know that;

• in whatever fraction of his full power he's using, Final form Frieza is too powerful to even be touched by Piccolo, Gohan and Krillin combined [DB #305].
• they cant see him move, though Vegeta can and kicks Gohan out of the way of an attack. Vegeta also manages to surprise Frieza with a max power ki blast, but it was delt with easily enough.
• Goku is more powerful than Vegeta when he arrives to face Frieza as he could tag him when Vegeta couldn't [DB #307], but not powerful enough not to have to use Kaioken x10 while doing it [DB #312].
• Goku had to use Kaioken x20 to roughly match Frieza at 50%.

If Goku roughly matched Kaioken x20 to 50% Frieza, that means Kaioken x40 would be roughly 100% Frieza and that Goku without Kaioken would be around 1/40th of Frieza's max. Knowing that Vegeta at his death is stronger than 3rd Form Frieza but weaker than Goku Kaioken x10/25% Frieza, due to Vegeta being able to cope with Final Form Friezas speed until he raised his power again, and knowing that Goku was weaker than Vegeta when both recovered from near evenly fatal wounds, Goku would have been stronger than Gohan but weaker than Vegeta when he recovered and began to fight Frieza - hence why he was using Kaioken x10 the whole time. So placing Goku somewhere around the Power Level of 3rd Form Frieza could be about right.

So I believe what's happened is that someone working on Daizenshuu 7 under Akira Toriyama has rounded down Frieza's first transformation to PL 1,000,000, his 2nd transformation made the fight like Piccolo+Goku vs Raditz, so is 3 times stronger (3,000,000) and based on Goku's kaioken x20 and Frieza's 50% has made Frieza's final transformation 40x stronger to make it a PL of 120,000,000 and assumed Goku to be 3,000,000 based on that.

You only have to look at Toriyama's choices for power levels after Goku arrives to fight the Saiyans to know he prefers nice round numbers, so it seems fitting that Frieza's

• 1st Form <2x< 2nd Form <3x< 3rd Form <40x< Final Form, and not something like
• 1st Form <1.887x< 2nd Form <2.72x< 3rd Form <44.11x< Final Form

So using these multipliers against Frieza's 1st Form Power Level of 530,000, his max power is likely much closer to 127,200,000, which is not too far away from the 120,000,000 in the Daizenshuu, but it does seem as if the Daizenshuu writers conveniently forgot about the 30,000 that also needed to be multiplied.

According to an interview in Super Exciting Guide: Story Volume, Akira Toriyama explains why Goku's hair turned gold as a Super Saiyan. He follows the answer up with:

Only, at the time, it was considered that his strength would increase 50-fold when he became a Super Saiyan, but that was a bit of an exaggeration. My feeling as the creator is that, while drawing it, I felt that it was about a 10-fold change from what it was up to that point.

Goku's use of the Kaioken means it couldn't be the case that Super Saiyan was only 10x stronger. As I've already shown, Frieza at max power was 40x stronger than Goku since 50% Frieza was roughly equal to Kaioken x20.

I think that Akira Toriyama is referring to a discussion with his editors on his initial ideas of what the Super Saiyan would be like. There are a number of accounts described by Toriyama about clashes with the editors about what would happen in the series. This sounds like another one, that while presenting the character and storyboard, he felt Super Saiyan should be 10x stronger and the editors felt it should be much larger like 50x.

If I had to guess, I would think that this discussion took place while the fight with 3rd Form Frieza was taking place and either has already been part published, or had already been inked. Why do I say that? because it seems clear that the 1st transformation is 2x higher and the 2nd transformation is 3x higher. It would make sense that the 3rd transformation be 4x higher.

Imagining for a moment that when Goku arrived, was only half as strong as 3rd Form Frieza instead of about the same. That would make final form Frieza 8x stronger than him. Goku would still be able to use the Kaioken, but instead of using Kaioken x10 like it was nothing, it would be more like Kaioken x4 as used against Vegeta and ruin his body, like Kaioken x20 did, giving Frieza the advantage again. Goku then turns Super Saiyan and can remain at 10x power for the rest of the fight, over-powering Frieza.

What happened though, was instead of Frieza's smaller power increases which were regarded by Frieza as huge power increases of 2x and 3x multipliers, his 3rd transformation is suddenly 40x higher, which seems far out from what it should be when looking at the other two. If 2 and 3 times higher is considered "huge" by Frieza, what the hell must he consider 40x to be? When you think of it, it really has little effect on most of the fight but for a couple of pages.

So it looks like this is where Akira Toriyama had to adapt his ideas because of the editors and change Frieza's power-up to match more closely Goku's Super Saiyan 50x multiplier imposed upon him. Whatever the point it happened, a 50x multiplier makes sense and the fact he says "at the time" and "while drawing it" shows that he's talking about a time before it was actually published. This is an admission in a round about way by Toriyama that Super Saiyan has a 50x multiplier, but he was never happy about it.

SUPER SAIYAN 2 and 3

In the same release, Super Exciting Guide: Story Volume, there is a section that describes the multiplier of the other transformations.

If Toriyama had to change Super Saiyan from x10 to x50, and Frieza's 3rd transformation from x4 to x40, he dragged things back under his control with Super Saiyan 2 being 2x stronger and Super Saiyan 3 being 4x stronger. In turn these figures highlight the size of the x40 and x50 multipliers of Frieza and Gokus transformations. Nevertheless, these are official releases and according to the introduction of the Super Exciting Guide′s training section, all the information in it is based on data that was supervised by Toriyama, however the clincher for me that these are Toriyama's idea is that SS2 and SS3 multipliers are in line with the low ones Frieza initially had..

As for the nature of the transformations, in an interview in Saikyō Jump June 2014 Issue, Toriyama said:

This explains why Gotenks can transform into Super Saiyan 3 and why Vegeta doesn't bother to try in Dragonball Super. There's is no real need to be able to transform into Super Saiyan 2 to be able to transform into Super Saiyan 3 as they are both just powered up versions of the Super Saiyan.

When Gohan failed to destroy Cell quickly enough, he chose to self-destruct and kill everyone. Goku used Instant Transmission to take Cell away from Earth and allowed Cell to explode on King Kai's planet and he couldn't think of anywhere more remote and he needs a Ki to lock on to in order to use Instant Transmission. It makes sense. But Cell didn't die. One tiny part of him remained, his core, and as long as it remained in tact, he could regenerate. When he did and recovered he learned Instant Transmission, having seen it 4 times by this point, and came back to Earth even more powerful than he was before. He made a claim at this point that he was capable of destroying the Solar System [DB #416].

Now you imagine that he means destroying the Solar System in one almighty blast or bomb but all you really need to do is kill the Sun, the rest will follow. At 99.86% of the Solar Systems mass, if you can destroy the Sun, the planets are small fry.

