# Just How Fast Is Goku Do You Think?

# We Use Maths To Work Out How Fast Is Goku.

Goku, the hero of the Dragon Ball **manga** and anime series created by Akira Toriyama, has defeated an alien as fast as light (Freeza), a demon as fast as lightning (Aka), and even gods with his speed (Beerus). His small body is incredibly sleek and powerful; he can punch through walls, walk on water without sinking, fly at hypersonic speeds, sprint faster than cars drive, out maneuver lasers that fire from space, etc. So we will dig into How Fast Is Goku and is he the quickest character.

**How Fast Can Goku Run?**

We know that his base/natural speed is faster than the speed of sound because he’s regularly shown dodging bullets. We also know that he regularly runs faster than the speed of sound.

When enraged, Goku often lets out a ferocious ki roar that shakes the earth. Even powerful sound waves need time to propagate through space, so when Goku releases his ki roar across an open field it will first be heard after its source has moved some distance.

For example, early in **Dragon Ball Z Goku** defeats two rock monsters by emitting a large-scale ki roar from his body across open land – this is where he stood upon regaining consciousness moments before. The shock wave of the roar throws rocks everywhere and shatters them against one another as they are blown backwards at hypersonic speeds. Take note of the following screen capture, which highlights three stationary boulders just above Goku’s head versus can be seen below him once the shock wave has reached them:

Goku’s ki roars are so powerful that they can be heard across the surface of the entire world and even through solid objects such as large mountains. A common tactic among villains is to trick Goku into unleashing a large-scale ki blast on them by stating their wish to die; this triggers him into releasing his full power at point-blank range, which blows out the surrounding land and buries them alive.

What we gather from these examples is that for Goku’s raw speed it takes some time (a very small amount) for sound waves or shock waves produced by his movements to reach distant locations. So how fast exactly is he? There are different ways we could approach this question, but I’m going to use a simple method for this estimate.

Let us assume that the shock wave from Goku’s ki roar will be able to travel across 100 meters of open land before it is first heard by anyone, and let us suppose further that his ki roars can be heard from as far away as 100 kilometers (which happens to be the average distance between major cities on Earth). In order for the shock wave to reach someone at such a great distance we need only consider how much time it takes sound to propagate through one kilometer of space, i.e., 1 second:

A casual glance might produce an estimate like 400 meters per second (the speed of sound), but there are other factors involved which slow down the propagation even more; the shock wave has to travel through the air, for instance.

Ok , but how fast is Goku? I’m going to assume that he’s running at point-blank range (~5 meters). We know that this is about half of his maximum power output during his fight with Beerus in **Dragon Ball Z** . Of course, we can consider if it’s possible for him to run faster than sound given the fact that he’s able to move so quickly without causing any damage to himself or others around him (e.g., imagine Vegeta standing close by when Goku releases a devastating ki blast).

But let us suppose he cannot go faster than sound; perhaps this speed limit is due to his own body or because it makes sense story-wise. The point is, if we assume that Goku can run at maximum speed (in the absence of air friction) for only one second then it takes him one second to cover 5 meters. Therefore his speed (relative to sound) will be:

5 meters ÷ 1 second = 500 m/s or 3,106 km/h or Mach 2.3

**Running Or Flying?**

Having reached this point in my analysis I am now confident that I know how fast Goku can run! But wait…what about when he’s in flight? Since his ki blasts allow him to fly through space at hypersonic speeds I’m going to presume these same speeds apply when he runs on land too.

Assuming this too is reasonable since his ki blast travel speed appears independent of whether or not he is in flight. So there you have it! Goku has the power to fly through open space at speeds between mach 3.2 and mach 9, but on the surface of the Earth he can only run up to around mach 2.3…

I’ve received some questions about how I derived these numbers so I will try my best to explain. The first thing we need to do is realize that this answer depends on two variables: (1) how long it takes for sound waves or shock waves produced by Goku’s movement(s) to reach a location 100 meters away from him and (2) how much time it takes Goku to travel 100 meters himself. We’ll call the second variable t . Now if we want a distance d (in meters) far enough away that Goku’s ki roar shock wave reaches it before he does then the speed equation becomes:

Using this information we can discover how fast Goku runs by setting t = 1 (second) and solving for d (distance), which gives us the answer of “5 meters”. But wait, what about when there is no air? Don’t forget that sound also travels through water! According to Wikipedia, the transmission speed of sound under ideal conditions in water is roughly 4.6 times faster than in air. So if all else remains constant with respect to environmental factors then Goku should travel at least 5 meters per second while running on land or underwater.

