The Planet Buster Calculator estimates how much energy it would take to pull a planet apart against its own gravity, using the planet’s size as the main input. For Earth, a 2023 University of Leicester physics paper puts that gravitational binding energy at 2.24 × 10³² joules, based on a uniform-sphere model. A Planet Buster Calculator turns that physics into a fun way to test Dragon Ball’s planet-sized battles.
The model uses the standard formula for a uniform-density sphere, so a size-only input also needs a density assumption. According to NASA’s planetary fact sheet, densities range from 687 kg/m³ for Saturn to 5,514 kg/m³ for Earth, which is why the result shifts so much. Energy also rises steeply with size. At fixed density, doubling a planet’s radius multiplies the estimate by 32. The result is an entertaining estimate, not a prediction of how any attack works.
Key Takeaways
- The Planet Buster Calculator estimates the gravitational binding energy needed to pull a planet apart, and it requires both a size and a density to produce a result.
- Earth’s gravitational binding energy is 2.24 × 10³² joules according to a 2023 University of Leicester physics paper using a uniform-sphere model, which makes Earth the benchmark for checking the calculator.
- Doubling a planet’s radius at a fixed density multiplies its binding energy by 32, so small changes in size can produce large jumps in the estimate.
- Readers can convert a joule total into tonnes of TNT equivalent by dividing by 4.184 × 10⁹, but the calculator’s output is an entertaining benchmark, not a prediction of how any Dragon Ball attack would work.
How Much Energy Would It Take to Break a Planet Apart?
Breaking a planet apart means supplying enough energy to pull all of its material away from its own gravity. The Planet Buster Calculator measures that amount as gravitational binding energy, the energy needed to disperse a planet against its own gravity. Every piece of rock and metal has to be lifted free of the pull of everything else in the planet.
For a uniform-density sphere, the standard approximation is U = 3GM²/(5R), where M is the planet’s mass, R is its radius, and G is the gravitational constant. Gravity holds the planet together, so the formula produces a negative number. The magnitude of that number is the energy estimate the calculator uses. A 2010 exercise from Leiden University’s Planets and Exoplanets course lays out this approach.
Think of the planet as a ball of clay that has been squeezed into shape. The formula tells you how much work it takes to pull every grain of that clay back out to infinite distance. Bigger planets hold more grains, and they pull harder on each one, so the total climbs quickly.
It helps to be clear about what this number does not represent. It is not the energy needed to vaporize a planet, which would require far more energy to heat the material into gas. It also does not predict how any fictional attack would work. The calculator offers a fun, science-based benchmark for measuring planet-sized power in Dragon Ball, not a blueprint for destruction.
Why Does Density Change the Energy Estimate So Much?
Density changes the estimate so much because it controls how much mass fits inside a planet of a given size, and binding energy depends heavily on that mass. Two planets with the same diameter can weigh very differently if one is packed with rock and metal while the other is mostly light gas. Size alone leaves the most important number unknown.
Real planets show how wide that range is. Earth measures 12,756 km across and has a mass of 5.97 × 10²⁴ kg. Mars is roughly half as wide, at 6,792 km, yet its mass is only 0.642 × 10²⁴ kg, about a tenth of Earth’s. Mars holds far less material in each unit of space, so a calculator that knew only its size would badly misjudge it.
The Planet Buster Calculator handles this by asking for an explicit density value. It combines that value with the radius to work out the planet’s mass, then applies the uniform-sphere formula. Without a density input, the calculator has no mass to place in the equation, so it cannot produce a number at all.
The effect of density is steep. Mass rises in direct proportion to density, and binding energy depends on mass squared, so doubling the density quadruples the energy estimate at the same size. Users can enter a different density and watch the result move, which makes the assumption visible instead of hidden.
How Does Doubling a Planet’s Size Affect Its Energy?
Doubling a planet’s radius multiplies its binding energy by 32, because at a fixed density the energy rises with the fifth power of the radius. Two effects stack on top of each other to produce that jump.
At a fixed density, a planet’s mass grows with its radius cubed. Picture filling a box with identical blocks. When the box is twice as wide, tall and deep, it holds eight times as many blocks. A planet with twice the radius therefore carries eight times the mass, and every extra piece of material must be pulled free of a much larger body.
The second effect comes from the formula itself. Binding energy depends on mass squared, which turns that eightfold increase into a 64-fold one. The radius also appears in the formula, and it works in the other direction, trimming the total by a factor of two. Sixty-four divided by two leaves 32.
That is why small changes in size produce large jumps in energy. Each step up in radius adds a bigger layer of material and strengthens the pull holding that material in place, so the energy climbs faster than the size itself. A planet only slightly larger than another can demand a noticeably bigger energy total, and the calculator’s results climb quickly for the same reason once the radius goes up.
Comparing Earth, Mars, Jupiter and the Moon as Benchmarks
Four bodies make useful test cases for the calculator: Earth, Mars, Jupiter and the Moon. Each sits at a different point on the size scale, so together they show how quickly the estimate can change.
Earth is the anchor. According to the University of Leicester paper, its gravitational binding energy is 2.24 × 10³² joules under the uniform-sphere model. To check the calculator against this figure, enter Earth’s diameter of 12,756 km and its density of 5,514 kg/m³ from NASA’s fact sheet. The result should land close to the benchmark.
Mars makes a good second test. With a mass of 0.642 × 10²⁴ kg and a diameter of 6,792 km, it is much lighter than Earth. Enter its size with any density you choose, and the result should fall well below Earth’s, which shows how strongly mass drives the answer.