Going by the previously calculated numbers Cell's power level is at either 11,245,000,000 (416) or 11,055,000,000 (408), right?

THE SUN

The thing is, the Sun is ionised gas with a density just 1.41x greater than water. Its essentially a giant ball of condensed protons, and Hydrogen and Helium nuclei. There's so much of it that the gravity it creates (28x that of Earth) causes an immense outward pressure at the core called Electron Degeneracy Pressure -which resists the compression of sub-atomic matter into a smaller space- to be overcome, fusing protons in a process that will lead to Hydrogen nuclei and fusing Hyrdogen eventually into Helium nuclei.

It would be very difficult to vaporise something like the Sun which is literally only bound together by it's huge gravity. You can't break bonds that dont exist, all that would happen is that Cell would simply be adding energy to the system.

But what about that energy? When these fusions take place they release energy in the form of radiation and this energy pushes outward expanding the star, which is why the Sun has only the density of 1.41 tonnes per cubic metre. If you increase the energy within a closed system, the pressure rises. In the Sun, introducing a huge amount more energy into the 14 million Kelvin core would increase the pressure even more greatly and two things would happen:

1. The rate at which fusion happens would increase greatly, creating more energy and adding to,
2. The pressure pushing outward, which would also increase greatly.

SUPERNOVA

99% of nuclear fusion takes place in the central 24% of the Sun [http://science.sciencemag.org/content/316/5831/1591], a ball 432,000km in radius which contains 0.2 solar masses, or 20% of the Suns mass. Cell doesn't need to input enough energy to vaporise the Sun, he only need to input the energy required to vaporise the core - but this wont vaporise the core, it will only add energy, in huge quantities.

The addition of vast quantities of energy equivalent to a 647.5 yottaton yield nuke (20% of 27,055,102x the yield to vaporise the Moon) or 2.709 trillion yotta-joules of energy (2.709 x 10^36 J) (4.184 gigajoules per ton [https://en.wikipedia.org/wiki/TNT_equivalent]). This is around 82,000 times more than the total energy output of the Sun for an entire day (3.3 × 10^31 J [https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)#.3E_1025_J]).

If Cell added this amount of energy to the core of the Sun, the Sun would react by expanding the core at an explosive rate as the Sun suddenly gains 269 years of energy output within a few seconds. To do this Cell would need a Power Level of 2,248,721,676 (Piccolo 415 PL vs Moon) or 2,210,791,431 (Piccolo 408 PL vs Moon).

So rounding off (Toriyama likes nice round numbers), Cell would need a Power Level of 2,250,000,000 (415) or 2,210,000,000 (408) to make the Sun go Supernova, and that would constitute destroying the Sun and just a small proportion of that (15,741,052 or 15,475,540 - 0.14% in both cases) would be needed to destroy the rest of the Solar System.

SUPER PERFECT CELL vs FRIEZA

Using my figures for Frieza (PL 127,200,000) Super Perfect Cell is either 17.7x stronger or 17.4x stronger than Frieza, with a mean average of the two being 17.5x stronger. The question is, is it plausible for Cell to be 17.5x stronger than Frieza?

Before reading the following, it's worth remembering what even a small difference in strength can mean. The simplest and probably most well known example of power classes is in boxing. If you have two equally skilled fighters in two different weight categories, the heavier fighter will invariably win. These are the Olympic weight classes:

• Light-Flyweight 49kg
• Flyweight 52kg (1.06x Light-Flyweight)
• Bantamweight 56kg (1.08x Flyweight)
• Lightweight 60kg (1.07x Bantamweight)
• Light-Welterweight 64kg (1.07x Lightweight)
• Welterweight 69kg (1.08x Light-Welterweight)
• Middleweight 75kg (1.09x Welterweight)
• Light-Heavyweight 81kg (1.08x Middleweight)
• Heavyweight 91kg (1.12x Light-Heavyweight)
• Super-heavyweight over 91kg

There are similar differences between weight classes as there are between Vegeta (24k) and Dodoria (22k) & 1st form Zarbon (~23k). In both of those fights, Vegeta was victorious and Dodoria especially was easy. Zarbon was similar to a Flyweight vs a Light-Flyweight, while Dodoria was similar to a Heavyweight vs a Light-Heavyweight. When Vegeta (24k) faced Cui (18k), the difference was similar to a Heavyweight vs a Welterweight. When Goku faced Recoome, the difference was similar to a Heavyweight fighting a Light-Flyweight.

I realise that these fighters are not boxers, but the analogy applies. You would never put a Light-Flyweight in the ring with a Heavyweight. It would mean annihilation. Even jumping just one weightclass is risky, like Dodoria and Vegeta. So bare this in mind when reading the rest because how the fights on Namek and their comparative powers help to judge the following fights and comparisons.

COMPARATIVE POWERS

FRIEZA superseded himself as MECHA-FRIEZA and thought himself now roughly equivalent to SS Goku on Namek, making Mecha-Frieza about PL 150,000,000, or 1.18x stronger than Frieza on Namek:

TRUNKS too is likely around about SS Goku's power level on Namek and Gohan recognises the Ki. Most people assume Trunks to be stronger than Frieza because Frieza is beaten so easily, but Trunks doesn't simply deflect, endure or block Frieza's high powered initial ki blast, he escapes it. Likewise, Frieza and King Cold escape his and as they escape, Trunks comes from behind and above and cuts Frieza in half with a sword. As you can imagine, two more-or-less equal characters fight and one has a sword, the guy with the sword is gonna win, especially if he sneaks up from behind. There's no evidence that actually suggests that Trunks IS stronger than Mecha-Frieza, especially considering the above when Gohan suggests Frieza isn't at full power. It suggest Trunks won because as he said [DB #331] he'll give no mercy. So I think Mecha-Frieza, SS Goku (Namek) and SS Trunks are all more or less the same strength, give or take a couple of per cent.

GOKU on returning to Earth after a year, three hours after Trunks killed Frieza, had a confrontation with SS Trunks in which Trunks attacked Goku with a sword and Goku stopped him with a finger [DB #334] after covering it with protective Ki. After the test, Trunks is impressed with Goku's abilities but Goku points out that Trunks was holding back.

It's not really possible to compare these two characters just from that confrontation, but you do imagine that Goku is more powerful after a year than he was. However he does say that he trained with the inhabitant of planet Yardrat that he only had time to learn one technique but he wasn't there very long. Although he's been away a year and surely has gotten stronger, since Goku spent the rest of the time out in space in a Ginyu Space Ship he probably hasn't gotten that much stronger. But this isn't as important as the 3 years of training until the Androids arrive.

When Goku starts fighting Android 19 [DB #340] the sweat on his face tells you he's struggling from the beginning. Nevertheless he is easily winning, but Piccolo notes that Goku is already fighting all out and should be far stronger.

