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Strength

Humanity's Strongest Soldier actually boasts some incredible and superhuman and beyond strength. An important thing that people have to acknowledge is that the titans, whether it's the Nine Titans or fodder titans, are actually extremely durable. A titan about 4 meters tall wasn't even bothered by getting hit by an axe in the nape multiple times. And a single hit from Levi Ackerman has no problems moving, piercing and slicing them.

After all, as aforementioned, the Ackermans can borrow and utilize the strength of that of a pure titan. Pure titans(particularly the tall ones) possesses some strength much beyond that of most Superhumans, creating huge holes in buildings.

Levi is also hyped up to be as strong and mighty as an entire bridgade. (that is usually consisted of over 1,000 men, and he also scales above Mikasa who has hype of being as strong as 100 men)

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There most likely is a very deep connection between physical strength and the speed you can achieve with the ODM gear, given that:

1) Weight wouldn't be much or at all of a factor(as seen with Mikasa and Kenny, and Levi actually weights 65kg), and same woud go for size(may contribute a little, but not by much).

2) Levi is just too much stomp gaps ahead of every other ODM gear user to the point where it simply can't only be a matter of skill(although skill does play an enormous part). He doesn't just shift or fight faster, he also travels/moves in a straight line far far faster than everyone.

3) ODM gear would require a lot of leg and core strength in general, since one must be strong enough to carry and shift their own body weight. Levi would have to move his own body weight as if it is a feather if he was to perform his blitzing moves, when it comes to both pulling and shifting.

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Anyways,

Every single one of his blows cuts a part or creates a scar on the Female Titan

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Cut all the way through the limbs of the Beast Titan's arm in an instant and slices it up to multiple pieces

Almost completely cuts off the very thick ankles of the Beast Titan, each ankle with one strike

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These three feats display Levi cutting the hands of titans, and in the third one, completely obliterating the hand, and the second one being close to that(we should acknowledge that the Beast Titans hand would be bigger than that of the abnormal titan's)

Severs the muscles of the left side of the Jaw Titan's face with one blow

Completely decapitates an abnormal titan

With one blow, decapitates a pure titan, and questionably was close to or doing the same thing to the second titan based on how its head was twisted (not panel doesn't make things 100% clear)

One-shots & completely cuts off a titan's arm

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And most importantly,

Legit boxes the Jaw Titan and exchange 3 blows with it, all while severely injured and weakened

Keep in mind how insanely strong the Jaw Titan is, able to crush metal tanks and artillerys with its casual strikes (I'm not going to get to the 'Power of the Jaw' itself and claim that Levi matched that, since the 'Power of the Jaw' is centered around its particular claws/jaw more than striking strength, and the Jaw Titan Levi matched was made of Warhammer hardening)

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Anyways, Levi was able to box it three times, he didn't matched the 'Power of the Jaw' but he did matched a Jaw Titan's strength, and without his sword getting damaged, a display of absurd striking strength and AP

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Also is shown to be legit clashing and matching an attack from the Warhammer Titan, that too of course an absurd feat of striking strength/AP

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Intercepted an attack from the Female Titan and blocked it with his leg when protecting Mikasa from it (he does get his foot hurt in the process, but it's an impressive feat of leg strength nevertheless)

After that, uses the Female Titan's hand and his legs to quickly launch himself towards her mouth, and pushing its hand down in the process (also a showing of impressive leg strength, and he performed this after he hurt his foot protecting Mikasa)

Literally kicks a titan in the face

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One thing that is very overlooked about Levi in his fights against titans is that he creates legit shockwaves with his strikes, and that he does it so casually(and the scale of the shockwaves are actually very large)

Acknowledge that for the first gif, the shockwave hit literally caused the Female Titan to drop down/collapse on the ground (although it also should be noted that Levi had previously damaged its feet & legs, but neverthelesss the Female Titan was able to keep her balance and leaned against a tree, it was only when Levi performed the strike it dropped at a sitting position)

Anyways, acknowledge that the Female Titan is 14 meters tall and extremely strong, its strikes could create massive shockwaves/explosions from impact that effected multiple city blocks, alongside one shotting a huge tree and Eren's neck (although of course acknowledge that Levi had previously damaged it a lot)

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The pure titan that got hit by Levi's shockwave strikes in the second shockwave gif also collapsed (but for its case, it's rather unclear whether it was due to the force or just the titan simply dropping to the ground when it died)

