*Update 2/4/16 7:24 PM ET: after comment from /u/higi1024 on reddit, it’s suggested to change the acceleration from a constant force to a impulse, as these are basically sudden forces from the jump or from the knee. The calculations are recalculated basee on this info, with the formulas now reflecting A = (20,076,831.64 – 0) / .1 And A = (130329263.05 – 0) / .1 respectively.*
So I am a nerd. I mean a real nerd. For fun I will some times organize and calculate things of insignifigance. This is another one of those instances.
In the manga and anime “One Punch Man”, Saitama, also nicknamed “One Punch Man” for his ability to kill most enemies with a single punch. is an absurdly powerful hero with not observed limitations. The entire joke runs around the fact that, as a hero, he has become so strong that no enemy can challenge him, which has left him incredibly bored with his power.
So the question becomes, as he does more absurd things, exactly how powerful is Saitama? It’s hard to judge based on some of the footage in the show so far, but I’m setting out here to determine a minimum observable base from some of the footage provided.
As a disclaimer: the following disucssion contains spoilers in the first series recently finished up at the end of 2015. If you have not seen this series I suggest you watch it and then come back
So the problem with measuring Saitama’s power is there has been no observable upper limit to his strength and abilities, as well as little in the way of clearly gauging his effects. He’s dug through concrete with his bare hands, he’s obliterated giant monsters with a single punch, destroyed an entire cliff side with just the force of air from a pulled punch, punched through a meteor, and cleared a torrential storm with a punch to an enemy. But there is one scene that can actually be easily measured and observed, allowing us to calculate some base minimums for his strength AND resistance.
Saitama vs. Boros – TO THE MOON ALICE!
In the season finale, Saitama takes on Boros, the Dominator of the Galaxy, a being so powerful he has to lock his power within armor, and was the first being to withstand Saitama’s normal punch, as well as survive his consecutive normal punches. Within episode 12 we’re given the perfect measurable data to get a base minimum for Saitama’s strength when Boros kicks Saitama to the moon, and Saitama subsequently jumps back to earth. With this scene, we can measure the force that Saitama exerted from his jump as well as withstood from Boros’s kick.
The TL;DR: if you want to skip to the final conclusions, here are the stats:
Saitama’s jumping force (calculated at a minimum, not accounting for air resistance): 2,324,897,103.91 N
Saitama’s resilance (calculated at a minimum, not accounting for air resistance): 91,230,484,135 N
So we’ll need to do a few things here in establishing our assumed constants, known constants, and variables:
- Although “One Punch Man” and our earth are different (with One Punch Man’s land mass reflecting that of the Saitama prefecture in Japan), things like distance of the moon and gravitational force are the same.
- Time in the show for these scenes is not being shown as a disconnected cut, but rather a reflection of real time (if it takes 19.15 seconds to watch (the time from Saitama jumping from the moon to landing on the ship), then it took the same amount of time to happen in the show).
- Distance from earth to moon: 238,900 mi
- Saitama’s Weight: 70 kg
- Saitama’s Heigh: 5′ 9″
- Saitama’s travel time to moon:
- Saitama’s travel time from moon: 19.15 seconds
- Gravitational pull of Earth = 9.807 m/s²
- Gravitational pull of the moon = 1.622 m/s²
- Seconds per hour = 3600
- Force = F
- Speed = S
- Acceleration = A
- Mass = M
- Moon weight = W
So now we need to do some calcualtions. Factors I will not be considering here is Air resistance and gravitational pull. This will be easier for Saitama’s jumping ability so we’ll start with this first.
So first we’ll measure Saitama’s speed achieved jumping from the moon.:
S = 238900 * (3600 / 19.15)
calculated out, s = 44,910,704.96 mph, the speed Saitama achieve to jump from the moon to Earth in 19.15 seconds.
Next we need to calculate Saitama’s weight on the moon.
Weight = mass * acceleration due to gravity
Saitama’s weight on Earth
70 kg = m * 9.807 m/s²
70/9.807 = m
m = 7.14 kg
Saitama’s weight on the Moon
W = 7.14* 1.622 m/s²
W = 11.58 kg
Finally, we need to calculate Saitama’s force exerted by his jump.
Newtons equation for force
F = m*a
F = Force
m = mass measured in kilograms
a = acceleration measured in meters per second squared m/s^2
We need to break down his travel speed into m/s^2.
1 mile = 1609.34 meters
1 hour = 3600 seconds
44,910,704.96 * 1609.34 = 72,276,593,920.33 meters per hour
/ 3600 seconds
= 20,076,831.64 m/s
Then calculate his acceleration.
Acceleration = A
Velocity (initial)= Vi
Velocity (finish) = Vf
Time = T
We’re counting this as an impulse from the impacts to reach maximum velocity, with a time of .1 s
A = (Vf-Vi)/T
A = (20,076,831.64 – 0) / .1
A = 200,768,316.4 m/s/s
So now we have this equation:
F = M * 200,768,316.4
for M we will plug in his weight on the moon
F = 11.58 * 200,768,316.4
And finally, we have his measured Force in Newtons (N)
F = 2,324,897,103.91 N
So this is the measurement of the force exerpted from his jump from the moon to the earth. The kicker though is his resilience far exceeds this. My reasoning: Boros’s kick that sent him to the moon in the first place was even stronger. Mind you, it should have left a much bigger crater than the one Saitama left due to this, but suspension of disbelief. The reason for this is his weight (which we are using as a calculation for his mass in relation to force) and velocity were greater on Earth than on the moon.
M = 70 kg
T = Boros’s kick’s travel time = 2.95 seconds
S = 238900 * (3600 / 2.95)
S = 291,538,983.05 mph
291,538,983.05 * 1609.34 = 469,185,346,983.05 meters / hr
469,185,346,983.05 / 3600 = 130329263.05 m/s
A = (130,329,263.05 – 0) / .1
A = 1303292630.5 m/s/s
F = 70 * 1303292630.5
F = 91,230,484,135 N
Again, neither of these calculate for the air resistance Samtama’s body would experience within Earth’s atmosphere.
So we just scienced and figured out a bare minimum cap for Saitama’s strength and resilience. Again, these are not even top limits for this fictional character. In the scene Saitama stands up on the moon as though nothing happened, brushed himself off, and jumped right back to earth. If he really was to push himself it’d be easy to expect he wouldn’t have a problem exceeding this.