It would be easy to take what's said here and imagine that SS Goku should be several times stronger than the Androids, but as I've already proved, Toriyama considers 2x or 3x multipliers to be "huge" power-ups. Given that Goku is stronger than Android 19 but not strong enough to kill him with a single punch, it's reasonable to say that Goku is less than 1.3x stronger than A19 during this fight (1.3x being how much stronger Vegeta was than Cui when he nearly killed him with a single punch), but still strong enough at this level to not even be touched by the Android, so at least Vegeta/Dodoria proportions higher in power. However, when the tables turn after 19 absorbs a Kamehameha, Android 19 has a similar fight with Goku as Vegeta did with 1st form Zarbon (PL ~23k), so about 1.05x stronger than Goku.

VEGETA fought a stronger Android 19 than Goku did as he absorbed Gokus Kamehameha, much of which went to replenishing his reserves to be as strong as before and then an increase on top while Goku's power dropped. 19 then jumped on Goku and absorbed much more of his power becoming even stronger. Vegeta takes on the Android easily but loses more energy than he lets on before eventually destroying Android 19 [DB #345]. In the end, Vegeta deals with Android 19 with similar ease as he did Dodoria when Vegeta had a Power Level of 24k and Dodoria 22k and so I would estimate that Vegeta is a similar level above 19 as he was above Dodoria, about 1.1x stronger and probably 1.2-1.3x stronger than 19 before the fight.

At this point, Piccolo is not stronger than Android 20 [DB #346], but he explains he can focus his attacks to be stronger just after tearing the arm off of him.

TRUNKS vs ANDROID 17 was a complete mis-match. Even though Trunks is a Super Saiyan, and Android 17 is holding back, he still nearly takes Trunks out in a single punch. When Android 18 throws Vegeta at him, it finishes him off. This is very similar to when Vegeta killed Cui, except that instead of finishing Trunks off with a Ki blast, he was just delivered another blow and Android 17 was not going all out, but he still put effort into the punch, much the way 18 did against Vegeta when not going all out. If she hadn't she wouldn't have hurt him.

Someone can only go "all out" for short periods, they will quickly tire (obviously not the Androids but the point is the apparent effort). Metabolically, you can put 70% effort in and last a long time, but 70% effort is still substantial effort. This is how I feel the androids and other fighters initially test each other because they can't sense each others power levels. Once you hit 75% you start to tire more quickly and a human body will need energy much more quickly. The Androids dont need to concern themselves with this, but they WERE human. So I imagine that Android 17 was at 70-75% effort when treating Trunks like Vegeta did Cui. This would make Android 17 about 1.75x more powerful than Trunks.

ANDROID 18 is actually very similar in strength to Vegeta when they fight [DB #352]. It's even at first but they're both holding back. Then 18 uses her full power and she beats down Vegeta for a short time until Vegeta uses full power and the fight is even again. Vegeta only starts losing because because he wears himself down at such a pace while Android 18 has an infinite power supply. Stamina aside, they are roughly equal.

ANDROID 17 and PICCOLO (fused) were both stronger than Android 18 to the point that they are equal [DB #367]. The question is, how much stronger than her were they? There are no clues, but they are twins and both engineered in the same way as cyborgs with infinite batteries and a bomb if needed, so it's difficult to imagine they are anything but close in power, but they both have Dr Gero's data on the fighters and each other so there's no reason to believe 17 isn't stronger, even if the difference is small.

When Android 18 was fighting Vegeta, 17 took out SS Trunks, Piccolo and Tien with ease and didn't kill them even though he could have. Vegeta is the only one who stands roughly level, but his stamina lets him down. Likely there are only 1-2% difference between them, since they are twins and built the same way with the same power sources.

IMPERFECT CELL and ANDROID 16 are equals. Stamina aside, Android 17 and Piccolo are equals. When Cell arrives to absorb the androids [DB #370], he's so much stronger than Piccolo that Piccolo doesn't even try to fight at first and just allows him to walk by, but this is more through being stunned by the increase in Cells power than it is fear. Android 17 is still capable of dodging a number of Cells attacks, but they are simple and Cell quickly grabs a hold of him and takes control. And he takes on Piccolo's hits without even looking and Piccolo's full power blast doesn't even hurt him and one real punch from Cell breaks Piccolo's neck.

This again, is like Vegeta taking out Cui, though not quite to the same extent as Piccolo had been weakened by the Ki blast he fired at Cell by the time he was punched, but I think it's close to the same, so I'd say Imperfect Cell and Android 16 are about 1.25x stronger than Piccolo and Android 17.

SEMI PERFECT CELL is a much easier concept. He absorbed the power of Android 17. So Semi-Perfect Cell is the same as Imperfect Cell + Android 17, and now has an infinite power source to compliment his own enormous Ki.

If Trunks's Power Level before he trained in the Hyperbolic Time Chamber was 150,000,000, based on these estimations, the following table is true:

CONCLUSION

From the point Cell becomes Perfect to when he becomes Super Cell, which is effectively Cell turning Super Saiyan 2, Cell is injured and recovers three times. One heavy injury against Vegeta which he laughs off, and another after his fight against Goku in the "tournament". The heavy injury he endured because of Vegeta was something he recovered from using Piccolo's cells. Like Piccolo, this used up energy, but Cell was so far ahead of Vegeta it made little difference. However it was still a serious injury and once Cell had fully recovered after his fight with Trunks, due to his Saiyan cells he would have gained in strength.

The same can be said of Cell after his fight with Goku when he ate a senzu bean to recover after using up a lot of energy, but the third is the largest and it's when Cell came back from the verge of death after he self destructed. Cell recovered and gained the ability to power up the same way Gohan did. Considering from the point he first becomes Perfect Cell to Super Perfect Cell, the increase in Power Level only needs to increase by between 2.6x and 2.65x.

Cell only need increase his strength by 1.3 - 1.32x by recovering from his injuries before doubling his Power Level in his Super Saiyan 2 transformation (note the electricity) [DB #413].

I find it perfectly reasonable and even likely that yes, Super Perfect Cell had a Power Level of between 2,210,000,000 and 2,250,000,000.

DABURA

Goku and Vegeta guess that Dabura is about the same level as Cell (most likely Perfect). Goku admits that Dabura is tougher than he thought when he actually sees him fight, but that Gohan has been slacking off and is weaker now than when he was a kid. Since they are fairly evenly matched at Gohan being a Super Saiyan and not using Super Saiyan 2, this puts Dabura and SS Gohan of the Buu saga somewhere between Cell before he self-destructed and Gohan before he turned SS2 since Dabura is stronger than Perfect Cell but Gohan is weaker than he was against Cell.

Knowing that Cell recovering from near death gave him the SS2 power-up, his full power previous to self-destruction should have been half Super Perfect Cell at somewhere around 1,115,000,000 and Dabura and Buu Saga SS Gohan should still be above this. It's difficult to tell how much stronger than this SS Gohan was during the Cell Games because Cell was still hiding his power level when they fought. It was only when Gohan surned SS2 that Cell went full power. But if Cell was 2,230,000,000 (an average of 416 and 408, how powerful was SS2 Gohan?