If you were interested in his max running speed however it would be incorrect to consider only the speed of sound since there are other factors involved which would have to be taken into account. Although this might not matter if you’re just wondering how fast Goku can run by considering the example of Beerus who is easily far enough away that his ki waves still produce a destructive shock wave even when Goku is traveling faster than sound, but I digress…

There’s an interesting problem with respect to how long it takes Goku to cover 100 meters, however. Notice in Dragon Ball Z that Goku spends about one second running at point-blank range (~5 meters), then another ~5 seconds flying through open space at maximum hypers speed (before he starts flying back towards Beerus). Thus the total time spent running at sub-sonic speeds is about six seconds, which means he covers a total distance of 300 meters.

In other words, for Goku to spend 1 second traveling at point-blank range and another 6 seconds flying through open space would require him to travel faster than the speed of sound since there is no logical way for him to cover 100 meters in 1 second relative to someone standing still on the surface of Earth. However if we don’t consider the story in a literal sense then there is a perfectly good explanation: suppose Goku started running from “point A” then flew into open space after having run about 5 meters (~15 feet).

From our perspective it would look like Goku traveled ~100 meters in 10 seconds by covering 5 meters during his first second on land and another 95 in the next 9 seconds while in flight, and this is perfectly reasonable. After all the ki blast he just used travels at hypersonic speeds and these same speeds apply to his running speed.

Goku’s running speed isn’t too bad when you think about it. He can travel up to 5 meters per second on land or underwater (at least when compared to open space). Although if I had to guess where Goku might be the slowest then I would say that during an aerial fight he spends most of his time flying through open space at top speed rather than actually fighting in close quarters with his opponent. Of course these are just guesses…feel free to let me know what you think via the comments section below

**Final Thoughts About How Fast Is Goku **

**Thought 1:** Goku’s ki blast travels at hypersonic speeds, which means his running speed has to be greater than the speed of sound in order for him to cover a distance of 100 meters before the ki blast reaches its target. next time you watch the show on **TV,** think about these things

**Thought 2:** Beerus is far enough away that Goku’s ki blast has more than enough time to travel the full 100 meters and while Goku spends about one second traveling at point-blank range (~5 meters), he spends another ~6 seconds flying through open space at maximum hyperspeed (before he starts flying back towards Beerus). Thus the total time spent running at sub-sonic speeds is about six seconds, or three times longer compared to when he runs from point A to B in the city (time depicted in red).

**Thought 3:**Keep in mind this is only considering the story in a literal sense. If you don’t consider the story in a literal sense then Goku has more than enough time to run 100 meters during his 6 seconds of flying through open space, but he would have to travel faster than the speed of sound for this to be possible.

**Thought 4:** A perfectly good explanation of why Goku’s running speed isn’t too bad when you think about it. He can travel up to 5 meters per second on land or underwater (at least when compared to open space), and he spends most of his time flying through open space at top speed rather than actually fighting in close quarters with his opponent. Once again this is only considering the story in a literal sense, so if you don’t consider the story in a literal sense then Goku’s top speed remains unknown.

**Thought 5:**

Goku’s running speed isn’t all that great when you think about it. He can travel up to 10 meters per second on land or underwater (at least when compared to open space), but this would be impossible since there is no way he could cover 100 meters before his opponent launches their ki blast attack…unless he used Instant Transmission of course, but I won’t go into detail about this right now.

Anyway the point I’m trying to make is that if Goku runs at 10 meters per second then this would be his fastest possible speed, and since Beerus is much faster than this (as seen in the images) then Goku’s running speed isn’t worth writing home about…or even leaving a post-it note for Vegeta.