Aaaand that’s all she wrote. Well, actually, there’s Boruto… but much like Dragonball Super, I can’t get into it and probably never will.
This post is so people can easily find Naruto calculations that I’ve done. Before really diving in, I recommend checking out Naruto Tidbits/Heights, while also using Explosions and Energy Required to Destroy Stuff as reference, because I’ll be using those things often for the calcs.
Power and speed calculations will be separated for the sake of simplicity and neatness.
And that about does it. As with all series I finish, I occasionally realize errors or corrections that need to be made. Sometimes I even calculate something new if I missed a feat. Again, I don’t see myself going through Boruto, but never say never, I suppose.
Reading through the Shinobi World War was an odd experience. It felt both rushed and drawn out at the same time. I think that’s due to the focus on only a few characters. A lot of others got lost in the fold, and there are legitimately five different villains throughout the war. lol
Still, it was interesting to see how far Naruto had come in regards to power output. It feels like in Part One, the intention was for even the strongest characters to maybe be multi-city block level, aside from the Bijuu. In Part Two, though, that attitude changed. And then in the Shinobi World War, it totally went off the rails and we got continent level Naruto and Sasuke!
I suppose I’ll continue on with the rest of the HST, now. Thanks for reading!
Naruto’s Youton Rasenshuriken slices the god tree in half and sends it flying. Interestingly, the inside of the god tree doesn’t appear to be hollow.
As previously established, the first Bijuu Bomb craters are 1,737.742 m in diameter. The crater measures 12 pixels compared to 297 for the battleground crater.
I estimated where Naruto cut the trunk and will be considering it a truncated cone. The crater battleground is 551 pixels compared to the lower tree diameter at 57, the upper tree diameter at 10, and the length at 291.
57 / 551 = .104 * 43,009.115 = 4,472.948 m, lower diameter of tree
10 / 551 = .018 * 43,009.115 = 774.164 m, upper diameter of tree
291 / 551 = .528 * 43,009.115 = 22,708.813 m, height of tree
Treating it as a truncated cone, the cut part of the tree comes to a volume of 143,096,208,579 m^3
Madara, as previously established, is 1.79 m tall. He’s 65 pixels here compared to the cut thickness at 81.
81 / 65 = 1.246 * 1.79 = 2.23 m, cut thickness
Lower diameter of trunk is 328 pixels compared to 94 for launch height.
Alright, first, my assumption is that a lack of debris here means the cut part of the tree was at least turned to ashes. There is clearly a high amount of heat involved in the attack, so I feel it’s a reasonable conclusion.
Density of wood depends on the hardness, but we can go with the minimum for firm here, considering the tree size. So 565 Kg/m^3.
565 * 143,096,208,579 = 80,849,357,847,135 Kg, weight of wood turned to ash
We’ll be using 538 C temperature for the cutting of this tree. It’s the minimum temperature to turn wood to ashes.
538 – 20 = 518 C, temp change
Minimum specific heat capacity of wood is 1,300 J/kg C.
1,017,134,466,203,447,024.328 + 54,443,957,574,260,709,000 = 55,461,092,040,464,156,024.328 J, or 13.26 Gigatons
Madara’s Meteors, the Sequel
With Chibaku Tensei, Madara creates a bunch of gigantic meteors and rains them down on Naruto and the others. To start, I’ll figure out the amount of energy it took for him to fragment rock from the earth, then raise them up to form the meteors. Then, we can figure out how much energy each meteor has behind it.
… holy shit, what have I gotten myself into? This beautiful mess of scaling will probably be difficult to follow. I’ll do my best to organize it, though. Also, I have pretty much ignored any of the smaller floating rocks, as I assume they’ll be combining with some other meteors after the end of what this scan depicts.
As a reminder, the battleground crater is 43,009.115 m. It’s 109 pixels here. Before getting started, though, I want to figure out how high up these meteors are.
Some are as low as 135 pixels, while the highest ones are 333.
Interestingly, all are above the mesosphere, but only some of the meteors catch fire. I’d probably chalk that up to inconsistency. Still, these heights will come in handy for later (Potential energy). Ok… now for the pain in the ass… I’ll be going from bottom to top, right to left.
29 / 109 = .266 * 43,009.115 = 11,440.425 m, diameter 1 of meteor 1
39 / 109 = .358 * 43,009.115 = 15,397.263 m, diameter 2 of meteor 1
V = 1,055,179,796,059.779 m^3
29 / 109 = .266 * 43,009.115 = 11,440.425 m, diameter 1 of meteor 2
44 / 109 = .404 * 43,009.115 = 17,375.683 m, diameter 2 of meteor 2
V = 1,190,761,607,718.162 m^3
26 / 109 = .239 * 43,009.115 = 10,279.179 m, diameter 1 of meteor 3
31 / 109 = .284 * 43,009.115 = 12,214.589 m, diameter 2 of meteor 3
V = 675,762,889,717.853 m^3
38 / 109 = .349 * 43,009.115 = 15,010.181 m, diameter 1 of meteor 4
40 / 109 = .367 * 43,009.115 = 15,784.345 m, diameter 2 of meteor 4
V = 1,862,074,468,908.629 m^3
30 / 109 = .275 * 43,009.115 = 11,827.507 m, diameter 1 of meteor 5
38 / 109 = .349 * 43,009.115 = 15,010.181 m, diameter 2 of meteor 5
V = 1,099,438,596,349.229 m^3
33 / 109 = .303 * 43,009.115 = 13,031.762 m, diameter 1 of meteor 6
38 / 109 = .349 * 43,009.115 = 15,010.181 m, diameter 2 of meteor 6
V = 1,334,722,037,589.401 m^3
32 / 109 = .294 * 43,009.115 = 12,644.68 m, diameter 1 of meteor 7
38 / 109 = .349 * 43,009.115 = 15,010.181 m, diameter 2 of meteor 7
V = 1,256,609,207,852.801 m^3
23 / 109 = .211 * 43,009.115 = 9,074.923 m, diameter 1 of meteor 8
31 / 109 = .284 * 43,009.115 = 12,214.589 m, diameter 2 of meteor 8
V = 526,700,072,502.028 m^3
27 / 109 = .248 * 43,009.115 = 10,666.261 m, diameter 1 of meteor 9
39 / 109 = .358 * 43,009.115 = 15,397.263 m, diameter 2 of meteor 9
V = 917,205,316,387.188 m^3
23 / 109 = .211 * 43,009.115 = 9,074.923 m, diameter 1 of meteor 10
31 / 109 = .284 * 43,009.115 = 12,214.589 m, diameter 2 of meteor 10
V = 526,700,072,502.028 m^3
22 / 109 = .202 * 43,009.115 = 8,687.841 m, diameter 1 of meteor 11
23 / 109 = .211 * 43,009.115 = 9,074.923 m, diameter 2 of meteor 11
V = 358,645,428,372.681 m^3
28 / 109 = .257 * 43,009.115 = 11,053.343 m, diameter 1 of meteor 12
28 / 109 = .257 * 43,009.115 = 11,053.343 m, diameter 2 of meteor 12
V = 707,097,925,689.767 m^3
27 / 109 = .248 * 43,009.115 = 10,666.261 m, diameter 1 of meteor 13
39 / 109 = .358 * 43,009.115 = 15,397.263 m, diameter 2 of meteor 13
V = 917,205,316,387.188 m^3
28 / 109 = .257 * 43,009.115 = 11,053.343 m, diameter 1 of meteor 14
45 / 109 = .413 * 43,009.115 = 17,762.765 m, diameter 2 of meteor 14
V = 1,136,309,104,495.788 m^3
18 / 109 = .165 * 43,009.115 = 7,096.504 m, diameter 1 of meteor 15
27 / 109 = .248 * 43,009.115 = 10,666.261 m, diameter 2 of meteor 15
V = 281,254,663,751.885 m^3
27 / 109 = .248 * 43,009.115 = 10,666.261 m, diameter 1 of meteor 16
38 / 109 = .349 * 43,009.115 = 15,010.181 m, diameter 2 of meteor 16
V = 894,147,084,006.681 m^3
32 / 109 = .294 * 43,009.115 = 12,644.68 m, diameter 1 of meteor 17
48 / 109 = .44 * 43,009.115 = 18,924.011 m, diameter 2 of meteor 17
V = 1,584,263,805,486.935 m^3
35 / 109 = .321 * 43,009.115 = 13,805.926 m, diameter 1 of meteor 18
52 / 109 = .477 * 43,009.115 = 20,515.348 m, diameter 2 of meteor 18
V = 2,047,427,786,765.576 m^3
31 / 109 = .284 * 43,009.115 = 12,214.589 m, diameter 1 of meteor 18 (EDIT: WHoops)
40 / 109 = .367 * 43,009.115 = 15,784.345 m, diameter 2 of meteor 18
V = 1,233,056,292,041.468 m^3
32 / 109 = .294 * 43,009.115 = 12,644.68 m, diameter 1 of meteor 19
45 / 109 = .413 * 43,009.115 = 17,762.765 m, diameter 2 of meteor 19
V = 1,487,047,628,268.138 m^3
28 / 109 = .257 * 43,009.115 = 11,053.343 m, diameter 1 of meteor 20
40 / 109 = .367 * 43,009.115 = 15,784.345 m, diameter 2 of meteor 20
V = 1,009,746,789,534.319 m^3
29 / 109 = .266 * 43,009.115 = 11,440.425 m, diameter 1 of meteor 21
36 / 109 = .33 * 43,009.115 = 14,193.008 m, diameter 2 of meteor 21
26 / 109 = .239 * 43,009.115 = 10,279.179 m, diameter 2 of meteor 22
V = 337,065,025,724.44 m^3
35 / 109 = .321 * 43,009.115 = 13,805.926 m, diameter 1 of meteor 23
47 / 109 = .431 * 43,009.115 = 18,536.929 m, diameter 2 of meteor 23
V = 1,849,981,950,874.078 m^3
Well… that took a while… I’m not showing the math for this as typing it out would be murder. Instead, I’ll tell you that the total volume of rock gathered by Chibaku Tensei comes to 24,585,291,758,751.353 m^3.