The fact is, Gohan was a LOT stronger than Perfect Cell. When Cell became Super Saiyan 2 [DB #413] he killed Trunks. Vegeta was so enraged that even though he knew he stood no chance at all he charged and blasted Super Cell out of rage [DB #414]. Cell knocked him unconscious then decided to kill him. Gohan dives into the way and shields Vegeta from the attack. It's at this point Cell decides to finish Gohan off and starts a full power Kamehameha. Gohan stands to take it and accept his fate until he hears Goku's words of encouragement from Otherworld using King Kai. Gohan doesn't see the point in fighting because he's lost half his energy, but as usual Gohan doesn't know how strong he really is.

It's unclear if Gohan really did lose half his energy or if he just thought it did, like how his Ki used to plummet immediately after doing something extraordinary - such as against Raditz or 3rd Form Frieza - and it just needed Goku to make him see he still had it. Either way, even injured Gohan had more than enough power to take on and defeat a fully powered Super (SS2) Perfect Cell.

This is similar to, how Goku (PL 8000) Kaioken x3 Kamehameha was equal to Vegeta's (24,000) Gallic Gun, then Goku went Kaioken x4 [DB #231]. Vegeta survived because his armour took some of the blast as he told Krillin and Gohan it would [DB #291] and because the kamehameha blew him high into the atmosphere. Cell stood his ground, has no armour and was torn apart. So it's suggestible that SS2 Gohan was 1.3x as Super Perfect Cell with a PL 2,900,000,000, meaning SS Gohan was 1.3x as strong as Perfect Cell with a PL of 1,450,000,000.

This means Dabura and Buu Saga SS Gohan were between 1,115,000,000 and 1,450,000,000 in power level, and given Goku's noticing how much Gohan must have been slacking off in peace-time, I'd say it was on the lower end of that range, and knowing Toriyama's liking for nice round numbers, it would seem practical to place their powers to around 1,200,000,000 each.

SS2 GOKU AND VEGETA

One of Babidi's top fighter's, Yakon, has a power Level of 800 Kilis. When the lights go out to suit Yakon in his fight, Goku turns Super Saiyan to light the place up and is measured to have a power level of 3000 Kilis [DB #451]. But what is a "Kili" worth?

Well I can tell you what it isn't worth. In a 2004 issue of VJump in a section called Capsule Corp Q&A someone called Dr Dragonball says "I will teach you DB's magic", and people ask Dr. DB questions such as "Was Nappa always bald?" only to get the answer "He is bald! Thank you , next issue!!" so it's not the best. Nevertheless Dr Dragonball answered a question on Kilis which is the only information I have ever been able to find on the issue.

But this isn't true, nor is it official. It's just a guy's opinion. Goku is far stronger in the Buu saga than when he first became a Super Saiyan, Vegeta mentions when they first fight that Goku was "Impressive" because as Super Saiyan 2 he was stronger than Gohan when he fought Cell. So 3000 Kilis is not equal to 150 million and so 1 Kili does not equal a power level of 50,000.

Logically, if SS Goku is 3,000 Kilis then:

• Goku = 60 Kilis
• Majin Vegeta = 60 Kilis
• SS Gohan = <3,000 Kilis
• Dabura = <3,000 Kilis
• Majin SS Vegeta = 3,000 Kilis
• SS2 Goku = 6,000 Kilis
• Majin SS2 Vegeta = 6,000 Kilis
• SS3 Goku = 24,000 Kilis

So you might think that in the anime, Dabura claimed to be able to beat people with powers over 4,000 Kilis, how could he do that if he's less than 3,000 Kilis himself? Well, Dabura also said [DB #451] it would take more than power to defeat him. He does breathe fire and conjure swords, and Goku can see he uses magic, this is how Dabura can punch above his weight, just because he can beat 4,000 Kili warriors doesn't mean he needs to be one.

You might also think that with base Goku only having a PL of 60 Kilis that he wouldn't stand a chance against Yakon. Well he dodged Yakons attack it's true, but Yakon thought he'd be a piece of cake. At the same time as dodging, Goku kicked Yakon square in the face and the only thing Yakon seemed to notice was the dodge. Goku also thought Yakon would be slow but he wasn't. Though when you think about it, he may have been fast up against base Goku, but for a character more than 13x stronger, yes, he was pretty slow.

Goku and Vegeta are more or less even from the way they fight [DB #458] Vegeta notes that Goku is more powerful than Gohan when he fought Cell. The problem is knowing just how much stronger Goku is - whatever it is, it's not a lot more, at least, it's not made to sound like a lot more. None of the translations I've seen have made the surpassing of Gohan sound substantial, including my own using a Text Capture program and an online translator.

With that in mind and with Cell Games SS2 Gohan's PL at 2,900,000,000, it's possible and very convenient that Buu Saga SS2 Goku (and therefore SS2 Vegeta) are at PL 3,000,000,000. Were this to be the case 1 Kili would be 500,000, not 50,000.

TRUNKS and GOTEN

This is one of the more difficult ones and uses one of the larger assumptions. During the World Tournament arc when Mr Satan (Hercule) suggests there should be a Battle Royale [DB #453], Goten and Trunks have dressed up as Mighty Mask and take on Android 18 together. Eventually they turn Super Saiyan to try and beat her and when Android 18 see's the yellow aura, she knows why Mighty Mask has a strange body shape. Trunks fires a not-full powered Big Tree Cannon and Android 18 only just avoids it. Realising how power they've become she knows she needs to end the match quickly and throws a Destructo Disc to split hem up so she can win through their disqualification.

Unless the still human part of her managed to, Android 18 shouldn't be able to sense Power Levels and the only other time she felt the need to dodge a Ki blast was Vegeta's and it was to show her speed not lack of resilience. When this happens, Android 18 realises she needs to end the fight quickly or she'll be taken down. Given that she only just dodged it and the power makes her sweat, this beam is likely near her limit, but the beam itself is not full power meaning that SS Trunks is actually stronger than Android 18. The fact this is a strong but relaxed Big Tree Cannon suggests this is somewhere in the region of 70-75% of Trunks power meaning SS Trunks has a Power Level of around 350,000,000.

Trunks is slightly stronger than Goten, but they are more or less equal, so there's likely only around 2% between them, giving SS Goten a Power Level of roughly 343,000,000.

There are any number of equations invented to account for the fusions and how the power levels work out but there is only one that was ever release in any kind of official capacity - the Super Exciting Guide: Story Volume page 63. It explains that fusion multiplies the powers.

As far as I can tell there has never been a separate one published for the Fusion Dance but there has never been a suggestion in the series that the results are any different. In fact Akira Toriyama himself said in an interview for Daizenshuu 6 that the reason he came up with the Potara fusion was because one of the movies had already used the Fusion Dance with Goku and Vegeta.