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Throws a chair with impressive force, the military police mistaking it for a person, with the impact even creating a legit dust cloud

Cuts a man completely in half with one strike

Overpowers Kenny Ackerman

Sticks his sword on a tall titan's ass, making it squeal

(notable move when the titans are shown to have great pain tolerance, such as when Sasha repeatedly slammed an axe on a titan that was only twice as tall as a human, and the titan wasn't bothered at all)

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Hand to hand combat

Levi is extremely proficient in pure hand to hand combat as well, winning a fight over a much older and larger opponent when he was a tiny boy without much trouble. His mastery in hand to hand combat was one of the things Levi was well known for among the people in the underground when he was a famous thief.

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His h2h proficiency & physical strength in h2h could easily be seen in some of his interactions with his friend Eren.

In both these interactions, he breaks Eren's teeth with a single hit (in the second feat, he broke all of Eren's teeth in the left side of his face, and that was when he was exhausted after fighting and killing countless titans and traveling from within Shiganshina to somewhere far outside the wall twice)

Here, he knocks Eren and Jean down by landing a single punch on each person(even causing one of them to barf)

Skillfully breaks someone's arm while interrogating him

Swiftly tackles someone to the ground and knocks the guy out

In the story of how Levi met his underground friend Furlan, when they first met, Furlan sent Levi to fight a groups of thugs single handedly to test the latter's strength, and Levi effortlessly passed the test

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Durability

As an Ackerman, Levi possesses superhuman durability. To be honest he doesn't have many notable feats at his disposal in that aspect, Levi Ackerman rarely gets hit after all.

Doesn't even blink an eye as Mike quickly slams into him, and shows no signs of being hurt in the slightest after being slammed through wooden boxes

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Gets his foot injured while saving Mikasa after she made the unwise mistake of cabling at the Female Titan's nape after it was incapacitated, but still manages to cut the Female Titan's facial muscles and shows some respectable pain tolerance

And also manages to quickly swoop in and cut the Attack's Titan nape with his foot injured

Slams hard into a table while flying at at least Mach 1 speed(judging by the mach cone), but quickly gets back up

No sells a punch from enraged Historia(there is context for why she's enraged there in the manga)

As hard as it is to take that feat seriously, despite her tiny stature, Historia actually possesses impressive strength

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His most notable feat in durability is however, taking this thunderspear explosion when he was standing right next to the thunderspear. And the thunderspears can damage the Armored Titan, the same Armored Titan that can obliterate a huge metal gate by slamming into it. Although gravely injured, he survived.

And two days later,

Gets back up and although not as good as at his best, is able to fight skillfully

Just like in the case with Mikasa, gets his legs bitten by a hardened snake-like Titan after saving Connie, and gets another severe nerf

What Levi does in less than two hours later

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Stamina

Levi Ackerman, along with his fellow Survey Corps, boasts insane stamina, fighting multiple titans for a long time and showing almost no signs of exhaustion. Not a single sweat or a single second where he tries to catch his breath.

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The only time he ever did showed clear signs of exhaustion was when he slaughtered all the titans that were lined up near Zeke for a long time and then maneuvered all the way towards Shiganshina, that being after he stomped Zeke and killed all the titans that were closest to the Beast Titan, and going all the way from Shiganshina to a place far ouside the wall.

In the third battle between him and Zeke, Levi doesn't show a sign of exhaustion or weariness after killing 30 abnormal titans that were most likely forcing him to stand on his toes during the entire battle, considering they were all near him and that they were designed by Zeke to be remarkably fast and being capable of climbing trees and performing long leaps

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After his third battle with Zeke, Levi didn't made the wisest choice to place a thunderspear on Zeke's stomach in order to keep the latter from turning himself into a titan by forcing him to not make sudden movements. However, Zeke at this point was in a state of madness, and decides to trigger the thunderspear, with the intention of getting himself blown up alongside his enemy.

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Levi after the damage, was only able to survive in the first place due to being an Ackerman and Hange curing him

Levi was drastically/severely hurt & nerfed after the incident, losing an eye, two of his fingers in his right hand, and was required to stay in bed. But like a true soldier, Humanity's Strongest Soldier fought till the last war.

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During the battle against Ymir Fritz & Eren, Levi, even while injured and nerfed to that level, displays great combat prowess and skill(outperforming every other non titan shifter human except arguably Mikasa).