60,070,017,353,229,388,146,745.417 + 196,682,334,070,010,824,000 = 60,266,699,687,299,398,970,745.417 J, or 14.4 Teratons
Hot damn! Nagato must be rolling in his grave. lol
Naruto and Sasuke Intercept Meteors
Naruto and Sasuke destroy some of the meteors headed their way. And dare I say? This may be a speed showing, too. But we’ll see.
Panel height is 640 pixels. Meteor smaller diameter is 130. I’m using angular size again to find the distance, and noting the panel is taller than it is wide, the visual field would be 135 degrees. There are four initial meteors lower than all of the others, so I have to choose which one I think the one I measured is. Based on the shape, I’ve chosen meteor 3. Its smaller diameter is 10,279.179 m and the larger diameter is 12,214.589 m.
640 / 135 = 4.74 pixels/degree
130 / 4.74 = 27.426 degrees, smaller diameter of meteor.
With the angular size calculator, I can plug in the size in degrees and actual size to get distance. The total comes to 21,063 m. We’ll save that for later to see if this is a decent speed showing.
Largest diameter of meteor is 170 pixels compared to 304 for the distance from center of meteor to ground.
304 / 170 = 1.788 * 12,214.589 = 21,839.685 m
Alright, so it’s inconsistent, then. We can still find energy to destroy these meteors.
Sasuke fractured it with Susano’o’s sword cuts. 8 J/cc.
Volume of Meteor 3 = 675,762,889,717.853 m^3 or 675,762,889,717,853,000 cm^3
1,055,179,796,059.779 * 2,700 = 2,848,985,449,361,403.3 Kg
Assuming a terminal velocity speed of 180 m/s, the kinetic energy of meteor 1 would be 46,153,564,300,000,002,048 J
46,153,564,300,000,002,048 + 91,800,642,257,200,773,000 = 137,954,206,557,200,775,048 J, or 32.97 Gigatons
Naruto shits on Sasuke… you love to see it.
But hold on, there’s more!
Naruto’s Bijuu Bomb Rasenshuriken annihilates what appear to be the last seven meteors sent down by Madara. In addition to an impressive destructive feat, this one may well be the most impressive speed feat for Naruto himself up to this point, and to some extent, Sasuke, too.
We can see here, by the way, that the meteors are ablated. Therefore, their speed would be in the neighborhood of 11,000 m/s.
I have to guess at which meteor I’m measuring here. Considering it’s one of the last seven and also one of the longer ones, I’ve chosen meteor 19, which has a smaller diameter of 12,644.68 m. It measures at 38 pixels compared to 235 for distance to the ground.
235 / 38 = 6.714 * 12,644.68 = 84,896.382 m, distance from meteor to ground
Same meteor at 115 pixels wide this time, compared to 288 for distance from its bottom to the ground. I’ve also measured its longer diameter at 127. This is to determine how far the meteor has traveled into the explosion after hitting the Rasenshuriken. One of the Bijuu Bomb explosions is 266 pixels… we’ll save that for later.
266 / 115 = 2.313 * 12,644.68 = 29,247.145 m, diameter of Bijuu Bomb Explosion
This is not the true total because we need to figure out energy required to halt the meteor’s momentum. That would be equal to the energy of the meteors themselves.
Madara’s meteors would have varying degrees of energy behind them. So I will do the smallest and slowest to the fastest and largest for a range. These aren’t a range of possibilities, mind you. Each meteor has different properties and there’s no way I’m going through each one. lol
Smallest meteor is meteor 15 at 281,254,663,751.885 m^3.
Density of rock is 2,700 Kg/m^3
281,254,663,751.885 * 2,700 = 759,387,592,130,089.5 Kg.
Assuming a terminal velocity speed of 180 m/s, the kinetic energy of it would be 12,302,079,000,000,000,000 J, or 2.94 Gigatons
Largest meteor that ablated is Meteor 18 at 2,047,427,786,765.576 m^3
2,047,427,786,765.576 * 2,700 = 5,528,055,024,267,055.2 Kg.
Assuming an 11,000 m/s speed, the kinetic energy would be 334,447,329,000,000,009,011,200 J, or 79.94 Teratons
Now then, back to Naruto. Combined volume of the meteors he destroyed is 8,936,977,254,691.183 m^3
8,936,977,254,691.183 * 2,700 = 24,129,838,587,666,194.1 Kg.
Assuming an 11,000 m/s speed, the kinetic energy would be 1,459,855,229,999,999,946,326,016 J
1,459,855,229,999,999,946,326,016 + 777,517,021,158,132,921,000 = 1,460,632,747,021,158,079,247,016 J, or 349.1 Teratons
Naruto and Sasuke’s Six-Paths Chibaku Tensei
To cap off the series, Naruto and Sasuke seal Kaguya within a Six-Paths Chibaku Tensei. They mention that it’s “nearly the size of the moon”, but I see no reason not to scale it. “Almost” doesn’t tell us much, honestly.
Main assumption here is that Kaguya’s dimension is Earth-sized. Pretty standard stuff, actually. Based on the planet curvature, the full diameter of the planet is 1,572 pixels compared to 360 for the Chibaku Tensei and 410 for the distance it was lifted. Earth’s diameter is 12,742,000 m, for reference.
360 / 1,572 = .229 * 12,742,000 = 2,917,918 m, diameter of Chibaku Tensei
That means it achieved escape velocity, or 11,186 m/s
As a sphere, Chibaku Tensei would have a volume of 13,008,219,900,000,000,000 m^3 or 13,008,219,900,000,000,000,000,000 cm^3. The ground was fractured, so 8 J/cc is what we’ll use here for the initial formation.
An incomplete Juubi’s Bijuu Bomb warps the environment. We can see it’s clear vaporization, too.
As previously established, the craters from the prior Bijuu Bombs were 1,737.742 m in diameter. One of them is 18 pixels here compared to 29 for diameter of the half-cylinder, 15 for the depth, and 236 for the length. Since the depth is about half of the diameter anyway, I figure it’s safe to treat this as a uniform half-cylinder.
29 / 18 = 1.611 * 1,737.742 = 2,799.502 m, diameter of half-cylinder
236 / 18 = 13.111 * 1,737.742 = 22,783.535 m, length of cylinder
Volume of a full cylinder would be 140,240,210,152.396, but we’re cutting it in half, so…
140,240,210,152.396 / 2 = 70,120,105,076.198 m^3
Rock is 2,700 Kg/m^3
70,120,105,076.198 * 2,700 = 189,324,283,705,734.6 Kg of rock vaporized
Vaporization point of rock is 2,470 C, and the temp change at standard temps would be 2,450 C. Specific heat of rock is 750 J/kg C.
347,883,371,309,287,327,500 + 908,756,561,787,526,080,000 = 1,256,639,933,096,813,407,500 J, or 300.34 Gigatons
Juubi’s Second Form Bijuu Bomb
The Juubi’s second form Bijuu Bomb creates a massive explosion and takes out many mountains in the process. Like all Bijuu Bombs before, this appears to be vaporization, to boot.
There’s going to be some guesswork involved here. As seems to be a common problem in Naruto, I can’t see what mountains were there before they all blew up. The blast appears to be taking place smack dab in the middle of a mountain range, though, so I feel that I can conservatively estimate how many were blown up. The tricky part here (sigh) is that I’ll have to use an “average mountain size”, which I hate doing, but there’s not much choice here. I mean, look at this panel, it speaks for itself. The results are going to be high, regardless.
Anyway, the Bijuu Bomb initial crater is 14 pixels compared to a nearby mountain at 18 and its diameter at 34 (Treating it as a cone). This will serve as our “average” mountain. I picked one that didn’t stand out as too large or small. The blast itself is 300 pixels compared to a nearby mountain at 15 (Meant to account for perspective).
18 / 14 = 1.286 * 1,737.742 = 2,234.736 m, average mountain height
34 / 14 = 2.429 * 1,737.742 = 4,220.975 m, average mountain diameter
The blast diameter makes little difference, btw. I just wanted to give an idea of its size. Now, I count 10 mountains in a row along the perimeter of the explosion. Here’s where the biggest estimation comes into play: My assumption will be that it destroyed 5 (Half) rows of 10 mountains, or 50 total. This is based entirely on the mountains around the perimeter. The actual number could be more or less; we don’t know.