So the Potara Fusion acts in place of the Dance so there's no reason to believe what they do is any different, only their method. But how can it work?

In the Buu Saga it's obvious that SS2 is not strong enough for take Buu down, but at the same time while SS3 appears to be stronger than Majin Buu, it lasts just a few minutes because it uses up too much stamina. SS3 though IS stronger than Majin Buu and Goku even tells Vegeta this. The Potara Fusion Vegito doesn't fight Majin Buu - Gotenks does. But the numbers are too vast:

• Trunks (base) - 7,000,000
• Goten (base) - 6,860,000
• Gotenks (base) = 6,860,000 x 7,000,000 = 48,020,000,000,000 or 48 trillion.
• This simply cannot be accurate because Majin Buu has to have a Power Level between 3,000,000,000 and 12,000,000,000, but when Gotenks first fought Buu he lost, and lost convincingly.

But then, you have to wonder why Akira Toriyama introduced this new way of measuring Power Levels, the Kili. As I've been through it already, I note that the Yakon and SS Goku Power Levels of 800 and 3,000 Kilis doesn't provide any kind of link at all with the Cell Games characters. If it was maintained that Dabura was as strong as Perfect Cell and he was given a Kili rating (which he isn't - even in the anime) then yes, that would be some kind of link, but as it is, the links to the Cell Games powers come from a comparison of Vegeta's and Goku's PLs with Gohans during the Cell Games and a comparison of Dabura with Cell. The Kili's dont actually add anything to the series at all...

Unless you have to use the Kili conversion as the Power Level you multiply to get the Fusion power. Using the previously determined value for 1 Kili:

• Trunks (base) - PL 7,000,000 - 14 Kilis
• Goten (base) - PL 6,860,000 - 13.7 Kilis
• Gotenks (base) - 14 x 13.7 = 192 Kilis = PL 96,000,000
• SS Gotenks - PL 4,800,000,000 = 9,600 Kilis

This method works and the results fit with the other calculated values. The formula for calculating the Power Level of a Fusion character is:

While the rest are on Earth struggling with Buu, the Elder Supreme Kai from 15 generations ago works for 25 hours and more to unleash Gohans latent power and increase it further, such is the Old Kai's ability. Trunks and Goten recognise, when the Elder Kai is finished, that new Mystic Gohan is stronger than Super (SS3) Gotenks.

According to my calculations, SS3 Gotenks (base fusion) has a Power Level of 38,400,000,000 or 76,800 Kilis. If Mystic Gohan is stronger, but not much stronger, and taking advantage of Toriyama's liking for round numbers, Gohan having a Power Level of 40,000,000,000 or 80,000 Kilis seems likely for this version of Gohan.

MYSTIC MULTIPLIER

When Gohan first lifted the Z-Sword, I have his Power Level as calculated at 24,540,000 at base. By the time his training with the Z-Sword has ended, he swings it around like it's nothing. Clearly he has gotten much stronger. In the real world, when weight training (and the Z-Sword is very heavy) how many reps you do for each set determines how you're body will react.

• 1-5 Reps Per Set = Mostly Strength
• 5-8 Reps Per Set = Strength AND Muscle Equally
• 8-10 Reps Per Set = Muscle With Some Strength
• 10-12 Reps Per Set = Muscle With Some Endurance
• 12-15 Reps Per Set = Endurance With Some Muscle
• 15-20 Reps Per Set = Mostly Endurance

You'll get something similar to the above from any workout program provider. Typically, the higher reps are done with lower weights, or with body weight. But in the case of Gohan, the Z-Sword starts of in the Mostly strength range and ends up in the Endurance range with the same heavy weight. That means his new Strength range is higher than it was before.

There are general calculations a person can use to calculate an estimation of their One Rep Max based on the weights they can lift and how many reps they can do it for. [One such calculator can be found here: http://strengthlevel.com] Using any arbitrary weight such as 100kg changing the rep number from 1 to 20 will increase the One Rep Max estimation to 166.5kg on a shoulder workout, which is where Gohan will feel most of the weight. At high reps the ORM is 1.665x higher than when the weight was ORM itself. Applying this to Gohan's Power Level through the use of the Z-Sword would put Gohan's PL at 24,540,000 x 1.665 = 40,859,100. I only use this as an estimation of the increase in Gohans power through his use of the Z-Sword and how it may apply to the increase he gains from going Mystic. It suggests that Mystic Gohan is 1,000x stronger than Gohan base.

But is the increase from 24.54 million PL to 40 million PL reasonable?

This is the first time Gohan [DB #472] and Goku lifted the sword for comparison.

Goku is clearly stronger that Gohan who can barely lift the sword. Goku on the other hand can swing it but finds it difficult. This is consistent with their base Power Levels of 24,540,000 vs 30,000,000 as I've calculated. But by the time Goku arrives [DB #478], Gohan has gotten stronger already and is approaching and close to Goku's strength.

A few hours later, Gohan is more than capable of handling the Z-sword with one hand only.

You might think it unreasonable that Gohan inprove so much in just one day, but Gohan has never trained like this before, he has a lot to gain from it. On his journey to Namek, Goku got 10x stronger in just 6 days of training, which is 1.67x stronger per day on average, and Gohan as we all know has greater potential to increase his power than any pure-blood Saiyan ever has. So it's perfectly reasonable for Gohan to increase his strength from 24,540,000 to 40,000,000 in just a day with training from Kibito and Supreme Kai using the Z-Sword.

Based on the above, it's my opinion that Gohan's Power Level after training with the Z-Sword is 40,000,000 and that the Mystic form is a 1,000x increase.

MAJIN BUU

Against SS2 Vegeta, Buu has no problems at all. Even when Vegeta self-destructs Buu recovers [DB #467]. Nothing can be gained by comparing Buu's resilience between attacks as would normally help because Buu is so easily damaged, even by bullets from a machin gun, his regeneration ability is so outstanding that he barely ever raises a defence.

But when Buu attacks SS2 Vegeta using physical attacks, Vegeta gets pummelled and Buu is only playing. Against SS3 Goku [DB #484], it's a different story, his punches affect but dont really damage Goku, and Buus Kamehameha is easily batted back to him. The difference in levels is similar to that between Super Vegeta and Semi-Perfect Cell, but a little larger as Buu's punch doesn't make Goku's lip bleed like Vegeta's does, which would put SS3 Goku about 1.2x stronger than Majin Buu which would mean Majin Buu had a Power Level of 10,000,000,000 or 20,000 Kili.

SUPER BUU

Super Buu was born when Majin Buu separated himself from the evil in him - creating Evil Buu - and was then absorbed by it in the form of chocolate. When he fights SS Gotenks in the Hyperbolic Time Chamber [DB #490] the fight is completely one sided, barring the fact that Buu is easily damaged but regenerates every time. Super Buu is as strong as Majin Buu except with a fighting body and the ability to sense Ki.