Is shown to be consistently fighting when surrounded by multiple titans in the manga

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Although, he is indeed much more impressive in the anime

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1) Dodges through the Beast Titan(made of hardening)'s barrage

2) Swiftly slashes a hardened Warhammer Titan's nape before slicing a hardened Female Titans arms with his signature fidget move

3) Slices the name of the Female Titan and then proceeds to literally box the Jaw Titan(insane display of striking strength) and matches 3 of its blows

4) Kills that Jaw Titan by quickly maneuvering over to its nape

5) Dodges an attack from a Warhammer before maneuvering a great distance and quickly taking it out

Literally clashes with/match the blow of a Warhammer Titan

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1) Saves Jean from a hardened Jaw Titan with immense speed, Jean wasn't able to react to either the Jaw Titan's attack or Levi slamming into him

2) Comes flying and is shown as a blur as he saves Connie from a Titan(presumably Beast?) in the form a snake

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Jean is a master of extremely high caliber with ODM, and possesses inhuman reaction speed, dodging through a barrage of bullets by the artillery on the Cart Titan

In the case for Connie, the action took a heavy toll to himself. Levi went too close with the titan when saving his subordinate, and the serpent-like Titan bites Levi's legs.

Levi gets another damn nerf, this time during the battle, after saving Connie's life.

And still, after all of that, decapitates/one shots Zeke with incredible speed after jumping out from Falco's flying Jaw Titan

The previous distance (albeit a few seconds did passed by after the moment in the screenshot)

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Levi plays a very important part at the end of the battle, maneuvering through pieces of a Colossal Titan in mid-air, before landing a thunderspear in the opponent's mouth

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Levi's entire fighting style itself is a testament to his remarkable intelligence when it comes to combat.

As aforementioned,

Levi is shown to wield one of his two swords in a reverse grip, and this method has greatly helped in his ability to slay the Titans. The method is holding his right sword backhanded with the blade facing out and being behind him, not in front. By doing this, Levi can utilize spinning and other rotating attacks, and become, basically: a fidget spinner of death.

The most perfect way to slay titans, and for those physically capable of performing it, the most convenient.

Instantly gets into close range with the Female Titan's face by wheeling through its arm, using her attack as a driveway, and then quickly takes out her eyes

Uses his cloak to shield/hide himself quickly, making Kenny miss

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Distracts Kenny by talking about life values and then quickly fires at him with a gun

Uses a chair as a decoy before instantly taking out the policeman

Counted all the members of the anti personnel control squad in the large crystal cavern in an instant

Spots & picks up a pouch filled with gasoline that was lying around at some point of time in the second fight between him and Kenny, and uses it to create an explosion by having Kenny's gunfire igniting it

Then uses the resulting explosion to unexpectedly get close to his opponent and then overpowers him, landing a successful blow

Cables at the nape area, making Zeke raise his hand up to defend it, and then takes advantage of that by swiftly targeting the eyes instead, and blinding him

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Cuts branches to confuse Zeke, and also to hide behind one of them, using the trick to get close to the Beast Titan without much trouble

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Since this is a respect thread, I decided not to post the calc I have done for the speed of the bullets of the anti-personnel squad or that of ODM gear when Levi is using it. I will post screenshots though. Anyway,

For estimating the absolute high end speed for Levi Ackerman when he's equipped with ODM gear, this moement seems to be the most appropriate to use/display.

Here, Levi Ackerman with his ODM gear matches the pace with three bullets shot from the guns of the anti-personnel-mobility-gear. All in astonishing fashion.

And that was moving 2D directionally onlyafter the third shot.

Screenshot of the moment Levi realizing it's an ambush

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The first and second fire

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The third fire (the moment where Levi actually starts moving 2D directionally)

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Where the first and second bullet landed

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Where the third bullet landed

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This is what basically happened between Levi and the third gunfire shot.

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Also keep in mind that the guns of the anti-personnel-mobility gear are completely different from the average modern handgun. The bullets of the anti personnel mobility gear guns are depicted as to travel far faster, which can be easily seen here.

The aftermath of the area that the shot hit when Levi dodged it

The impact of the fire created a large hole in a brick cuboid.

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This feat of Levi would have required him a movement speed of mach 2/supersonic (the calcs), based on the measurements of the distance and movement as shown in the manga panels.