Volume of average mountain = 10,423,664,200 m^3
10,423,664,200 * 50 = 521,183,210,000 m^3 of total rock vaporized.
Rock weighs 2,700 Kg/m^3
521,183,210,000 * 2,700 = 1,407,194,667,000,000 Kg of rock vaporized
Vaporization point of rock is 2,470 C, and the temp change at standard temps would be 2,450 C. Specific heat of rock is 750 J/kg C.
2,585,720,200,612,500,000,000 + 6,754,534,401,600,000,000,000 = 9,340,254,602,212,500,000,000 J, or 2.23 Teratons
Again, there’s some guesswork here, but I believe it to be reasonable given the landscape of the battlefield being a mountainous region.
Might Guy’s Night Elephant
Might Guy opens the eighth chakra gate and unleashes Night Elephant on Madara. With air pressure alone, he shoots Madara down into a cylinder-shaped crater which appears to be vaporization due to the intense heat. As stated by Madara himself, this is an “air canon” or even simpler, a shockwave. We can get both power and speed from this… it’s been a while since Naruto has had a notable speed showing that I could calculate.
Madara is 1.79 m tall. He’s 34 pixels here compared to 197 for hole radius.
197 / 34 = 5.794 * 1.79 = 10.371 m, radius of hole
Diameter = 20.742 m
Panel length is 665 and hole diameter is 12. We’re using angular size here to figure out how far the hole is, AKA the height of the cylinder. Using the vertical vision field because it’s bigger in this panel: 135 degrees.
665 / 135 = 4.926 pixels/degree
12 / 4.926 =2.436 degrees, size of hole
Now, plugging these into the angular size calculator and solving for distance, we get 487.79 m, height of cylinder.
With our height and diameter, we find that the cylinder has a volume of 164,825.36 m^3
It was vaporized, so… you know the drill at this point, I’m sure.
164,825.36 * 2700 = 445,028,472 Kg of vaporized rock
445,028,472 * 750 * 2,450 = 817,739,817,300,000 J
Now we need to find latent heat of vaporization. Stone has a latent heat of vaporization of 4.8 KJ/g, or 4,800,000 J/Kg
445,028,472 * 4,800,000 = 2,136,136,665,600,000J
2,136,136,665,600,000 + 817,739,817,300,000 = 2,953,876,482,900,000 J, or 705.99 Kilotons
While it’s clearly in a league above Morning Peacock, I’m surprised that this would hurt Madara. Of course, it could be argued that he took the brunt of the damage and not the environment, but the real main event is speed.
Although I don’t believe a shockwave would normally vaporize something, I’m making an exception here because it’s constantly stated that Guy is using air to attack, not just here, but throughout all of Part 2 Naruto. He always uses Taijutsu (Physical attacks), so to chalk this up to anything besides a shockwave wouldn’t make a whole lot of sense.
As I’ve done in the past, I’ll be using the Rayleigh Pitot Tube Formula. A pitot tube measures the speed of of aircraft, and in the case of supersonic jets, the shockwave is measured by them to determine speed. Guy’s fist will be the “jet” in this case.
First up…
F = w / d
F is force, w is work (energy), and d is distance.
We have energy, and the distance is the height of the cylinder; that’s how long it acted upon the ground.
2,953,876,482,900,000 / 487.79 = 6,055,631,486,705.344 N, force of shockwave exerted on ground
Next we need area effected by the shockwave, which would be the area of a 20.742 m circle.
However, this is only the minimum pressure applied by the end of the shockwave. A pitot tube gets the shockwave immediately and measures its pressure to determine an aircraft’s speed. With inverse-square law, we can figure out the initial pressure that a pitot tube attached to Guy’s arm would be reading.
S/4 pi r^2 = I
Where S is the source strength, r is the “radius” or distance from the initial attack, and I is the final intensity. We’re solving for S here.
S / 4 * 3.14 * 487.79^2 = 17,921,371,668.261
S / 2,988,514.896 = 17,921,371,668.261
S = 53,558,286,187,350,368.916 Pa or 53,558,286,187,350.369 KPa
With the Rayleigh Pitot Tub formula, we can find the Mach number:
Pt / P = ( ( y + 1)^2 M^2 / 4y M^2 – 2 (y – 1) ) y / y – 1 (1 – y) + 2y M^2 / y + 1
Pt = Total impact pressure (KPa)
P = Atmosphereic pressure. (KPa)
Y = Specific heat ratio (Commonly 1.4, which is what I’m using.)
Hooo boy, that’s fast! Mach 715.59 Guy punches. Six Paths Madara wasn’t able to dodge them, but there was one point where he gets his shield up in time to block one… barely.
RESULTS
Juubi First Form Bijuu Bomb – 300.34 Gigatons
Juubi Second Form Bijuu Bomb – 2.23 Teratons
Might Guy’s Night Elephant Power – 705.99 Kilotons
Hachibi’s Whirlwind carves up a huge chunk of ground and uproots a large amount of forest. I have a method on uprooting trees, and some of them are flung away which is calculable, but it appears the majority of them were destroyed, which, unless they were turned to ash (I see no signs of burning), I am unable to calculate. So this’ll be low-end to begin with.
Hachibi’s width from tail to tail is 60.853 m. Here, he’s 25 pixels wide compared to the inner crater at 125 in diameter and 9 in depth. The full crater is 795 pixels. Distance from crater to off-panel is 145 (For later). The tree nearby is 21 pixels and its roots are at 8. We’ll use that for a little later.
For the larger crater’s depth, I’m going to use Hachibi’s size as the yellow line goes just above his head. It’s a tricky perspective, but I feel this is a good estimation.
In the dome calculator, the larger crater’s volume comes to 89,604,985.217 m^3
However, we need to account for the inner crater.
89,604,985.217 – 801,933.368 = 88,803,051.849 m^3
88,803,051.849 m^3 = 88,803,051,849,000 cm^3
88,803,051,849,000 * 87 = 7,725,865,510,863,000 J
Ok, but how about those trees? The more I think of it, the more it feels right to calculate them getting sent off-screen. We truly only see around 20 or so of them still in-tact and flying, but I figure the energy required to destroy them all is higher than to send them flying, right?
Tobi is 1.75 m tall. He’s 48 pixels here compared to 316 for distance between the tree he’s standing on and the one next to him.
316 / 48 = 6.583 * 1.75 = 11.52 m, distance between trees.
There’s a third tree layered ahead. Assuming it’s a similar distance, that would mean for every three trees, there is 132.71 m^2 of land.
132.71 / 3 = 44.237 m^2 per tree
We’ll use this as our average for the portion of the forest wiped out by Hachibi.
A = pi r^2
3.14 * 967.563^2 = 2,939,599.419 m^2 of destroyed forest
2,939,599.419 / 44.237 = 66,451.148 or 66,451 (Because ,148 of a tree would be a stump >_>) trees destroyed or sent flying.
Behold! Hachibi is the greatest culprit of deforestation! Not greedy humans!
Now, how much energy would it take to uproot all of these trees?
60 kN per tree, from the look of it. But we need energy. How much were the uprooted by? That’s what the tree root scaling was for. The answer is 19.473 m.
60 kN – 60,000 N
w = d*f
19.473 * 60,000 = 1,168,380 J per tree.
1,168,380 * 66,451 = 77,640,019,380 J
One more thing to take care of, though. If these trees were flung away, then how far? Well, the best we can come up with is off-panel. The other issue is that it could be from several places, going in several directions. Because it’s an omni-directional attack. For this reason, I’ve decided to come up with an average distance of sorts.
As we know, the full crater diameter is 1,935.125 m. The radius would therefore be 967.563 m.
Distance from end of crater to off-panel is 352.947 m.
967.563 + 352.947 = 1,320.51 m, max distance.
1,320.51 + 352.947 = 1,673.457 / 2 = 836.73 m, average distance launched
Assuming an optimal launch angle of 45 degrees and using a projectile launch calculator, we find that the average tree would have a launch speed of 90.584 m/s.
As for the mass, well, as I showed above, the tree is 50 m tall. Calculating the weight of a tree is a difficult task. I did, however, find some research on a 24 m tall oak tree which weighed 14,385 Kg. I’ll use this as my low-end weight.
KE = .5mv^2
.5 * 14,385 * 90.584^2 = 59,017,778.6 J, energy to launch a single tree.
59,017,778.6 * 66,451 = 3,921,790,405,748.6 J, total energy to send the trees away.
An awful lot of work for something that the Hachibi could probably do in his sleep, but there was another purpose to this calculation anyway (Stay tuned) and it’s nice to know what his non-Bijuu Bomb output is.
Bijuu Bombs Destroying Landscape
This one is tough because it’s clearly stated and shown that these Bijuu Bombs are destroying mountains. The problem is that we can’t see which mountains they’re destroying and therefore can’t scale how big they are. Still, I can get an idea of how much destruction was caused in the ground from later scans. Just no way for me to account for the mountains, unfortunately.
The perspective is rough, here. We have to low-ball it. I chose the closest in the background from where Hachibi’s crater was. As you may recall, that crater is 1,935.125 m in diameter. It measures 88 pixels here compared to 79 for the nearest Bijuu Bomb.
79 / 88 = 0.898 * 1,935.125 = 1,737.742 m, diameter of Bijuu Bomb.
