How Many Peanut Butter Sandwiches Does It Take to Fuel a Hulk?

Superheroes do superhero things: They jump, punch stuff, run fast, and sometimes shoot beams out of their eyes. These activities require energy, just like normal human activities. When you get up in the morning, that takes energy. Walking around takes energy. Running a mile requires even more energy—but not nearly as much as it would take to fly a human-powered helicopter for one minute. (Yes, that’s real.) All of that energy comes from food. If superheroes also get their energy from food, just how much would they need to eat to pull off their high-energy moves?

In honor of the new Disney+ series that started August 17, I'm going to focus on moves by the Hulk and She-Hulk. I think we can assume that the two of them get their energy from food. A recent clip from the series shows the Hulk (Bruce Banner) telling She-Hulk (Jennifer Walters) that they can drink as much alcohol as they want, since hulks have such a high metabolism. That implies their energy comes from eating and not some strange mechanism or source, like an extra dimension.

We measure the energy in food in terms of calories. For example, the wrapper on a single candy bar may say a serving has 200 calories. (Here are some examples with exact values.)

But there’s a difference between the way nutritionists talk about calories and the way physicists do. To physicists, a calorie is the amount of energy that you would need to raise the temperature of 1 gram of water by 1 degree Celsius. But that's not the same as a food calorie. Food labels actually list things in terms of kilocalories, which means the 200-calorie candy bar is really 200 times 1,000 calories, or 200,000 calories.

That’s confusing. And to be honest, we physicists don't really like to use either of these units for energy. Instead, we often use joules, where 1 joule is equal to the energy needed to push with a force of 1 newton over a distance of 1 meter. Lifting a textbook off the floor and putting it on a table takes about 10 joules of energy. One food calorie is equal to about 4,184 joules.

But for this demonstration, I think it’s best if we make up our own unit of energy. Let's call it the PBJ—the peanut-butter-and-jelly-sandwich unit of energy. This is the amount of energy you get from eating one of these sandwiches, which is around 380 food calories or 1.59 million joules. With this PBJ unit, I can calculate the energy cost of superhero moves in terms of sandwiches. I just think that will be fun.

Simply staying alive requires energy: to breathe, pump blood, and even blink your eyes. The amount of energy it takes is called the basal metabolic rate, or BMR. A typical mortal human could have a BMR of around 1,500 to 2,000 food calories a day. Converting to my preferred energy unit, a person uses about 4 to 5 PBJs a day. (Your mileage may vary.)

A BMR value depends on a person’s age, weight, and height—but the Hulk and She-Hulk aren't normal-sized humans, so they won't have normal BMRs. Let’s figure out their weights and heights.

I'm going to start with the Hulk, since I've actually looked at his dimensions before. From my analysis of his appearances in the Marvel Cinematic Universe, he is about 2.5 meters tall. Finding his mass is a bit more complicated since you can't directly see this value, like you can with his height. However, if I assume the Hulk has the same density as a normal human, around 1,000 kilograms per cubic meter (similar to water), then I can estimate his volume to get the mass.

The problem is that volume calculations for bodies aren't trivial. Here's a way to roughly estimate the Hulk's volume: Suppose that we take a normal human in the shape of a cylinder with some length (L) and radius (r). With that, I can easily calculate the volume (V).

If you increase the height of a body (the length of the cylinder), but keep the shape the same, then there will be a relationship between L and r such that r = a × L where a is just a constant. This means that I can write the volume as the following:

I can use this volume equation along with the height, mass, and density of a normal human to find this length-to-radius ratio (a) with a value of about 0.06. Just to be clear, that's the length-to-radius ratio for a normal human.

What about an extreme example? If you double the height of a human, but keep the shape (a) the same, then you will increase the volume by a factor of 8 (since 2³ = 8). So bigger people will be much more massive.