When fighting Super Gotenks (SS3 Gotenks - base fusion) Super Buu struggles and ends up in a situation where SS3 Gotenks can kill him because of how much energy and regeneration has been needed [DB #491], but the fusion wears off. Any time that Buu hits Gotenks is purely down to Gotenks being childish, not paying attention and believing his own hype. Something that should've given Piccolo a heart attack.

After absorbing Piccolo and SS3 Gotenks, a plan Buu came up with when he sensed the Elder Kai making Gohan stronger [DB #499], Super Buutenks was stronger than Gohan by enough that Gohan could barely touch him and like Majin Buu Kamehameha against SS3 Goku, Gohan's Kamehameha against Super Buutenks was batted back. On that basis, my estimate would be that after absorbing Piccolo and SS3 Gotenks would be roughly 1.2x as powerful as Mystic Gohan, maybe slightly more.

PICCOLO

Knowing that Piccolo always trains, and knowing all characters advance much more quickly when fighting with a partner instead of alone, I'll work on the basis that in peace time in the last 7 years, Piccolo has doubled his Power Level in roughly the same way that Vegeta had in that time before turning Majin, and add an extra 7th on top for the year he spent in the Hyperbolic Time Chamber by himself before the Cell Games, giving him a Power-Level of 600,000,000 or 1,200 Kilis.

When Goku arrives and distracts Super Buutenks by slicing him up with a Destructo Disc, Buu leaves a part of himself down on the ground. When the transformation of Gotenks wears off Super Buutenks becomes Super Buuccolo with a Power Level of Buu + Piccolo + base Trunks and Goten, and he absorbs Gohan with the part of himself on the ground, gaining all of Mystic Gohan's power and becoming Mystic Buuhan. This new form is exceptionally strong, only superseded by SS Gotenks (SS fusion) up to this point.

But his enormous power is what convinces Vegeta to form Vegito (base fusion) with Goku, and when they do fuse, using the Fusion equation, they had a Power Level of 90 Billion, just under 1.8x as powerful as Mystic Buuhan at 50,613,860,000.

KID BUU

After Vegito is absorbed according to his plan (making Buu think it was his) [DB #505], but is protected from absorption by a force-field he created. The ploy was to get Buu to transport Vegito inside Buu where the others were taken. The as of yet unknown time of the fusion wears off and they remove Gohan, Piccolo, Trunks, Goten and Fat Buu, turning Super Buu into Kid Buu, and he gets even stronger than Super Buu was [DB #507].

The fight between Kid Buu and Goku [DB #510] is very even. Everything about it is tit-for-tat, from the physical fights to the Ki blasts, that is until Goku starts to wear down through his use of Super Saiyan 3. Sadly for Goku and co. Buu can take punishment from someone his equal and not lose power or the ability to regenerate, but the point here is that in terms of attack power and strength Kid Buu and SS3 Goku are on the same level.

This means that Kid Buu's Power Level is the same as Super Saiyan 3 Goku, but we're also told that the innocence of the Grand Supreme Kai weakened Buu and calmed him down, like he was actively fighting Buu the entire time, cancelling out some of his energy - thats why Kid Buu is stronger than Super Buu. The difference is logically the Power Level of both the Grand Supreme Kai and of the 'innocent' Fat Buu.

----------

All of the above on Buu serves to show that the transformations Buu goes through and the powers he gains through absorption and his confrontations with other characters are consistent with the calculations I have used.

• Super Buu - PL 10,000,000,000
• Super Buutenks - PL 49,000,000,000
• Super Buuccolo - PL 10,613,860,000
• Mystic Buuhan - PL 50,613,860,000
• Kid Buu - PL 12,000,000,000

Unlike the rest of Dragonball, the Manga is not judged to have canonical superiority over the Anime as Akira Toriyama works on both equally, therefore to make my points I will be using both.

THE CONDITIONS

I and others have held a theory for a while now that God Ki does not scale in the same way as other Ki. If a character with a Power Level of 1,000,000 has one tenth of the energy of another character, that other character has a Power Level of 10,000,000. But God Ki follows some seemingly strange rules, which are provided relative to Beerus:

1) When SS2 Vegeta got a rage boost and became stronger than SS3 Goku momentarily [DBS Ep 8], Beerus used "one tenth" of his power to defeat himself:

2) Less than 10% of Vegeta SSB is equal to less than Super Saiyan God [DBS #13]:

3) Comparatively, if Super Saiyan God is a 6, Beerus is a 10 and Whis is a 15 [Dragon Ball Z: Battle of Gods Anime Comics interview with Akira Toriyama]:

4) Super Saiyan Blue Kaiokenx10 must be less than Beerus full power:

THE RATIONALISATION

1: ONE TENTH

"One Tenth" is a more vague term than you might at first think, it's not as solid a term as "10%", and of course it can mean "10%" but it can also mean something entirely different, especially if considering magnitudes, such as of earthquakes.

Earthquakes are measured in magnitude by the Richter Scale and the Moment Magnitude Scale, both of which measure the energy of the earthquakes energy. Each step on the scale is x101.5 more than the previous step and 103 times the step before that. Thus a Magnitude 7.0 has about 32x more energy than a Magnitude 6.0 and 1,000 times more energy than a Magnitude 5.0. When Beerus says "one tenth" it could also equate to "Magnitude 1" out of 10 on his power scale.

2: SS GOD vs SS BLUE

As Beerus confirms, Super Saiyan God is equal to more than under 10% of Super Saiyan Blue. This suggests that SSG is equal to 10% of SSB. Which also allows for Akira Toriyama to finally get his way.

I've already been through the concept of how his Editor would make him change things about the series, but Toriyama originally wanted the Super Saiyan transformation to have a 10x power up. Super Saiyan Blue is the Super Saiyan God power having gone through a Super Saiyan transformation. Given Toriyama's desire for the Super Saiyan multiplier to be 10x the base (which he wasn't allowed) and the idea of less than 10% of SSBlue dipping under SSGod, it makes sense that Super Saiyan Blue is 10x more powerful than Super Saiyan God.

3: SIX, TEN & FIFTEEN

Like the "one tenth" quote, many take Toriyama's use of the numbers 6,10 and 15 to mean that SSG Goku is 60% as strong as Beerus and that Whis is 1.5x as strong as Beerus. But this doesn't make any sense at all if SSB is 10x stronger than SSG and even SSB Kaioken x2 doesn't concern Beerus. If, however, the 6, 10 and 15 are relative on a magnitude, or logarithmic scale, its entirely possible for these figures to make sense along with SS Blue.