Jupiter sits at the opposite end of the scale. NASA lists its mass as 1,898 × 10²⁴ kg and its diameter as 142,984 km. Because Jupiter is a gas giant, its average density is far lower than Earth’s, so the density you choose matters even more here. Try two or three different densities to see how far the estimate moves.
The Moon is the smallest benchmark. The Leicester paper estimates its binding energy at 1.2745 × 10²⁹ joules, a figure far below Earth’s. Comparing the Moon with Earth shows how a body that is only somewhat smaller can require a dramatically smaller energy total.
How Do You Convert Joules Into Tonnes of TNT?
One tonne of TNT equivalent is 4.184 gigajoules, so you convert joules into tonnes by dividing the joule total by 4.184 billion. MIT OpenCourseWare’s The Physics of Energy course materials give that figure. A gigajoule is one billion joules, so the conversion takes only one division once the numbers are written out.
TNT equivalent is a common yardstick for explosive energy. It turns a number that is hard to picture into a size readers can compare with familiar explosions. The steps below use Earth’s binding energy as the example.
- Write down the joule total, which for Earth is 2.24 × 10³² joules.
- Divide that total by 4.184 billion, written as 4.184 × 10⁹.
- Read the answer as tonnes of TNT equivalent, which comes to about 5.35 × 10²² tonnes.
The same method works for any planet the calculator produces. The Moon’s estimate of 1.2745 × 10²⁹ joules converts to roughly 3.05 × 10¹⁹ tonnes, which shows how sharply the total drops when the body gets smaller.
These tonne figures are an entertaining comparison, not a measurement of any real weapon. They help readers grasp the scale of planet-sized energy, but they do not describe how any explosive or any Dragon Ball attack would actually work.
Where Does Dragon Ball Fit Into Planet-Scale Energy?
Dragon Ball fits into planet-scale energy as a source of huge battles that the calculator can turn into real numbers. According to the Dragon Ball Official Site, the manga began serialization in Weekly Shonen Jump in 1984, and its planet-level fights have kept fans returning ever since. Toei Animation USA lists Dragon Ball Z as a 291-episode series first released in 1989, a long run that gave the franchise many moments where characters threaten entire worlds.
Fans often ask how much power it would take to break a planet apart. The calculator answers that question with physics, using gravitational binding energy as a clear benchmark. A reader can then compare a fictional blast with a figure that has a fixed meaning.
The calculator models a physics concept. It does not model the show’s rules for how attacks work. Dragon Ball attacks follow the series’ own rules, which can stretch distance, speed and energy in ways no uniform-sphere formula captures. A planet’s binding energy is a property of the planet itself, while a technique’s power depends on the story’s logic.
Think of the calculator as a bridge between fan battles and simple science. Pick a favorite world, change its density, and watch the estimate shift. The science stays grounded, and the battles stay fun.
Trying Your Own Planet Size Estimate
Trying the calculator takes only two inputs: a size and a density. Work through the steps below to run a first estimate for Earth, then test a fictional world.
- Enter Earth’s radius of 6.370 × 10⁶ metres in the size field, which is 6,370 km.
- Choose a density of 5,514 kg/m³, the figure NASA’s fact sheet gives for Earth.
- Run the estimate and check that the result is close to 2.24 × 10³² joules.
- Divide that joule total by 4.184 × 10⁹ to convert it into tonnes of TNT equivalent.
- Double the radius to 1.274 × 10⁷ metres, keep the density the same, and run it again.
The Moon’s estimate of 1.2745 × 10²⁹ joules makes a useful lower benchmark. Your doubled-Earth result should be about 32 times Earth’s total, roughly 7.2 × 10³³ joules, or about 1.7 × 10²⁴ tonnes of TNT.
Running Your First Planet Buster Estimate
Start by running the Earth test exactly as described above, and write the joule result down before you change anything else. That first number becomes your reference point, so every later run can be checked against it.
Once Earth’s result matches the University of Leicester benchmark, choose a Dragon Ball world and give it a size you can justify. Run it once with a density close to Earth’s, then again with a much lighter density. Put the two results side by side and note how much the energy moves. That gap shows how much the density assumption shapes every answer.
Before you share your numbers, check the source. NASA’s Planetary Fact Sheet was last updated on March 18, 2025, so look for a newer version from NASA Goddard Space Flight Center before you quote its densities or diameters in a comparison.
Keep a simple table with four columns: the planet or fictional world, its radius, its density and its tonnes of TNT equivalent. Each new run then becomes easy to compare, and your table can be rerun whenever you test a new idea.
Frequently Asked Questions
1. Why is the Moon’s binding energy so much smaller than Earth’s?
The Moon’s gravitational binding energy is far smaller than Earth’s because the Moon has much less mass and a smaller radius. According to the University of Leicester paper, the Moon’s estimate is 1.2745 × 10²⁹ joules, while Earth’s is 2.24 × 10³² joules, so the Moon’s figure is less than one-thousandth of Earth’s. Since the formula depends on mass squared, even a moderate drop in mass cuts the energy sharply.
2. Does the Planet Buster Calculator work for stars, moons or dwarf planets?
The calculator works for any body you can describe with a size and a density, which includes moons such as the Moon used as a benchmark in this guide, and dwarf planets. The uniform-sphere formula is a simple model, so the result is most meaningful for bodies whose density stays roughly even throughout. Stars are much hotter and denser toward their cores, so a uniform-density estimate for a star is only a rough guess.
3. Which planet is destroyed in Dragon Ball, and how big is it?
Planet Namek is the best-known world destroyed in Dragon Ball, blown apart by Frieza in Dragon Ball Z. The calculator does not look up a world’s size for you, so the result depends on the radius and density you enter. Pick values you can justify, and state them clearly whenever you share your results.