That’s a big explosion :o… but eyes on the prize. First, we can see the smoldering the right from a Bijuu Dama where a crater is made. My assumption is that this crater is a perfect half-sphere and the same diameter as the explosion scaled above.
Volume as a sphere would be 2,747,606,380, but it needs to be cut in half for the crater.
2,747,606,380 / 2 = 1,373,803,190 m^3
This is clear vaporization.
We’ll have to use latent heat and specific heat capacity to figure out the energy required.
Rock is 2,700 kg/m^3, so the total weight of vaporized rock is 3,709,268,613,000 kg. Vaporization point of rock is 2,470 C, and the temp change at standard temps would be 2,450 C. Specific heat of rock is 750 J/kg C.
17,804,489,342,400,000,000 + 6,815,781,076,387,500,000 = 24,620,270,418,787,500,000 J, or 5.88 Gigatons
Alright, and onto the big one… it’s the result of a clash between the five Bijuus and a 9-tails powered Naruto Bijuu Bombs. The initial Bijuu Bomb crater is 85 pixels compared to the massive explosion at 554, the diameter of its crater at 408, and the depth of its crater at 89.
554 / 85 = 6.518 * 1,737.742 = 11,326.602 m, size of explosion.
408 / 85 = 4.8 * 1,737.742 = 8,341.162 m, diameter of crater
89 / 85 = 1.047 * 1,737.742 = 1,819.416 m, depth of crater
Treating it as a dome, the crater would have a volume of 52,863,655,601.100 m^3
However, we need to subtract the damage already done by Hachibi.
683,951,695,981,843,680,000 + 261,825,258,618,049,533,750 = 945,776,954,599,893,213,750 J, or 226.05 Gigatons
Hooo boy, that’s a big one! Of course, having read through Naruto before, I know it’ll get even higher.
The way things shape up, assuming Naruto contributed one half and the five Bijuus contributed the other half:
9-Tails fueled Naruto Bijuu Bomb: 113.03 Gigatons
Each Individual Bijuu Bomb from other Bijuus: 22.61 Gigatons
More Onoki Atomization Shenanigans
Oh lawd, I could have lived without ever having to do another one of these atomization calculations again… never mind another day later! At least this one looks like it may be impressive, though. He uses his dust element to atomize thick tree roots made by Madara.
Onoki is 1.30 m tall. Here he’s 5 pixels compared to 628 to diameter of atomized root. 17 pixels for the “average” space between roots. Yeah, accounting for the space between each root he destroyed would take way too long and is probably impossible based on the drawing anyway. What I’ll do instead is take the size of the space between those roots and subtract that from the crater, to make up for the eventual half-sphere volume calculation. In my opinion, this will be a good way to account for that empty space.
628 / 5 = 125.6 * 1.30 = 163.28 m, diameter of atomized root
17 / 5 = 3.4 * 1.30 = 4.42
163.28 – 4.42 = 158.86 m, adjusted diameter
As a perfect half-sphere, the volume comes to 1,049,572.155 m^3 of root atomized.
Alright, now for the hard part. Wood is made up of as follows:
We need the enthalpy of atomization and molecular mass of all of these, adjusted to their percentages and added up to make the totals for wood.
1,049,572.155 * 565 = 593,008,267.575 Kg or 593,008,267,575 g of wood atomized.
593,008,267,575 / 20.126 = 29,464,785,231.79 mol
29,464,785,231.79 * 483.322 = 14,240,978,927,799.206 kJ or 3.4 Megatons
Now that’s more like it, Onoki!
Madara Perfect Susano’o Sword Swing
Massive destruction ensues when Madara’s Perfect Susano’o swings its sword. Up to and including the two mountain peaks, just above everything is explosively fragmented. The peaks themselves appear to have been cut and shut up into the air (Potential energy), but there’s a lot to cover here.
First and foremost, the first structure it hits are the remnants of the meteors originally dropped by Madara.
As a reminder, the second meteor had a longer diameter of 862.584 m. It’s 302 pixels tall here compared to 330 for distance from pillar to pillar (For later), and 26 pixels for width of chunk taken out of the meteor with a length of 170. For measurements of the pillars themselves, I will go in order from left to right and be treating them as rectangular prisms.
330 / 302 = 1.093 * 862.584 = 942.804 m, distance from the two furthest away pillars
26 / 302 = .086 * 862.584 = 74.182 m, width of missing chunk
170 / 302 = .563 * 862.584 = 485.635 m, length of missing chunk
Alright, now for the pillars themselves, again, from left to right.
162 / 302 = .536 * 862.584 = 462.345 m, height of pillar 1
43 / 302 = .142 * 862.584 = 122.487 m, width of pillar 1
V = 6,936,592.166 m^3
169 / 302 = .56 * 862.584 = 483.047 m, height of pillar 2
45 / 302 = .149 * 862.584 = 128.525 m, width of pillar 2
31 / 302 = .103 * 862.584 = 88.846 m, length of pillar 2
V = 5,515,880.918 m^3
203 / 302 = .672 * 862.584 = 579.657 m, height of pillar 3
35 / 302 = .116 * 862.584 = 100.06 m, width of pillar 3
18 / 302 = .06 * 862.584 = 51.755 m, length of pillar 3
V = 3,001,814.812 m^3
129 / 302 = .427 * 862.584 = 368.323 m, height of pillar 4
62 / 302 = .205 * 862.584 = 176.83 m, length of pillar 4
V = 11,517,036.233 m^3
Volume of the second meteor Madara dropped is 2,043,563,130 m^3, but we need to account for the missing triangular prism shaped chunk. For that we also need the smaller diameter of the second meteor, 752.054 m.
As a reminder, width from the two furthest away pillars was measured at 942.804 m. That measures 433 pixels here compared to Susano’o blade thickness at 2, length of destruction at 485, height of destruction at 104, width of destruction at the end at 71 (This is to fix perspective issues), height of mountain peak 1 (Left) at 66, diameter at 148, mountain peak launch height at 35, mountain peak 2 height at 46, peak diameter at 96, and mountain peak 2 launch height at 45.
There’s more to calculate, though. The cut into each mountain. I’ll treat both of those cuts as cylinders with heights of 5 cm each (Estimated thickness of blade). 727 J/cc is the bare minimum for cutting through stone. The same should apply to rock.
Mountain 1 cut volume = 151,745.104 m^3 or 151,745,104,000 cm^3
I don’t know how good this translation is, but Tobi does call Gedo Mazo “Heretical Demon Statue”. Along with “Mountain Sandwich”, I hope these names are canon. lol
Anyway, an incomplete Gedo Mazo obliterates some large chunks of rock with a lightning release. Looks to be a combo of vaporization and explosive fragmentation, so we’ll use cratering, here.
Chouji’s big toe is 6 pixels compared to a nearby ninja at 13. We’ll assume a height of 1.70 m for the random ninja.
6 / 13 = .462 * 1.70 = .785 m, length of Chouji’s big toe.
Chouji’s big toe is 8 pixels here compared to Gedo Mazo’s calf at 33. I know, comparing appendages isn’t exactly great, but there are very few shots of Gedo which show his true height, which is an issue. If I find something better later on, I may come back to this and make edits.
33 / 8 = 4.125 * .785 = 3.238 m, width of Gedo Mazo’s calf.
My assumption here is that the two halves of the “mountain sandwich” make a perfect half cylinder. Mazo’s calf is 5 pixels here compared to thickness of the mountain sandwich at 44 and the quarter cylinder at 363. For some other time, I also scaled Mazo’s full height at 178 pixels.
44 / 5 = 8.8 * 3.238 = 28.494 m, thickness of cylinder
363 / 5 = 72.6 * 3.238 = 235.079 m, half of cylinder
235.079 * 2 = 470.158 m, full diameter of half cylinder
178 / 5 = 35.6 * 3.238 = 115.273 m, Gedo Mazo’s full height
Now, if this were a full cylinder, the volume of the mountain sandwich would be 4,946,875.29 m^3, but since it’s a half-cylinder…
4,946,875.29 / 2 = 2,473,437.645 m^3 or 2,473,437,645,000 cm^3
2,473,437,645,000 * 87 = 215,189,075,115,000 J, or 51.43 Kilotons
Tsuchikage Clash Atomizes Cliffs & Sand
The clash between Onoki and Mu’s sub-atomic separation techniques results in the atomization of some cliffs and the sand below. This is going to be a tough one to calculate. Not only due to the odd shapes, but because atomization involves the breaking up of all elements within a material. Rock, for example, is comprised of several elements, which I must account for when finding the enthalpy of atomization… but enough complaining. Let’s get started.
Just realized too that the above panels are probably a tribute to the Kamehameha vs Galick Gun clash from Dragonball.
Lots to unpack here. We’ll start with the hole in the sand, then go from left to right with the rock formations. A the third Raigake is 2.05 m tall. He’s 29 pixels here compared to the diameter of the hole at 335. For simplicity’s sake, I will be assuming that each part of the rock formations destroyed was a half-cylinder. Obviously this isn’t perfect, but accounting for the curve of the sphere from the clash would be outrageously thorough and time-consuming. I also don’t know if I’d be able to get accurate results due to the angle. If anything, the lack of angles in my assumptions will make this low-end.