4: SSB x10 < BEERUS MAX

In DBS Ep 39 Goku explains to Hit that he's been holding back his trump card, the Kaioken, and that he was hoping to use it against Beerus one day, which shocks Beerus. When Goku doubles his power with Kaioken x2, Beerus is not concerned about it, but is stunned Goku held back such a handy technique and can probably see it's potential to be a problem in the future. When Beerus has no further reaction to Goku SSB Kaioken x10, it must be assumed that Beerus's reaction would be the same, because if Kaioken x10 SSB reached Beerus's level or went above it Beerus would surely have a greater level of shock, and Goku himself would know that he had achieved a level capable of beating Beerus.

The fact that Goku hopes to improve it and use it against Beerus "one day" also shows that Goku himself knows that SSB Kaioken x10 as it is at this point is not enough to defeat Beerus.

ADDITIONAL CONDITION

In DBS Episode 13, the combined power of Beerus and Goku created a Super Dense Universe Busting Bomb. There's then a Push'o'War between them and Beerus is clearly the superior, no matter how much Goku's energy grows he struggles and Beerus easily produces more energy to push Goku back.

The combination of their energy is too much for Whis to be able to handle, who acknowledges that the energy ball is a Universe destroying bomb and even he cannot stop it. At no point does Beerus put in more effort than he needs to so Beerus' power during this part of their fight, so Beerus is only ever matching or slighly over-coming Goku's level at SS God. Goku reaches his limit and Beerus recognises it, much like he recognised that Goku still had SS3 kept in store when they first fought. So at this point at an allowed stale-mate, the Bomb is created by two SSG level characters and the resulting combination of their power exceeds that of Whis.

In neither a linear scale nor a logarithmic scale where the numbers increase, the double of the 6th term in a sequence or the 6th magnitude will not exceed the 15th term or the 15th Magnitude. Therefore a simple addition of SSG + SSG to determine the power of the Universal Bomb wont work, but a multiplication of two powers in the same way a Fusion works would increase the 6th term above the 15th in every example but logarithmically in none.

The only way for the 15th Magnitude to be exceeded by the 6th is either by powering the 6th Magnitude by an order of more than 2.5. But what about a top limit? For that, there is one clue - the Elder Kai said that the energy has become more dense.

As an oblate spheroid, the energy of Goku's Kamehameha and Beerus's bomb has a comparative volume (V = 4/3 x π x a^2 x b) of 302,762.1, while the Super Ultra High Density Energy Ball has an comparative volume of 1436.76.

This means the Super Ultra High Density Energy Ball has a 210.7x higher density than the original energy ball, giving the Bomb a 210.7x higher energy, in a similar way to gravity increases with higher density and in line with Dragonball, how the power of an attack can can increase by focusing Ki on a small area. 210.7 is a highball as at no other point shown in DBZ was Ki focused and increased by this high an amount, and it's obvious that the Beerus side of that ball as I have outlines is not solidly energy and the real energy is in the centre. So the absolute highest limit is Magnitude 6 squared then multiplied by 210.7.

In terms of a logarithmic scale to use to determine the Power Level conversion for God Ki, Magnitude 6 Squared multiplied by 210.7 must be a higher value than Magnitude 15 (Whis) in order to be considered, and therefore cannot be Base 6 or higher.

If the true energy in the bomb was originally concentrated in a sphere like the following picture shows, the comparative volume of the energy ball previous to increasing in density is 113,097 meaning the SUHDE Ball is 78.72x as dense, and therefore Magnitude 6 Squared multiplied by 78.72 must be a higher value than Magnitude 15 (Whis) in order to be considered, and therefore cannot be Base 5 or higher.

NECESSARY ATTRIBUTES OF SCALE

So a scale is needed that:

• is logarithmic in nature,
• ensures 100x Magitude 6 (10x SSB or 100x SSG) is less than Magnitude 10,
• is a Base 5 scale or less, likely Base 4 or less.

FINDING THE SCALE

The following is a table that shows a range of values from Log Scales with Bases of 2, 3, 4, 5 & 6.

• Magnitude 1 is the equivalent of what Beerus used against SS2 Rage fueled Vegeta as "one tenth"
• Magnitude 6 is equivalent to SS God
• Magnitude 6 x 10 is equivalent to SS Blue (SS God is 10% of SS Blue)
• Magnitude 6 x 100 is equivalent to SS Blue Kaioken x10
• Magnitude 10 is Beerus Max
• Magnitude 15 is equivalent to Whis's Power Level
• (Magnitude 6)^2 x 78.72 is the more likely relative power value of the Universal Bomb
• (Magnitude 6)^2 x 210.7 is the absolute highest relative power value of the Universal Bomb

The relative power value of the Universal Bomb MUST be larger than Whis's relative Power Level otherwise Whis would be able to stop the Bomb from destroying everything. SS Blue Kaioken x10 MUST be less than Beerus's Max, otherwise both Beerus and Goku are wrong about the power gap between them.

The table is pretty clear - a Base 4 Logarithmic Scale is the only scale than meets ALL necessary conditions as set by Akira Toriyama in interviews, the Manga and the Anime. It's somewhat irritating for me since I have said on a number of occasions that I thought it would be Base 3, but having now looked more in-depth into the details this time around I am happy that this is the correct option, and that if Toriyama did indeed sit down and decide God Ki would be scaled in magnitudes like Earthquakes (common knowledge in Japan), it was a Base 4 logarithmic scale he used as it's the only one that fits.

THE SCALE

The following table based on the above provides a multiplier for each level relative to Beerus's "one tenth" power he used against SS2 Rage Vegeta [DBS #3] [DBS Ep 8]:

GOKUs BLOCK

Just before the Buu saga, the last time we see Goku weight training is in Otherworld where Goku is made to carry 40 tonnes which flying, which he can barely hold, slowly sinking to the ground. At the start of Dragonball Super [DBS #2], Goku is seen to be dragging a huge block on King Kai's planet. Because the drawings of the block are done using perspective, its possible to work out its size.

From the Top image, comparing the block to the height of Goku using his waist as a standard distance, the front face of the Block is 1.082m x 1.157m, or 1.252m^2. From the Bottom image, using perspective the Block is 1.5x longer than it is wide, so is 1.736m long. This means the block has a volume of 2.173m^3.

GOKU's STRENGTH

This workout is called Sled Pulling and it strengthens your core, glutes and hamstrings. It will help with sprinting and deadlifting. Generally speaking to gain strength-endurance from this you would use 40-45% of their bodyweight to drag [https://breakingmuscle.com/learn/sled-training-basics-plus-a-go-to-sled-workout]. This obviously doesn't work with Goku but the principle of bodyweight can also apply to a deadlift. The average man of 83.6kg (average male weight in the UK) can deadlift 1.25x his bodyweight. At the elite end, a man can deadlift around 2.5x his bodyweight. Goku is obviously elite. SO 42.5% of 2.5 will give us a multiplier for Goku's deadlift at the beginning of Super, that being 5.88. SO Goku's Deadlift should be 5.88x higher than what he's dragging here.

