After-Thoughts: How Strong is Super Perfect Cell?

Have you ever gotten into an argument with someone? Not just any old argument where the opposing side takes issue with everything you say just because they don't like you, I mean more along the lines of "Everything you said is reasonable but one particular thing you said doesn't add up with my beliefs," or something to that effect? If you have, then you've probably run into the Dragon Ball fanbase.

The Dragon Ball fanbase, by and large, has the greatest group of people who like to say things with nothing really supporting it, or nothing substantial anyway. Many of them tend to be emotional even if only on specific topics and have a tendency to not understand where the criticism is coming from. You do get this a lot with teenagers, which is a large portion of Dragon Ball's fanbase but with dragon ball, you do get it from people who should be much more mature than that.

I've talked about Seth the Programmer before, about how he tends to misunderstand the criticism he receives and how he likes to paint people who don't want to talk to him as cowards who won't defend what they say. He has fairly recently begun to recognize that he may be part of the problem at least, and while he may not understand why as of yet, the fact that he recognizes that much is an important first step.

Then you have Just A Robot, or JAR for short who did a series of comparison videos of Goku vs Superman all versions and in the 3rd part, he went on a tangent where he complained that anti-powerscalers don't think that Super Perfect Cell is capable of destroying a solar system. Now, in this he states all of the evidence he has for it, which I never really found convincing because the series itself never actually supports any of the evidence he suggests. He then ends it by saying that for this none of it matters because Super Perfect Cell wasn't actually the Cell that Goku fought against.

I then left a comment expressing my disagreement, agreement, or elaboration on certain things and my annoyance toward JAR not just for straw-manning the incorrect demographic (in reality, anti-power-scalers don't make that argument, power-scalers with different pieces of evidence make that argument) but also for picking an unnecessary fight in the first place.

I ended up telling him that he never actually addressed any of the arguments I would make and he never responded. In fact, someone else responded with a bunch of out of nowhere claims and while his claims were mostly unfounded, it did get me thinking, how powerful are these characters?

That was an incredibly huge amount of setup for what is basically going to be a physics class but I promise my findings are interesting.

Okay the main argument that drew my attention was Super Perfect Cell is capable of destroying a solar system because "If we use power scaling" we can see he can do it because he's many times stronger than Frieza who is many times stronger than Saiyan Saga Vegeta who was capable of destroying a planet.

Now my immediate reaction was "Okay, but that proves nothing. Without concrete numbers that's not sufficient to argue that Cell is telling the truth here." However, his thought process was the kind of thing I can verify with my own findings so I decided to run through it.

So before we begin, I want to discuss the method by which Super Perfect Cell would be destroying the Solar System. Firstly, I want to disregard any notion that Cell's power is enough to destroy "Mass equivalent to the whole solar system" because if that were the case, he wouldn't have said Solar System, he would've said White Dwarf Star which, although very dense, has about the same mass as our Solar system, so just destroying an equivalent amount of mass isn't the problem.

Immediately the first problem I have with this is the area of the Solar Kamehameha. Being a beam, it doesn't seem to be capable of destroying a whole solar system due to lacking area of effect. This is something that commentor actually got wrong, he said the Solar Kamehameha didn't destroy Earth by being near it because of Area of Effect keeping all of the energy within a certain point. However, Area of Effect in terms of demolition is simply the range of a blast radius upon explosion that grades out until it stops affecting anything. Once that happens, everything within that area is the area of effect. That's why it's called area of effect.

Anyway, given the sheer distance and space between each of the planets and the sun, this likely means that the Kamehameha isn't what's destroying the Solar system. So, what is? Well, one of the video games, which JAR referenced, suggests that the beam is coming in contact with the sun and the explosion of the sun is what's destroying the rest of the solar system, by sheer blast wave.

If this is the case, then this actually lowers the necessary power threshold because it changes the game from wiping out the whole thing with just your attack to transmitting your attack through a medium that then does the rest. With that in mind, Cell doesn't need the power to destroy a whole solar system, just around double the amount of energy it would take to destroy the Sun.

Okay, so now we have a threshold for how we're going to be calculating this. So now we need a baseline level of energy to work with and, fortunately, since we're just proving or disproving this person's methodology, we can just use the difference between Vegeta -> Frieza -> Cell.

So there are several ways we can do this but I think the easiest one is to just substitute Vegeta's power level into the amount of energy needed to destroy Earth. Given that no character weaker than him has that amount of power we can just use him as a baseline.

So here's how we're setting this up:

Vegeta's power level = 18,000 = uOfEarth

uOfEarth being the gravitational binding energy of Earth.