335 / 29 = 11.552 * 2.05 = 23.682 m, diameter of hole.
We’ll be saving the above for later, as the hole is crater-shaped, but we can’t see the bottom here.
Rock formation 1:
89 / 29 = 3.069 * 2.05 = 6.292 m, height of rock formation 1
22 / 29 = 0.759 * 2.05 = 1.556 m, diameter of rock formation 1
V = 11.965 / 2 = 5.983 m^3, volume of rock formation 1 atomized
Rock Formation 2:
72 / 29 = 2.483 * 2.05 = 5.09 m, height of rock formation 2
41 / 29 = 1.414 * 2.05 = 2.9 m, diameter of rock formation 2
V = 33.621 / 2 = 16.811 m^3, volume of rock formation 2 atomized
Rock Formation 3:
84 / 29 = 2.897 * 2.05 = 5.94 m, height of rock formation 3
37 / 29 = 1.276 * 2.05 = 2.62 m, diameter of rock formation 3
V = 32.024 / 2 = 16.012 m^3, volume of rock formation 3 atomized
Rock Formation 4:
85 / 29 = 2.931 * 2.05 = 6.01 m, height of rock formation 4
39 / 29 = 1.345 * 2.05 = 2.757 m, diameter of rock formation 4
V = 35.879 / 2 = 17.94 m^3, volume of rock formation 4atomized
Rock Formation 5:
34 / 29 = 1.172 * 2.05 = 2.403 m, height of rock formation 5
20 / 29 = .69 * 2.05 = 1.415 m, diameter of rock formation 5
V = 3.78 / 2 = 1.89 m^3, volume of rock formation 5 atomized
Rock Formation 6:
79 / 29 = 2.724 * 2.05 = 5.584 m, height of rock formation 6
37 / 29 = 1.276 * 2.05 = 2.62 m, diameter of rock formation 6
V = 30.105 / 2 = 15.053 m^3, volume of rock formation 6 atomized
5.983 + 16.811 + 16.012 + 17.94 + 1.89 + 15.053 = 73.689 m^3, total volume of rock atomized
Rock has a density of 2,700 kg/m^3.
2,700 * 73.689 = 198,960.3 Kg of rock atomized
Now for the hard part. Rock is made up of several elements. They are as follows:
We need the enthalpy of atomization and molecular mass of all of these, adjusted to their percentages and added up to make the totals for rock.
116.034 + 126.312 + 26.406 + 20.75 + 6.408 + 2.996 + 2.314 + 3.066 = 304.286 kJ/mol, Enthalpy of Atomization of rock
14.912 + 7.78 + 2.186 + 2.8 + 1.443 + .644 + 1.017 + .51 = 31.292 g/mol, Molar Mass of rock
198,960.3 Kg = 198,960,300 g.
198,960,300 / 31.292 = 6,358,184.2 mol
304.286 * 6,358,184.2 = 1,934,706,437.481 kJ
Well that was a pain in the ass… how about we do that with sand, too? 😛
As a reminder, 23.682 m is the diameter of the hole in the ground. It measures 143 pixels here compared to 224 for full diameter of the sphere, and 195 as distance from top of sphere to where it cuts into the sand. The final figure is important to figure out the volume of sand atomized. That way we can get the depth of the crater.
224 / 143 = 1.566 * 23.682 = 37.086 m, full diameter of sphere
195 / 143 = 1.364 * 23.682 = 32.302 m, distance from top of sphere to hole in the sand
37.086 – 32.302 = 4.784 m, depth of sand atomized
With that said, using the dome calculator, the volume of atomized sand comes to 1,110.958m^3
56,031,668.567 * 423.45 = 23,726,610,054.696 kJ, energy to atomize the sand
23,726,610,054.696 + 1,934,706,437.481 = 25,661,316,492.177 kJ, or 6.13 Kilotons
Not quite as high or impressive as I had expected, especially for all of that work. Still, it was something different. Assuming they contributed equally, Mu and Onoki would’ve put 3.07 Kilotons a piece into their attacks.
Madara’s Meteors
Madara summons a meteor to crush everyone on the battlefield. Well, there’s some argument as to whether he summoned it or used the Rinnegan to attract it down to earth (Which to be fair he does do that later on), but that’s not explicitly shown. As a result, there’s a lot of arguments about the speed of his meteors and therefore the total energy of them. Guess what? I have a way to immediately nullify those arguments. 😉
But to start, let’s figure out the size of this first meteor. True to Naruto Part 2 fashion, this will be awkward to scale.
Gaara is 1.66 m tall. Here he is 77 pixels and the rock structure platform has a radius of 266.
266 / 77 = 3.455 * 1.66 = 5.735 m, radius of platform
5.735 * 2 = 11.47 m, diameter of platform
The platform below is 27 pixels compared to the height of meteor chunk at 184.
184 / 27 = 6.815 * 11.47 = 78.168 m, length of visible meteor.
However, this is nowhere close to the full meteor size. To find that, I must superimpose what we can see here onto a better view, matching the curvature of the partial meteor to the full one. IT’s going to look tiny, so I’ve outlined where it’s superimposed in red.
So as we can see, the small chunk of meteor is 29 pixels compared to 377 for its first diameter and 319 for its second as an ellipsoid. Conveniently, the second meteor is here, too. 320 pixels for its first diameter and 279 for its second.
377 / 29 = 13 * 78.168 = 1,016.184 m, diameter 1 of first meteor
319 / 29 = 11 * 78.168 = 859.848 m, diameter 2 of first meteor
320 / 29 = 11.035 * 78.168 = 862.584 m, diameter 1 of second meteor
279 / 29 = 9.621 * 78.168 = 752.054 m, diameter 2 of second meteor
Alright, so how do we figure out the speed of these meteors? We can at least see that they’re not ablated (Not on fire from shooting through the atmosphere), so that doesn’t leave us with many clues. Thankfully, though, we can figure it out thanks to the second meteor:
We can clearly see here that meteor 2 explosively fragments meteor 2. From that, we can get its kinetic energy, and from there, its speed. Meteor 1’s speed would likely be in the same ballpark, and we can then find its energy as well.
To start with…
Treating meteor 1 as an ellipsoid, the volume comes to 3,147,054,998 m^3
3,147,054,998,000,000 * 20 = 62,941,099,960,000,000 J or 15.043 Megatons, energy of meteor 2
Now that we have the energy behind meteor 2, we can easily find its mass and then the speed it was moving at. Finally, we can apply that to the original meteor and see what the Onoki/Gaara combo is capable of handling with their abilities.
Rock is 2,700 kg/m^3
2,700 * 2,043,563,130 = 5,517,620,451,000 Kg, weight of meteor 2.
v = sprt KE/.5 * m
sqrt 62,941,099,960,000,000 / .5 * 5,517,620,451,000 = 151.045 m/s
Now, applying that same speed to meteor 1…
3,147,054,998 * 2,700 = 8,497,048,494,600 Kg, mass of meteor 1
Well, that was some work! But I feel this is the definitive answer to the Madara meteor feats, in particular. Not nearly as much guesswork involved in the speed of the meteors thanks to good ol’ Kinetic energy!
RESULTS
Incomplete Gedo Mazo Destroys a Mountain Sandwich – 51.43 Kilotons
Onoki and Mu Atomize Rocks and the Sand – 6.13 Kilotons
Onoki Dust Release output – 3.07 Kilotons
Mu Dust Release Output – 3.07 Kilotons
Madara First Meteor Kinetic Energy – 23.17 Megatons
Madara Second Meteor Kinetic Energy – 15.043 Megatons
Back with some more Naruto calculations. There were a lot of plot developments between Pain attacking Konoha and this point, but all of the feats shown were pretty low-end or related to Genjutsu in some way (AKA not calculable).
With that said, some of the build up to the Shinobi World War have notable showings from characters, so here we go…
Might Guy’s Morning Peacock, Part 2
As established before, Might Guy’s Morning Peacock are simple punches which create friction in the air, allowing him to throw fireballs. This would require a minimum speed of Mach 6, but it’s not possible as far as I know to deride a true speed from what we’re shown.
However, we can also see that Guy’s Morning Peacock vaporizes the giant wave before him. Not only that, but was can compare the heat from Guy’s fists to the heat of a railgun projectile and use that as our temperature change for the vaporization.
Kisame is 1.95 m tall. Here he measures 20 pixels compared to the beginnings of his wave at 560, and the width at 884. For the depth, I used one of his water sharks as reference, 138 pixels. Since the wave has only just begin here, I feel it’s appropriate to treat it as a rectangular prism.
Density of sea water near the surface is 1,026.6 Kg/m^3
63,318.88 * 1,026.6 = 65,003,162.208 Kg of water vaporized
For the temperature change, instead of the standard minimum to vaporize water, I’ll be using the heat generated by a railgun projectile: 14000 K or 13,726.85
Assuming the water is 20 C… Specific heat of seawater is 3,850 J/Kg C.
I count 50 punches thrown (Though it could be more), so for each Morning peacock punch, it’d be 2.08 Kilotons
Deidra Flips a Giant Turtle
You’ve heard of “jumping the shark”, but how about “flipping the turtle”? This is a very silly feat for a manga like Naruto, but it’s still impressive. Deidra’s explosion knocks the giant turtle somewhat upward, then Manda 2.0 finishes the job. The turtle is massive, so it’s sure to be an impressive feat.
