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Collage featuring crying Pikachu, Sarah Michelle Gellar as Buffy and Chris Pratt as Star Lord with mathematical formulas Source images: Alamy, Marvel Studios/Disney and The Pokémon Company | Illustration: James Bareham/Polygon

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Using the power of math to calculate the actual ‘power of friendship’

We break down one of the most mystical energies in the universe

Stop us if you’ve heard this one before: Despite the odds, a ragtag [group of adventurers/gang of misfits/hockey team] overcomes a [superior opponent/powerful force/life or death scenario] by relying on each other through the power of friendship. Aside from the hero’s journey, it’s one of the most common tropes in any adventure story, be it in video games, movies or books. The power of friendship has saved the world many times over, from defeating rampaging alien warlords to powering the mechs that keep the planet safe from giant monsters.

But as a new specter looms over the Earth, is the power of friendship enough to save us?

Our pop culture preaches the “power of friendship,” but in these dire times, it’s important to understand what the phrase actually means. In physics, power has a specific definition: work over time, or more usefully, the rate at which energy can be transferred over a specific duration. As we face a global crisis due to our energy dependency, can we draw on this power in a real way to ensure the survival of humanity? Perhaps by understanding the true power of friendship in pop culture, we can, as a global society, learn how to effectively wield that power to solve real, global problems. And to achieve that understanding, we need math.

Let’s start with a tearjerker example: In the pivotal ending scene of Pokémon: The First Movie, Mewtwo’s psychic blast encases Ash in what appears to be a statue of steel, a metal with the melting point of 1,370 degrees Celsius. Assuming Ash is around the average 10-year-old’s volume of 32 liters, we can calculate the mass of the steel Ash statue at 253 kg (using this equation: volume = mass divided by density). If we assume an ambient temperature of 20 C, with the specific heat of steel being 0.49 kJ/kg, we can calculate the energy change with the equation Q = mcΔT (mass times specific heat times change in temperature), which gets us an energy of 167,359.5 kilojoules being transferred to Ash.

To find the power of friendship — i.e., the power of Pikachu’s tears to de-steel Ash — we have to get the power unit of the kilowatt (kJ/s) by dividing this energy figure by the amount of time during which the work happens. According to the scene, it takes 96 seconds from when Pikachu starts crying for Ash to be revived, which gets us a final power of friendship of 1,743 kilowatts for Pokémon tears. This is more than enough to satisfy the power needs of a single U.S. resident for an entire year, at 12,994 kWh/person/year (per World Bank Group).

pikachu and ash statue in pokemon the first movie Toho

Admittedly, the power of friendship contained in Pokémon tears may not be the definitive representation of the overall power of friendship that exists in the universe at large. Plus, there are tons of legal and ethical restrictions that would get in the way of constructing the Pokémon misery centers necessary for powering the world with tears. Luckily, in order to come up with a true, universal constant to represent the Power of Friendship (or pF), we have another illustration of the power of friendship in the Pokéverse: Pikachu’s move Return.

This move gains power through the bond between the Pokémon and the trainer, and maxes out at an attack power rating of 102. And though that number doesn’t have meaning on its own, we can use it in combination with another move in order to convert that attack rating into something more manageable. You see, Pikachu has an exclusive Z-move in the new games entitled 10,000,000 Volt Thunderbolt. This move has an attack rating of 195. From that, we can calculate the voltage of friendship using some simple ratio math to solve for x:

195 attack / 10,000,000 volts = 102 attack / x volts

10,000,000 * 102 = 195x

x = 5230769.23077

This means that the move Return generates roughly 5.2 million volts. To convert that into wattage, we’ll need to calculate the current as well, defined as the rate at which electricity flows through a substance. Since electricity literally flows through their veins, let’s assume a Pikachu is as conductive as an industrial 1,000 KCMIL industrial wire, with a maximum current load of 615 amps. Because power equals voltage times current, we can accurately calculate the power load of the move Return at a staggering 3,216,923,077 watts, or 3.2169 gigawatts — more than twice as powerful as Doc Brown’s time-traveling DeLorean, and just slightly less powerful than Plant Bowen, the United States’ largest coal plant (at around 3.5 GW). This is enough to power about 1.75 million homes for an entire year using the strength of just one Pokémon move. Really puts those power plants in the Pokeverse into context, huh?

With two data points — one from a relatively distilled version of the power of friendship in the form of Pokémon tears, and one that represents the power of friendship in its strongest form — we can confidently say that for Pokémon, the literal Power of Friendship can vary greatly, from 1,743 kW to a maximum power output of 3.2169 GW. But Pokémon are fantastical magical creatures — what of the power of friendship among us humans? What kind of power output can we expect if we were to channel all of our positivity toward a common goal?

Gamora, Peter Quill, Drax, and Rocket hold the Power Stone Marvel Studios

One possible test case here can be found in the final scene of Guardians of the Galaxy, in which Peter Quill is able to use the power of friendship to keep himself from being disintegrated by the Power Stone. Now, we know that the Power Stone is able to react with and destroy anything organic — up to and including entire planets — so we should be able to calculate the pF of this heroic moment by comparing the failure point of a human body to the failure point of the Earth, and doing some subtraction.