So to calculate the gravitational binding energy we need a few numbers. The formula is as follows:

u = 3GM^2

           5r

with G being the universal gravitational constant, M being the mass of the body, and r being the body's radius. So let's figure out all those numbers:

G = 6.6741 x 10^-11 Nm^2/kg^2

M = 5.9736 x 10^24 kg

r = 6.371 x 10^6 m

So plugging those numbers into the equation we get something like this:

u = 3(6.6741 x 10^-11 Nm^2/kg^2)(5.9736 x 10^24 kg)^2

           5(6.371 x 10^6 m)

So first I'm going to remove all of the units mathematically to get our final unit.

(Nm^2/kg^2)*(kg)^2

           m

So kg^2/kg^2 is gonna convert both units to the number 1, so they won't factor into the equation anymore.

(Nm^2)/m

m^2/m = m

So what we have left is a N*m, which is a very rudimentary way of saying Joules, which is a unit of energy.

So now we just go through the remaining numbers and our final number will be:

uOfEarth = 2.25 x 10^32 J

Okay, so what now? Well, we're still using straight power levels so we're going to take the dividend of Frieza's maximum power level with Vegeta's. Here it's going to get a little tricky because although Frieza's power level is recorded as 120 million in the Frieza arc, in the Trunks Saga it goes up somewhat. Frieza's power level at the time he fought Trunks was stated to be equal to Goku's on Namek with a level of 150 million but in the manga that was stated to be half of Mecha Frieza's max power. So we're going to translate this as 300 million for simplicity.

So here we go:

300 x 10^6/18 x 10^3 = Frieza

Simplifying that a little bit, we can remove x 10^3 on Vegeta and minus 3 from the exponent of Frieza, giving us:

300 x 10^3/18 = Frieza = Vegeta * 16666.67

The decimal is a repeating number so I just rounded up at the hundredths place for ease of calculation. It won't make much of a difference.

From here it gets a little complicated because power levels stop being used here. But we can get an estimation from Seth the Programmer, who states that the Super Saiyan form Goku fights Cell in is 500 times the base form. Given that Goku's power level against Frieza was in Super Saiyan, this means that he's roughly 10 times that. Super Saiyan 2, which Gohan had against Cell, doubles that. Meaning:

Cell = 20 * Frieza = 16666.67 * Vegeta

Simplifying further, this means Cell is 333333.32 * uOfEarth.

So now we take our former number and multiply it.

2.25 x 10^32 J * 333333.32 = 7.5 x 10^39 J of energy.

So as I said earlier, for Cell to accomplish this, he needs double the energy to destroy the Sun. But we actually haven't figured out what that means yet. So let's take our former formula and define our variables.

u = 3GM^2

           5r

G = 6.6741 x 10^-11 Nm^2/kg^2

M = 1.989 x 10^30 kg

r = 6.99 x 10^8 m

u = 3(6.6741 x 10^-11 Nm^2/kg^2)(1.989 x 10^30 kg)^2

           5(6.99 x 10^8 m)

Giving us our final number of 2.3 x 10^41 j. So with that in mind, let's do a quick comparison.

We're going to divide Cell's destructive power by the Gravitational binding energy of the Sun. If we do that, it'll come out as a percentage of necessary power. For this to work, the final number needs to be 2 or greater.

So from here we do this:

7.5 x 10^39 J/2.3 x 10^41 j = .0326

Which makes Super Perfect Cell's destructive energy a total of around 3.26% of the necessary energy to destroy the Sun.

Keep in mind there are other metrics to figure out Cell's destructive energy that might grant more leeway to the Perfect bug monster. Starting at Master Roshi's full power being capable of destroying the moon might give Cell a greater calculative buff due to the greater difference in Full Power Roshi's compared to Saiyan Saga Vegeta. You could also argue that feats are what matters and power levels don't. But 3 things. 1) Using Roshi wouldn't have changed the numbers too drastically because Cell needed to be at minimum 61 times stronger than this suggests he is, 2) if only feats matter, which I agree with, then nothing in the canon suggests Cell would be capable of it anyway, and 3) this wasn't necessarily about proving or disproving whether or not Cell can destroy a Solar System, just proving or disproving one particular person's methodology by following it through to its logical conclusion. And, using this guy's methodology, with the character examples he used, and substituting power levels for hard numbers and equations we can see that his methodology supports my thesis, not his.

Just wanted to tackle something a little different because I really love running numbers and doing math so I decided to use it to tackle another thing I like, which is proving somebody else right or wrong. If you have a different way to tackle it, feel free to let me know.

Have a wonderful day.