Yamato is 1.78 m tall. Here, he measures 21 pixels compared to the giant squid’s sucker at 46. I did my best to judge which sucker was closest so the perspective isn’t skewed. Technically, they’re all in the background, but clearly not far from the ship.
46 / 21 = 2.191 * 1.78 = 3.9 m, diameter of giant squid’s sucker.
Once again, the perspective makes things tricky. Manda 2’s eye is clearly in the background compared to the giant squid’s tentacle, though, so I chose the sucker which was the furthest back to compare. It measures at 5 pixels compared to Manda’s eyeball at 30.
30 / 5 = 6 * 3.9 = 23.4 m, height of Manda 2’s eyeball.
We’re comparing eyeballs, here. Riveting, I know. But Kishimoto relegated a lot of these to tiny panels and we never see Manda 2 or the turtle again after these chapters. lol
Manda’s eye is 6 pixels tall. The turtle has his eyes partially closed, but thankfully we can still measure from the sides. Width of the turtle eyeball is 26 pixels.
26 / 6 = 4.333 * 23.4 = 101.392 m, width of turtle eyeball.
The eyeball is 4 pixels compared to full length of the giant turtle at 632.
632 / 4 = 158 * 101.392 = 16,019.936 m, full length of turtle.
The leatherback sea turtle is considered the largest of the sea turtles. It’s on average 6 feet/1.83 m long and up to 2,000 lbs/900 Kg.
Using the cubed law, we can figure out the weight of this massive turtle island.
16,019.936 / 1.83 = 8,754.064
8,754.064^3 = 670,855,758,614.641
Now applying to the leatherback’s weight…
900 * 670,855,758,614.641 = 603,770,182,753,177.273 Kg, weight of the giant turtle.
That’s 600 times the weight of Mt. Everest, and I can’t even include all of the rock formations, trees, structures etc because there’s not enough shown in detail.
Next we find lifting force by using the angle the turtle island was tilted upward at. It’s much like flipping a tire at the gym. Based on what I see, Deidra’s explosion accounted for about 35 degrees of the lift, then Manda 2 finished the job. The remaining lift would only be an additional 55 degrees because after 90 degrees is reached, gravity helps and plays a big role in Manda dragging the turtle down like he did.
First, we need the adjusted weight (Because it’s not a complete lift).
603,770,182,753,177.273 * sin (35) = 346,308,349,798,587.254 Kg, adjusted weight
For lifting force, we assume the middle, or .5 as the fulcrum point.
.5 * 346,308,349,798,587.254 = 173,154,174,899,293.627 Kg-Force, or 1,698,062,389,272,707.75 N
For Manda 2, it’s…
603,770,182,753,177.273 * sin (55) = 494,579,579,483,003.336 Kg, adjusted weight
.5 * 494,579,579,483,003.336 = 247,289,789,741,501.668 Kg-Force, or 2,425,084,416,563,570 N
That’s all well and good, but we need energy, too. For that, we need to figure out the distance the turtle was flipped.
The turtle is 197 pixels long and 103 wide.
103 / 197 = 0.523 * 16,019.936 = 8,378.427 m, width of turtle
At a 35 degree flip, Deirda’s explosion moved the turtle 2,559.044 m
w = d*f
1,698,062,389,272,707.75 * 2,559.044 = 4,345,416,368,893,987,131.391 J, or 1.04 Gigatons
Wow! Didn’t know Deidra had it in him. lol
Now for Manda 2. Since he spun the turtle an addition 55 degrees, that would be 4,021.356 m
2,425,084,416,563,570 * 4021.356 = 9,752,127,769,054,411,600.92 J, or 2.33 Gigatons
That turtle feat was a pain in the ass to calculate. There’s something about the more modern manga authors and trying to cram everything into more and more panels. It gets really bad the further you get into One Piece, but I’m noticing it a lot in later Naruto chapters as well. Point being, it’s easier to miss things when there’s a lot going on with the smaller panels. Hopefully I don’t miss anything.
And yeah, as you can probably tell, this is around the point where Naruto’s feats are going to really escalate. Whether characters like Deidra hitting high mountain level feats without too much effort is an inconsistency or because of the Edo Tensei, I leave up to you!
RESULTS
Might Guy’s Morning Peacock, Total Energy Output – 104.04 Kilotons
Might Guy’s Morning Peacock, Per Punch – 2.08 Kilotons
Edo Deidra’s Explosion Flips a Giant Turtle – 1.04 Gigatons
Manda 2 Finishes Flipping a Giant Turtle – 2.33 Gigatons
Pain’s Chou Shinra Tensei destroys most of Konoha and creates a huge crater.
Of the three ninja standing atop the Konoha wall, Samui, is furthest to the right. She stands 1.68 m tall. She measures 25 pixels here compared to 81 for the width of a single wall slab.
81 / 25 = 3.24 * 1.68 = 5.443 m, width of wall slab
416 / 2 = 208 * 5.443 = 1,132.144 m, distance from outer crater to inner crater
120 / 2 = 60 * 5.443 = 326.58 m, depth of outer crater
Unfortunately, there aren’t many good views of the two craters. The best I can do is this scan here, and go by radius for the inner crater. Distance from outer crater to inner crater is 277 pixels compared to 759 for distance from outer crater to crater radius.
759 / 277 = 2.74 * 1,132.144 = 3,102.075 m, radius of outer crater
Outer Crater Diameter = 6,204.15 m
3,102.075 – 1,132.144 = 1,969.931 m, radius of inner crater
Inner Crater Diameter = 3,939.862 m
Hashirama is 1.85 m tall. He’s 31 pixels compared to his face carving on Hokage rock at 445.
445 / 31 = 14.355 * 1.85 = 26.557 m, height of Hashirama face carving
Hashirama face carving is 102 pixels compared to 235, the full height of Hokage Rock.
235 / 102 = 2.304 * 26.557 = 61.187, height of Hokage Rock
Hashirama face carving is 61 pixels compared to 501 for distance from top of Hokage Rock to bottom of inner crater.
501 / 61 = 8.213 * 61.187 = 502.529 – 61.187 = 441.342 m, depth of inner crater
Treating it as a dome, the inner crater would have a volume of 2,735,289,623.95 m^3
Next we arrive at the issue of the outer crater. It’s cut off by the inner crater, and so we need to figure out how this would affect volume. My plan is to take what percentage of the total depth that the outer crater has and then apply it to the results of the volume if it were a full crater.
441.342 + 326.58 = 767.922 m, total depth of both craters
326.58 / 767.922 = .426, percentage of depth for outer crater
Now, if we were to consider the outer crater a full crater, the volume would be 4,954,679,705.56 m^3. However, the true amount is actually 42.6% of this number based on each crater depth and what they contribute to the total depth.
But even this isn’t fully correct. You’ll notice that oddly enough, Hokage Rock and by extension a pie-shaped piece of land behind it are untouched by the destruction. This needs to be accounted for, but the issue is that we can’t see on-panel the full size of the land chunk. All we know is that it’s pie-shaped, and takes up a decent chunk of circle (See Bijuu Bomb scan above). I’m going to estimate that this chunk of land takes up 1/8th of the circle.
Alright then, so how was it destroyed? Well, there’s a big old crater, some vapor, and a lot of debris. The high amount of debris, however, is insignificant compared to how much rock was actually destroyed. To me, this is cratering for sure. 87 J/cc.
The rhino’s skull length is 71 pixels compared to 309 for full body length.
309 / 71 = 4.352 * 11.205 = 48.764 m, length of rhino
Now we need to do angular sizing. Since this is a narrow panel, I’ll be using the vertical field of vision, 150 degrees for this panel.
545 / 150 = 3.633 pixels/degree
51 / 3.66 = 13.934 degrees, rhino distance
Using this angular size calculator, we can solve for distance based on the rhino size in degrees, and how long it is in meters. The total comes to 199.53 m.
Now we can use projectile motion to find out the rhino’s acceleration. Inputting the the angle to 75 degrees (He’s aiming upward, but the rhino arcs as well so it’s not straight up) and the max height to 199.53 m, we find the rhino’s initial velocity to be to be 64.764 m/s.
Now we need to figure out how much distance Naruto’s arms acted upon the rhino to throw it in the air so we can find acceleration.
Naruto is 1.66 m tall. He’s 154 pixels here compared to his arm length at 64.
64 / 154 = .416 * 1.66 = .681 m, Naruto arm length
The motion of Naruto’s arms in the scan where he throws the rhino is half-circle for sure, but based on the trajectory of the rhino, some of that appears to be follow through. So instead of half, my assumption will be a 1/3rd circular motion. If Naruto’s arms i the radius of a circle, then he acted upon the rhino for 1.425 m.
a = v^2 / (2 * d)
64.764^2 / 2 * 1.425 = 1,471.711 m/s^2
f = ma
3,437,641.2 * 1,471.711 = 5,059,214,368.093 N
w = f * d
5,059,214,368.093 * 1.425 = 7,209,380,474.533 J or 1.723 Tons of TNT
I swear, lifting/throwing feats are never as impressive as I think they’re going to be!