In another topic [http://comicvine.gamespot.com/dragon-ball-universe/4015-56629/forums/dragonball-universe-standardised-feats-list-1847904/#148], I already calculated the density of the weights the Kai's made Goku wear as 1,613 Tonnes per cubic metre. If this Block was made of the same material King Kai and the South Kai made for Goku to wear, it would weigh 3,505 Tonnes, which means on King Kai's planet, because of his gravity being 10x than of Earths, Goku is pulling the Earth equivalent of 35,050 Tonnes.

Trying to account for friction (since I can't calculate the Friction Coefficient for a magic material on a Kai's planet) knowing that King Kai's planet is extremely dense but covered in a layer of soil, I'll use the Friction Coefficient for Concrete on soil, which is 0.3, meaning Goku is pulling the Earth equivalent of 10,515 tonnes. In turn this means Goku's deadlift would be in the region of 61,853 Earth Tonnes. This is the highball.

If however the Block was made of Concrete as would likely be the case on Earth, it would weigh the Earth equivalent of 52.15 Tonnes, meaning Goku has to apply a force over the equivalent of 15.645 Tonnes to overcome the friction and a deadlift of around 92 Tonnes. This is the lowball.

Or if it was Cast Iron like that of many training weights the Block would have an Earth mass of 158.63 Tonnes, meaning Goku has to apply a force over the equivalent of 47.59 Tonnes to overcome the friction and a deadlift of about 280 Tonnes. This is the midball (midball? lol).

In the total of 8 years of training both Vegeta and Piccolo did between the arrival of Perfect Cell and Buu they achieved double the strength. In fours years, assuming consistent gains, they'd have gotten around 1.41x stronger. Goku on the other hand always makes significantly more gains than Vegeta and Piccolo and in the same time it took them to double their power, Goku had increased beyond Gohan and achieved SS2 and SS3 forms. So in the 4 years between then end of DBZ and beginning of DBS, Goku is more likely to have doubled his power, but expecting much more than that is unreasonable. The closest to doubling 40 Tonnes to 80 Tonnes is if the block Goku is dragging is made of concrete, giving Goku a new deadlift of 92 Tonnes, meaning Goku has increased his power by 2.3x.

VEGETA's RAGE

When Beerus disrupted Bulma's birthday party, he back-slapped Bulma. This enraged Vegeta so much that his regular Super Saiyan 2 power exceeded that of Goku's SS3, causing Vegeta to be the first every non-God that Beerus has used "one tenth" of his power against [DBS Ep 8]. This is down to Vegeta's rage boost. All Saiyans have had them. Gohan was the first to go into a blind rage and momentarily jump in power when he burst out of the Space Pod to attack Raditz. Gohan has always been the easiest character to become filled with rage until he grew up and calmed down a lot, even struggling to feel anger toward evil people. When Goku fell into a rage he became a Super Saiyan for the first time, Vegeta Rage-attacked Beerus and Future Trunks Rage-attacked Goku Black and Future Zamasu.

The Rage boost (more than just anger) has always been an aspect of Dragonball, but lately because of Future Trunks in DBS it's been given an official term - Ikari, which means "rage".

Assuming because of Goku's requirement to farm that Vegeta has managed to keep pace with Goku at base over these 4 years, the Ikari must be greater than the 4x power-up equal to SS3. Goku's SS3 did seem interesting to Beerus, but not enough for him to feel like attacking back but for to end the fight. For someone as powerful as Beerus is, Vegeta would need to be more than just a little stronger than Goku for him to notice any kind of difference. When Goku transformed from Super Saiyan to SS2, Beerus noted the difference though it still wasn't strong enough for him to care. A noticeable difference over SS3 is all that needed for Vegeta to impress Beerus and call him "more fun".

Taking consideration of the above, it seems reasonably fair to call the Rage or Ikari power-up an 8x multiplier.

SAIYAN to GOD

When Fighting SS3 Goku, Beerus barely used any of his energy at all. Only when he fought Vegeta did he admit to having to use a level of his energy he had only ever reserved for other Gods. When Vegeta and Beerus first thought this was their initial exchange:

But when Beerus eventually strikes Vegeta back after raising his Ki though (anime only) this is the comparison between how both SS2 Rage Vegeta and SS3 Goku were struck:

The only real difference between these two events is that Vegeta got up sooner. This is likely because Beerus flicked Goku in the head before gently slapping his shoulder, where Vegeta was only given the slap. Given the apparent equality between Vegeta and Beerus, and Vegeta being twice the strength of SS3 Goku at this point, it seems more than reasonable to suggest that to do to Vegeta what he did to Goku, Beerus raised his Power Level to double that of Vegeta, and initially used the same power against Vegeta as he did against Goku.

This would mean that "one tenth" Beerus is 2x stronger than SS2 Ikari Vegeta and 4x stronger than SS3 Goku at the beginning of Super.

TRANSFORMATION

According to Akira Toriyama, the Super Saiyan God is not a standard level to be reached, but is in fact a Power-Up with a multiplier.

I've already determined that Super Saiyan Blue is a 10x multiplier over and above Super Saiyan God, in that Super Saiyan Blue is the form of transforming into a Super Saiyan after achieving Super Saiyan God, the Super Saiyan transformation multiplier is Toriyama's original desire for the multiplier for the original golden Super Saiyan of Goku vs Frieza. This means that whether it be SSG or SSB, they are not absolute levels, but multipliers.

The God Ki Scale shows that SSG is 1024x stronger than Beerus when he beats Vegeta, Beerus was twice as strong as Vegeta when he beat him, Vegeta is 8x stronger than he should be, and SS2 is 100x stronger than Vegeta's base. This means that Beerus was 1,600x stronger than Vegeta when he beat him and would be 1,024x stronger if he turned SSG and 10,240x stronger as an SSB at this point, all of which gives SSG a multiplier value of 1,638,400 - which may or may not be coincidental as the square of 1,280, if there is something special about that number.

It's also '102 x 47' times more than base Power Level, if anyone is looking for something a little more memorable than a seemingly arbitrary figure. The thing to remember is that God Ki does not scale linearly and will screw up any idea at all of an easy sounding value. The multiplier for SS Blue above base Power Level is '103 x 47', while SSB Kaioken x10 is '104 x 47'.

ABSORPTION

In the same interview Akira Toriyama also explained that Goku made the power of Super Saiyan God. This is made clear in the original movie Battle of Gods and in the Anime, but is absent in the Manga.

This essentially means that Goku now has two bases; his true base level and his base God level. It's possible to tell in the anime when Goku is using his God Ki in base because he can take on other characters that should be stronger than him, and if he becomes a Super Saiyan, he'll turn SSB. You know when Goku is not using God Ki if his power is more reasonable compared to others and if he turns Super Saiyan his hair is gold.