First, to destroy Earth, the Power Stone would need to be able to overcome Earth’s gravitational binding energy, the force that keeps the planet together. It turns out that approximately 2.4x10^32 joules would be sufficient to destroy Earth completely. Research on the failure point of humans has given us both the amount of energy it would take to completely vaporize a human being (142 million joules) and a more helpful formula for the amount of energy needed to kill a human using radiation (100 joules per kilogram of mass). Since Quill survives the scene, that’s what we’re going to use.

Assuming a weight of 185 pounds (84 kg), we can calculate that it’d take 8,400 joules to kill Quill. Now, since that didn’t happen in the scene, we must begin by subtracting 8,400 from 2.4x10^32 in order to give us the minimum amount of energy that the power of friendship must expend to push back against the power of the stone and keep Quill alive. This gives us an energy of 2,399,999,999,999,999,999,999,999,999,992,600 joules, which is functionally equivalent to 2.4x10^32, which in turn means I just did all that math and research for nothing.

Now that we have that joule rating, we simply need to divide that by time in order to get our rating in watts. According to the movie, barring any odd bullet-time shenanigans, Peter Quill is in direct contact with the stone for 135 seconds. This gives us a final rating of 1.78x10^30 watts, a number so large that scientists don’t even have a prefix like mega-, tera-, or giga- for it. This is 500 times more power than our freaking sun generates.

If we were somehow able to harness this power, utopian civilizations would not only be possible, but incredibly easy to build. But as we learn in Guardians of the Galaxy Vol. 2, Peter Quill is literally part-god, so perhaps this fact has skewed our numbers a little bit. Let’s try a different tack.

buffy season 4 primeval adam’s uranium core Warner Bros. Television

In the climactic final battle of season 4 of Buffy the Vampire Slayer, Xander, Willow, and Giles cast a spell that, in effect, lets them all band together to supercharge Buffy using the power of their shared bond with the heroine. They use this power to handily defeat Adam, a demonic cyborg humanoid that is powered by a rod of radioactive uranium. In the big scene, the supercharged Buffy overpowers Adam physically in a variety of ways, from subduing him through grapples in a direct contest of strength, to simply punching and kicking him in his stupid face a whole bunch, to finally killing Adam by ripping out his radioactive core. It follows, then, that the power of friendship bestowed unto Buffy is at the very least greater than Adam’s maximum power output. Therefore, if we can calculate Adam’s power, we’ll get a minimum power level for our pF to go along with our maximum god-mode pF of 1.78x10^30 watts.

Unfortunately, we only really have one image of the core, so we’ll have to use that to estimate its mass and work from there. Given the positioning of everything else in the scene, the core appears to be a cylinder, with length of about 15 cm and a radius of 2 cm. Since uranium’s density is 19.1 grams per cubic centimeter, we can calculate the mass of the cylinder pretty easily: 3.6 kg. According to the European Nuclear Society, 1 kg of the most common uranium isotope used in nuclear power, uranium-235, can produce 24 gigawatts (or 2.4x10^10 watts) of power. Therefore, the final pF shared between the Scooby Gang, the Group pF (or GpF), can be measured as >8.64x10^10 watts (or 86.4 gigawatts). That’s almost four times the power output of the Three Gorges Dam, the world’s largest hydroelectric power plant, and enough to power 43.2 million homes for a year.

This gives us a range of GpF figures for groups of four friends, from 8.64x10^10 at the lower end to 1.78x10^30 at the top, and an average GpF of 5.26*10^20 — which can, of course, scale up or down based on the size of the group.

Now that we have an idea of the sheer strength of the power of friendship, the only thing left to do is to — as is our duty as members of society — create a company that harvests the power of friendship and sells it to folks at a premium. Fortunately, we already know the market rate for friendship, thanks to The Goonies.

seven young people looking upward with rays of sunlight filtering down toward them Amblin Entertainment/Warner Bros. Pictures

Of course, the real treasure in The Goonies was the friends they made along the way, so if we estimate the value of One-Eyed Willy’s treasure, we can set a fair price. Since the hoard is mostly made up of gold coins, we can piggyback on other research and assume that Willy’s hoard is roughly equivalent to Black Bart’s treasure of 40,000 Portuguese gold pieces, valued at $10,512,000. And again, since the message of the movie is that the real treasure was the friends we made along the way, we can assume that the value of friendship exceeds that number.

So what have we learned? How can we save the world with this information? Must we wait until Elon Musk creates a global array of siphons that can conduct and redirect friendship energy before we can truly harness this awesome, inexhaustible power that we all share?

The answer is no. Now that we all understand just how powerful friendship is, it’s our job to stockpile as much of it as we can. That way, when the global economy changes and everything is powered by that sweet, sweet friendship juice, we will be in control of, by far, the world’s most valuable resource — instead of ruthless CEOs, warmongers, and oil tycoons. So buy your roommate a case of La Croix next time you go to the store. Call your high school buddy that you haven’t talked to in a while. Build a pillow fort with five of your closest friends, even though you’re an “adult.” Viva la friendvolution!

Sam Greszes is a writer and podcaster currently based in Chicago. He has written for internationally distributed print publications such as ION Magazine and prominent websites like Eater, Uproxx, Kill Screen, and Thrillist for over a decade.