6 Tailed Naruto’s Bijuu Bomb
6-Tailed Naruto’s Bijuu Bomb vaporizes some more rock within the Konoha craters. And in this case, there can be no doubt of vaporization, what with the lack of debris and high amount of vapor in the aftermath.
As previously established, the combined depth of the craters is 767.922 m. The total depth is 150 pixels here compared to 472 for full diameter of destruction.
472 / 150 = 3.147 * 767.922 = 2,416.651 m, diameter of destruction
Treating the destruction as a dome, the volume would come to 1,998,294,599.68 m^3. However, once again, we have to take into account a missing piece: the curvature of the craters. Some rock is missing that the Bijuu Bomb normally would have destroyed that we need to factor in. We can see in the scan above that there is a large triangle-like piece that’s essentially the Bijuu Bomb hitting empty air. I will assume that this is 1/8th, as 1/4th would take up much more of a circle, and anything lower would be insignificant.
1,998,294,599.68 * .125 = 249,786,824.96
1,998,294,599.68 – 249,786,824.96 = 1,748,507,774.72 m^3, true volume of vaporized rock
We can use latent heat and specific heat capacity to figure out the energy required.
Rock is 2,700 kg/m^3, so the total weight of vaporized rock is 4,720,970,991,744 kg. Vaporization point of rock is 2,470 C, and the temp change at standard temps would be 2,450 C. Specific heat of rock is 750 J/kg C.
22,660,660,760,371,200,000 + 8,674,784,197,329,600,000 = 31,335,444,957,700,800,000 J, or 7.49 Gigatons
This would also explain why Pain was so impressed with the Bijuu Bomb despite making a larger crater himself.
Pain’s Chibaku Tensei
Pain’s Chibaku Tensei gathers rock from the earth and forms a large sphere up in the air. Like literally all of the feats in this arc, it’s a pain in the ass to scale. But follow along and I think you’ll find that I have a decent method, if nothing else. It all has to do with the fake tree that Nagato and Konan are hiding in at the top of a mountain.
Typical Kishimoto. Doesn’t give Naruto’s full height or the tree width in the frame. But that’s alright. We got his arm length of .681 m earlier. 😉 His arm measures 55 pixels here compared to 102 for width of tree root. Then in the right panel, the tree root measures 8 pixels compared to the full height of the tree at 435.
102 / 55 = 1.855 * .681 = 1.263 m, width of tree root
435 / 8 = 54.375 * 1.263 = 68.676 m, height of fake tree
The fake tree at the top of the mountain is 6 pixels tall compared to the mountain height of 159.
159 / 6 = 26.5 * 68.676 = 1,819.914 m, height of mountain.
Now for the interesting part…
In the past, I recall people claiming that this mountain was one of the mountains shown in the scan of Chibaku Tensei where all of the mountains surround it. However, this is inaccurate. Why, you may ask? Look at the position of the sun in both panels. The sun is to the right from both the Chibaku panel view and Nagato’s point of view. This means that Nagato’s mountain can’t be one of the mountains shown in the Chibaku panel. It’s likely somewhere behind where our view is in the Chibaku panel.
At the same time, though, the above scan gives us a hint. Nagato, even from the mountaintop, still has to look up to see Chibaku Tensei in action. In other words, Nagato’s mountain is our minimum height that Chibaku Tensei is suspended in the air.
Distance from ground to bottom of Chibaku Tensei is 147 pixels compared to diameter of Chibaku at 235 and diameter of hole in the ground at 471.
235 / 147 = 1.597 * 1,819.914 = 2,906.403 m, diameter of Chibaku Tensei
471 / 147 = 3.204 * 1,819.914 = 5,831.005 m, diameter of hole in ground (This is for later)
With gravitational potential energy, we can find the total power required to pull this feat off.
U = mgh
Where m is mass of the object, g is gravitational acceleration (9.8 m/s^2), and h is height that the weight was lifted.
As a sphere, Chibaku Tensei has a volume of 12,854,823,600 m^3
Rock is 2,700 kg/m^3.
2,700 * 12,854,823,600 = 34,708,023,720,000 Kg, mass of Chibaku Tensei
In addition, Pain’s Chibaku Tensei fragmented the rock before lifting it up into the air. Fracturing is 8 J/cc.
12,854,823,600 m^3 = 12,854,823,600,000,000 cm^3
12,854,823,600,000,000 * 8 = 102,838,588,800,000,000 J, or 24.579 Megatons
24.579 + 147.95 = 172.53 Megatons, total energy of Chibaku Tensei
Naruto’s Sage Rasenshuriken
Naruto’s Fuuton Rasenshuriken crosses a long distance in 1 second, straight from the words of the narrator. In addition, I believe there is a kinetic energy feat hiding in there, so we’ll see how that goes.
We have already established that the Chibaku Tensei hole is 5,831.005 m in diameter. It measures 373 pixels compared to 227 for the full distance that FRS traveled in the 1 second time frame. In addition, we have a large boulder shot up into the air 70 pixels high, and as a triangular prism, it has measurements of 12, 5, and 6 pixels respectively.
Jugo attempted an ax-handle on Killer Bee, but he dodges and the result is a large crater in the stone platform.
The small pixel figure in the distance is impossible to recognize, but for the sake of being safe we’ll go with the low-end and say that it’s Karin. She’s 1.63 m tall. She measures 6 pixels here compared to the crater diameter at 64.
64 / 6 = 10.667 * 1.63 = 17.387 m, diameter of crater
Treating it as a half-sphere, the volume of destruction is 1,376.314 m^3
Since this is a crater and there are signs of vapor and debris, we’ll use cratering: 87 J/cc.
1,376.314 m^3 = 1,376,314,000 cm^3
1,376,314,000 * 87 = 119,739,318,000 J, or 28.618 Tons of TNT
Killer Bee Crashes Into a Platform
Killer Bee crashes into the stone platform and obliterates it along with a chunk of the hill.
Once again, we’re measuring Karin, who is 1.63 m tall. She’s 6 pixels here compared to platform diameter at 149 and depth at 26.
149 / 6 = 24.833 * 1.63 = 40.478 m, diameter of platform
26 / 6 = 4.333 * 1.63 = 7.063 m, depth of platform
Treating it as a cylinder, the volume would be 9,089.023 m^3
But there’s more to it than that. He also destroyed a chunk of the cliff.
Thickness of platform measures at 48 pixels compared to 173 for length of cliff destruction and 26 for height. I will also be assuming a third dimension: the width being equal to the platform’s radius. More than reasonable, based on the scan above.
173 / 48 = 3.604 * 7.063 = 25.455 m, length of cliff destruction
26 / 48 = .542 * 7.063 = 3.828 m, height of cliff destruction
40.478 / 2 = 20.239 m , width of cliff destruction
Treating the cliff destruction as a triangular prism, the volume would be 904.793 m^3
With the exploding rock and no signs of vaporization or pulverization, this seems to be a clear case of explosive fragmentation, so we’ll use 20 J/cc.
904.793 + 9,089.023 = 9,993.816 m^3
However, we must also account for Jugo’s crater.
9,993.816 – 1,376.314 = 8,617.502 m^3, true volume of fragmented rock
8,617.502 m^3 = 8,617,502,000 cm^3
8,617,502,000 * 20 = 172,350,040,000 J, or 41.193 Tons of TNT
8-Tails Bijuu Bomb
8-Tailed Bee unleashes a Bijuu Bomb which annihilates a large chunk of land and the hills nearby. For the record, everything about calculating this feat was a pain in the ass. The simple fact that we never get a good look at the environment before, combined with the head-scratching vapor behind 8-Tails after the blast… I decided to just scale the hills that he destroyed. I would have to make way too many assumptions as to whether he destroyed other land and to what extent. We don’t get a “before” pic to compare with the “after” so to speak.
Those little dots down there are Sasuke, Karin, and Jugo. I measured the smallest one at 3 pixels. I’ll assume that it’s Karin once more because she’s furthest to the right in the next scan. From tail to tail, Hachibi is 112 pixels wide. I did width here because his height in this scan is weird… it’s almost like he’s laying down.
112 / 3 = 37.333 * 1.63 = 60.853 m, width of Hachibi from tail-to-tail
This one’s a mess. I couldn’t scale the hill furthest to the right because it’s closer to our view than 8-Tails and would therefore be inflated. The rest, however, are either at the same depth or further off in the view, making this calculation low-end. Starting from the left…
152 / 63 = 2.413 * 60.853 = 146.838 m, height of hill 1
103 / 63 = 1.635 * 60.853 = 99.495 m, diameter of hill 1
Treating it as a dome, Hill 1 volume = 2,228,553 m^3
198 / 63 = 3.143 * 60.853 = 191.261 m, height of hill 2
156 / 63 = 2.476 * 60.853 = 150.672 m, diameter of hill 2
Hill 2 Volume = 5,368,451.7 m^3
68 / 63 = 1.079 * 60.853 = 65.66 m, height of hill 3
57 / 63 = .905 * 60.853 = 55.072 m, diameter of hill 3
Hill 3 Volume = 226,420.93 m^3
247 / 63 = 3.921 * 60.853 = 238.605 m, height of hill 4
207 / 63 = 3.286 * 60.853 = 199.963 m, diameter of hill 4
Hill 4 Volume = 10,859,357 m^3
166 / 63 = 2.635 * 60.853 = 160.348 m, height of hill 5
70 / 63 = 1.111 * 60.853 = 67.608 m, radius of hill 5
Hill 5 Volume = 3,309,961.35 m^3
184 / 63 = 2.921 * 60.853 = 177.752 m, height of hill 6
149 / 63 = 2.365 * 60.853 = 143.917 m, diameter of hill 6
Hill 6 Volume = 4,386,409.59 m^3
227 / 63 = 3.603 * 60.853 = 219.253 m, height of hill 7
187 / 63 = 2.968 * 60.853 = 180.612 m, diameter of hill 7
Hill 7 Volume = 8,327,337.09 m^3
117 / 63 = 1.857 * 60.853 = 113.004 m, height of hill 8
40 / 60 = .667 * 60.853 = 40.59 m, radius of hill 8
Hill 8 Volume = 1,048,029.45 m^3
Total Volume = 35,754,520.11 m^3
I see a lot of vapor and very little debris from this feat, so I’ll be going with vaporization on this one.