Now let’s try calculating the mass of the Hulk. He isn't just taller than a human, he's also bulkier. This means he would have a larger length-to-radius ratio (a). Let me just roughly approximate this value at 1.5 times that of a normal human. With his height of 2.5 meters and the same density as a human, this would put his mass at 313 kilograms (690 pounds).

Now we are ready for a BMR calculation. Fortunately, there are some online calculators that I can use. This puts the Hulk's daily resting energy consumption at 4,491 food calories or 11.8 PBJs. That's not too bad.

She-Hulk is also very tall, but she seems to be in the same shape as a normal-sized human. There's a nice shot of She-Hulk standing next to the Hulk, and using that to measure her height gives a value of 2.2 meters. That puts her mass at 136 kilograms (300 pounds). Using the same calculator gives a BMR of 6.8 PBJs (2,586 food calories).

Remember, these figures are just for basal metabolic rates—normal superhuman living—and not the energy needed for them to do any activities.

In this clip from the series, we see the Hulk pushing She-Hulk off a cliff. (Don't worry, she's fine. She jumps back up to the ground with relative ease.) How many peanut butter and jelly sandwiches would this move take?

In any kind of jump, the person will both start and finish the move with zero speed and with an increase in height of some value (Δy). In that case, there is only one type of energy change to consider—the change in gravitational potential energy. This is a type of stored energy due to a gravitational interaction between a mass (or person) and the Earth. We can calculate this change in energy as:

In this expression, g is the value of the gravitational field. On Earth, this has a value of 9.8 newtons per kilogram. Since I already have the mass of She-Hulk, I just need to estimate her change in vertical position as she jumps up from the bottom of the cliff. Really, this could be any value, because it depends on how tall the cliff is, but this one is by the ocean, and I'm imagining it's not too high. Maybe 10 meters or so. This would be an energy requirement of 20,089 joules or 0.013 PBJ. That's just a small bite of a peanut butter and jelly sandwich. But it's also just one jump.

The trailer for the series also shows the Hulk and She-Hulk tossing very large boulders. How much energy would this move take?

Honestly, this is very similar to the calculation for jumping—but with two differences. First, instead of using the mass of She-Hulk for the change in gravitational potential energy, we need to use the mass of the boulder. The second difference is that the rock doesn't just go up vertically. It also has some horizontal velocity. So, even at the highest point in the rock's trajectory, it will have both gravitational potential energy as well as kinetic energy.

Kinetic energy is the energy associated with the motion of an object. We can calculate this with the following equation:

In order to calculate the energy in this boulder toss, I need three things: the mass of the rock, the maximum height during the throw, and the horizontal velocity. Let's start with the mass.

Looking at the size of the rock next to the Hulk, I'm going to say that it's roughly spherical with a diameter of 1 meter. Assuming a spherical shape, I can calculate the volume (V = 4/3 × πr³, where r is the radius). Then using a rock density of 2,600 kilograms per cubic meter, I get a total mass of 1,361 kilograms.

Next, let's go with the maximum rock height. Honestly, I'm just roughly estimating this value from the scene in the trailer, and I think 6 meters seems fine. Finally, for the horizontal velocity, I can just estimate how far the rock traveled horizontally (which is maybe 30 meters) and the time (about 1.2 seconds from the video). This gives a horizontal velocity of 25 meters per second.

With these values, the change in gravitational potential energy for the giant rock is 80,000 joules and the kinetic energy would be 425,000 joules. This puts the total rock-throwing energy at 505,000 joules or 0.32 PBJs. That's at least a couple of bites of a sandwich to throw that rock.

You could argue that in this scene, the Hulk and She-Hulk aren't actually throwing rocks, they are just tossing them. In this other clip, we see the Hulk showing how to really throw a rock. He grabs a bigger one with a radius of about 2 meters and throws it so fast that it starts to heat up the air around it, like you would see with a meteor entering the atmosphere. Generally, you don't see significant thermal effects for objects unless they are going faster than the speed of sound, which is about 343 meters per second. Using the same calculations for the kinetic energy of the rock, it appears that the Hulk would need to eat 1,612 peanut butter and jelly sandwiches for just this one rock-throwing move.