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So the conclusion is, ODM gear is indeed actually very fast, far beyond what almost all people would expect for a gear using cables and gas cylinders and is built for a single person to wear. A special type of fuel that only exists under Paradis island is used for it after all. And it is a fictional equipment after all.

Here, in both the manga and anime, some of the Devils of Paradis are shown dodging countless bullets from an artillery on the Cart Titan. It wasn't even aim dodging, at least the first 5 bullets or so(the scouts didn't have the time to turn their backs completely to see the area where the shots were coming from), as the appearance of the Cart Titan was sudden and none of the Devils of Paradis realized it was there until the bullets were shot, and the artillery was shooting way too many bullets to the point aim dodging won't be enough.

Yes, even in the manga the Levi's movements using his ODM gear does create Mach cones

Just like in the anime

The ODM Gear speed in general is consistently hinted to be able to break the sonic barrier (as aforementioned, it is a fictional equipment after all, it does do things beyond what most people would expect from it):

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In the first two panels, we see Mikasa and Eren standing on top of Eren's titan while the Warhammer crossbow arrow that created a sonic boom was fired, yet Mikasa was able to get herself and Eren out of the way from that same said arrow (an insane showing of movement speed)

In the third panel we literally see Bertholdt creating a sonic boom while accelerating with his ODM gear (and he only used the gas, no use of the cables)

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Levi dodges a barrage of pieces of a titan thrown by the Beast Titan that was thrown in clear at least Supersonic speed, and in this case, the manga displays the speed/feat better

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Speaking of that barrage, he Beast Titan can throw large boulders at the speed of mach 3, and throwing things at absurd speed does indeed must have a connection to how fast one can move their arm

Not only did Levi blitz the Beast Titan here, he also moved significantly faster than its arm

And that was actually without the use of any cables of the ODM gear cables

So things people should take note of is:

1) Levi moved significantly faster than the Beast Titan's arm, the same arm that can be used to throw things at high supersonic speed

2) And that was after the Beast Titan had cut the wire of the ODM gear

3) The Beast Titan never was taken by surprise, as you can see how it managed to cut off the wire

4) Cutting off the wire is an impressive feat that would have required great speed, and Levi blitzed the Titan that performed it

After that, statues the pieces of the Beast Titan's arm that he sliced off

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The Nine Titans can attack at supersonic speeds anyway, as we can see by how Eren and Annie's punches and kicks are shown to be breaking the sound barrier

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And Levi has no problems blitzing the Nine Titans, and moving faster than their attacks

And also, in his fight against the Female Titan, based on the damage Levi has left to its body, according to this calc a sword swing every 0.014 seconds would have been required for Levi in the scene

Indeed the Titan Slayer can swing his sword and slash at absurd rate and speed

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Some of Levi's fanciest movements are conveyed with speed lines and the Titan Slayer is depicted as a literal flash in most of his fight scenes in the anime

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As aforementioned,

Like the other Survey Corps, Levi is also familiar with thunderspears, an explosive armament used in the Paradis military. Invented by none other than Hange Zoe, it was initially a technology specifically developed to fight against the Armored Titan, as the titan's armor made it invulnerable against their swords. Although it has later been adapted to be used in combat in general for the Devils of Paradis.

The Thunderspears have a lot of explosive power, each can have the potency of up to about 7GJ/building level.

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English translation:

•Thunder spears:

Though challenging to wield, it can deliver a concentrated blow comparable/equivalent to a strike of lightning.

(I feel very thankful to the person who gave the info)

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Damages the Armored Titan's armor,

the same armor that no sells any force attack from the Attack Titan when the latter's skin isn't hardened. In here, it also breaks parts of the wall(that is made of Colossal Titans' hardening).

And much more importantly, the armor can withstand a city level Colossal nuke.(not going to get into more detail here cause I'm not an expert when it comes to relevance between taking an AoE nuke and tanking a concentrated piercing explosive armament)

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Four thunderspears can obliterate a good part of the Female Titan's arm and severs its hand from its arm, or blow up the Beast Titan's nape.

Most notably, can also damage the Warhammer Titan(which is made of its hardening) severely, and the hardening of the Warhammer is consistently depicted as the strongest kind of titan hardening there is.

An attack with an axe made by its hardening casually obliterates Eren's own hardening.

The same hardening by Eren before obtaining the Warhammer does this to the Armored Titan.

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