We’ll have to use latent heat and specific heat capacity to figure out the energy required.
Rock is 2,700 kg/m^3, so the total weight of vaporized rock is 96,537,204,297 kg. The vaporization point of rock is 2,470 C, and the temp change at standard temps would be 2,450 C. Specific heat of rock is 750 J/kg C.
463,378,580,625,600,000 + 177,387,112,895,737,500 = 640,765,693,521,337,500 J, or 153.15 Megatons
This is just to give an idea, as the actual number may be higher. It’s simply too difficult to tell how much environment, if at all, the bijuu bomb destroyed. There are also serious perspective issues if Hachibi did create craters in the lake, so I likely wouldn’t be able to get a good idea anyway. So think of this result more as a minimum.
RESULTS
Jugo’s Crater – 28.618 Tons of TNT
Killer Bee Destroys the Platform – 41.193 Tons of TNT
Sasuke unleashes Kirin, his ultimate technique which destroys the Uchiha hideout along with the mountain that it sits on.
Sasuke is 1.68 m tall here. He measures 8 pixels compared to the large stone wall at 295.
295 / 8 = 36.875 * 1.68 = 61.95 m, height of stone wall.
Well, here comes the fun part. Lots of scaling here. I’m going to go from top to bottom. The mountain is layered like a cake almost, making it pretty simple actually. I’m going to treat each layer as its own cylinder. Starting from the top (layer 1)…
20 / 18 = 1.111 * 61.95 = 68.765 m, height of layer 1
79 / 18 = 4.39 * 61.95 = 271.961 m, diameter of layer 1
Layer 1 volume = 3,994,575.072 m^3
26 / 18 = 1.444 * 61.95 = 89.456 m, height of layer 2
151 / 18 = 8.39 * 61.95 = 519.761 m, diameter of layer 2
Layer 2 volume = 18,980,460.061 m^3
20 / 18 = 1.111 * 61.95 = 68.765 m, height of layer 3
204 / 18 = 11.333 * 61.95 = 702.08 m, diameter of layer 3
Layer 3 volume = 26,621,377.984 m^3
31 / 18 = 1.722 * 61.95 = 106.678 m, height of layer 4
254 / 18 = 14.111 * 61.95 = 874.177 m, diameter of layer 4
Layer 4 volume = 64,027,050.804 m^3
52 / 18 = 2.89 * 61.95 = 179.036 m, height of layer 5
388 / 18 = 21.556 * 61.95 = 1,335.394 m, diameter of layer 5
Layer 5 volume = 250,754,704.018 m^3
60 / 18 = 3.333 * 61.95 = 206.479 m, height of layer 6
481 / 18 = 26.722 * 61.95 = 1,655.428 m, diameter of layer 6
Layer 6 volume = 444,412,599.191 m^3
41 / 18 = 2.278 * 61.95 = 141.122 m, height of layer 7
569 / 18 = 31.611 * 61.95 = 1,958.302 m, diameter of layer 7
Layer 7 volume = 425,053,835.085 m^3
Total volume of destroyed rock = 1,233,844,602.215 m^3
Although a heavily heated method was involved (lightning), there is actually a lot of debris after the attack. This seems like explosive fragmentation to me, so 20 J/cc.
1,233,844,602,215,000 * 20 = 24,676,892,044,300,000 J, or 5.9 Megatons
Itachi’s Susano’o Formation Speed
Itachi was able to form his Susano’o before Sasuke’s Kirin could reach him. We clearly see that Sasuke’s attack starts and Itachi hasn’t reacted yet in the panel where Kirin activates, so this is a legitimate speed feat that often gets overlooked. If Susano’o can form that fast, what’s to stop it from moving that fast, after all?
I figure Zetzu’s 1/1,000 of a second statement was meant to be a setup to the feat in question, so that can be our time frame.
Itachi is 1.78 m tall. He’s 39 pixels here compared to Susano’o ribcage at 103. You might notice I scaled from about midway down Itachi’s body, because we don’t know how exactly Susano’o forms in this case. Top to bottom? Bottom to top? Or perhaps from the middle of Itachi? That’s the lowest end, anyway, and when we don’t know something for sure, I tend to go in that direction.
103 / 39 = 2.641 * 1.78 = 4.701 m, distance formed
Deidara’s C2 makes a large explosion. Simple enough.
Deidara is 1.66 m tall. He measures 8 pixels here compared to diameter of the explosion at 530.
530 / 8 = 66.25 * 1.66 = 109.975 m, diameter of explosion.
Using Taylor’s Law, we can figure out the explosive yield.
E = 8*pi*p*R^5 / [75(y-1)t^2]
Where p is density of the air, t is time after explosion has formed, R is radius of the explosion. y is specific heat ration (Will be using 1.4 here as is common)
For time, I’ll be using the speed of the explosion. There are no shockwaves present despite the explosion size, so I’ll be treating it as a low grade explosive. The minimum detonation velocity of a low explosive is 171 m/s, but due to the great size of this blast, I’m going to bring it up to 300 m/s, as it still needs to be subsonic without the presence of a shockwave.
109.975 / 2 = 54.988 m, radius of explosion.
54.988 / 300 = .183 s, time frame.
8 * 3.14 * 1.2 * 54.988^5 / [75(1.4 – 1).183^2] = 15,084,018,865.821 J or 3.605 Tons of TNT
Deidara’s Air and Ground C2 Combo
By combining his air C2 bombs with some that Tobi planted underground, Deidara sets off an even larger explosion than before that Sasuke is unable to escape.
As a reminder, Deidara is 1.66 m tall. He is 8 pixels here compared to the dragon skull at 37.
37 / 8 = 4.625 * 1.66 = 7.678 m, length of dragon skull.
Dragon skull is 11 pixels compared to 624 for explosion diameter.
624 / 11 = 56.727 * 7.678 = 435.55 m, diameter of explosion.
Once again, the Taylor formula will give us an answer to the yield of this massive explosion. I’ll use 300 m/s for this one too, as there are still no shockwaves, but the explosion is huge.
435.55 / 2 = 217.775 m, radius of explosion.
217.775 / 300 = .726 s, time frame.
8 * 3.14 * 1.2 * 217.775^5 / [75(1.4 – 1).726^2] = 933,784,148,027.935 J or 223.18 Tons of TNT
Deidara’s C0 Explosion
Deidara blows himself up, causing a massive explosion in the hopes that it would kill Sasuke. He states that the explosion will cover a 10 Km radius. Interestingly enough, though, some scans would suggest that the blast was smaller by a fair margin. So for this particular feat, I’ll do a version going by his statement, then a version going by a scaling. Fair enough?
Going by Deidara’s statement of a 10 Km blast radius is thankfully simple. Using the sd.net nuke calculator, we find that a yield of 51 Megatons would be required for near total fatalities at 10 Km radius.
Karin is 1.63 m tall. She measures 34 pixels here compared to the street width at 199. Yep, that’s going to be my comparison. A lot of people seem to be fixated on the buildings, but I feel that is much less consistent. Road sizes can of course change too, but they appear similar in size in the faraway shots of the crater.
199 / 34 = 5.853 * 1.63 = 9.54 m, width of road.
Road width measures at 2 pixels compared to 382 for crater diameter.
382 / 2 = 191 * 9.54 = 1,822.14 m, diameter of crater.
Keep in mind that the roads would have to be over 100 meters wide in order for this crater to be Deidara’s 20 Km claim, so people do have a good point when they question his figure. Still, it’s difficult because it’s a manga statement vs. a visual. Hence, why I am leaving it up to you, dear reader.
This crater isn’t deep enough to be 1/2 a sphere, so this time I’ll be going with 1/3rd. In addition, it’s a sphere that’s cut off, so that will need to be taken into account as well.
The volume of 1/3rd of a cutoff sphere for that size is 77,803,997.654 m^3
Pretty much all nukes crater their destroyed rock. That is in fact, where I got the figure from (See Sedan Crater for more details). So 87 J/cc here.
77,803,997.654 m^3 = 77,803,997,654,000 cm^3
77,803,997,654,000 * 87 = 6,768,947,795,898,000 J, or 1.62 Megatons
Cable's Calculations 