One of the Hulk's signature moves is clapping his hands. This isn't a normal clap that you might use to signal your approval when your favorite sports team scores, or a gentle clap showing that you are following the social norms of clapping when appropriate at a performance, even though you don't want to. No, this is a giant thunderous clap that's basically a type of explosion. It's such a powerful clap that it sends a burst of air—or something, I'm not sure of the exact physics—to knock over an enemy. So, when the Hulk teaches this move to She-Hulk, how much energy would it take?

While they are training, we see She-Hulk use the super clap and knock the Hulk backwards quite a bit. We have to make a choice about the super clap: Does it make a directed beam of moving air that only affects the object right in its path? Or is it a clap that disperses energy throughout a wider area, affecting whatever is nearby? I'm going with the second option. It will be more fun.

Suppose this super clap creates an energy blast that spreads outward in a half-circle pattern. That means anything within a 180-degree field of view from She-Hulk will get blasted. However, as this blast wave expands outward, it also gets larger. If the total amount of energy is constant, then this energy will be spread out over a larger and larger region.

Let's call this energy distribution the intensity (I) in units of joules per meter, such that it would have the following value as a function of distance (r) from She-Hulk.

Here, E₀ is the total blast energy produced by She-Hulk in the clap and πr is the length of half of a circle. Remember, we really want to get the value of E₀ so I can estimate how many sandwiches she needs to eat for this move.

We can find that value by looking at how the Hulk gets thrown back. When he gets hit with the blast, it looks like he moves back about 4 meters in a time of 0.5 seconds. This would give him a recoil speed of 8 meters per second. Since I know the mass of the Hulk (313 kg), I also know his change in kinetic energy, which is about 10,000 joules.

But the Hulk doesn't get all the energy from the super clap. Instead, he only gets a fraction. The ratio of the energy the Hulk gets (let's call it E_H) to the total clap energy (E₀) will be the same as the ratio of the width of the Hulk (w_H) to the total length of the clap wave. But the length of the clap wave depends on how far it is from She-Hulk. Let's call that r_s.

That gives the following relationship:

If I just estimate values for r_s and w_H, I can calculate the total energy of the super clap. I'm going to say that She-Hulk was 4 meters from the Hulk (so r_s = 4 m) and the Hulk is 0.75 meters wide. (I got that from a video measurement.) Putting all of this into my calculation gives a total super clap energy of 168,000 joules or 0.1 PBJs. That seems small, but remember, that's still a lot of energy for just one move that only takes a second.

Now let's get a rough estimate of how many PBJ sandwiches She-Hulk would need to consume each day. Of course, just staying alive to maintain her BMR means she needs to eat 6.8 PBJs. It would probably be closer to 14 PBJs if you include walking around, going up stairs, and other trivial stuff like talking. But what if she gets in a fight requiring super moves? She’s obviously going to need to eat more.

Let's say that in a fight she throws three rocks, jumps five times, and uses two super claps. For the thrown rocks, I am going to assume that she can really throw them, sort of like the Hulk did in his hypersonic example. However, since she's still just learning, let's say these rocks are 1 meter in diameter and just going at half the speed of sound. That would put her total energy usage for the whole day at 83 million joules, or 52.2 peanut butter and jelly sandwiches. That's not so much food that she’d have to constantly be at the grocery store, but 52 PBJs a day would get boring.

What if she wanted to mix it up? She could get the same energy, in joules, by eating 198 bananas. Or maybe she likes carrots? That would be 794 carrots. How about Krispy Kreme plain glazed donuts? Just over 104. Slices of Domino’s cheese pizza? About 87. Or just over 24 sticks of butter. Or 1,323 cups of celery. (Note: I do not recommend eating any of this stuff all in one day.)

You can see the script I used for my calculations here, just in case you want to check.