Kinetic Energy Calculator

Enter any two of mass, speed and energy and leave the third blank to solve for it, in whatever units suit you. Every result comes with the same mass at other speeds, because the useful thing about kinetic energy is not one number but the shape: speed is squared, so going twice as fast carries four times the energy.

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How this kinetic energy calculator works

Enter any two of mass, speed and energy, and leave the third blank to solve for it. Units are yours to pick on every field, so a car in pounds at miles per hour works as well as a lab problem in kilograms and metres per second. The second mode does gravitational potential energy, mgh, which is the same story told about height instead of speed.

Every result comes with a short table of the same mass at other speeds, because the single most useful thing about kinetic energy is not any particular number but the shape of the relationship, and a table shows that in a way a formula does not.

The formula

KE = ½mv²
PE = mgh
v = √(2 × KE ÷ m)
impact speed after a fall = √(2gh)

m is mass in kilograms, v is speed in metres per second, g is gravitational acceleration (9.80665 m/s2 on Earth, exact by definition) and h is height. The answer is in joules, which is one kilogram metre squared per second squared. Notice that speed appears squared and mass does not, which is the difference the rest of this page is about.

Worked example

A 1,500 kg car at 30 mph. That is 13.41 m/s, so KE = ½ × 1500 × 13.412 = 134.9 kJ.

The same car at 60 mph is 26.82 m/s, and the energy is 539.6 kJ. Not double. Four times. The speedometer went up by a factor of two and the energy went up by a factor of four, because the speed is squared and nothing else in the formula changed.

That has a consequence you can feel. Stopping the car means the brakes have to get rid of all of that energy, and at roughly constant braking force the distance needed is proportional to the energy. So the braking distance from 60 is about four times the braking distance from 30, not twice. A driver who thinks in speed and a car that behaves in energy squared are the reason the gap between "a bit fast" and "far too fast" is much narrower than it feels.

Why the square changes everything

Almost every quantity people meet day to day is linear: twice the distance takes twice the fuel, twice the hours earn twice the pay. Kinetic energy is not, and the intuition trained on everything else quietly misleads. Going from 20 to 40 mph does not add as much energy as going from 40 to 60, even though both are a 20 mph increase, because energy depends on where you started. The step from 40 to 60 adds 1.67 times as much energy as the step from 20 to 40, because the energy depends on the squares (3600 minus 1600, against 1600 minus 400) rather than on the 20 mph itself.

The same shape shows up wherever kinetic energy does. Wind power rises with the cube of wind speed, because the energy of each parcel of air goes as the square and the number of parcels arriving per second goes as the speed as well. A bullet's stopping power is dominated by its speed rather than its weight. A hailstone twice as fast hits four times as hard. And in the least intuitive case of all, a spacecraft's fuel needs are set by the change in speed rather than the distance travelled, which is why our delta-v calculator exists and why space is hard in a way that has nothing to do with how far away things are.

Two things this formula is not

It is not relativistic. Above roughly 10% of the speed of light, ½mv² starts to under-report, and the correct expression grows without limit as speed approaches c. That is the mathematical form of the statement that nothing with mass can reach light speed: doing so would take infinite energy. For anything you will meet on a road, in a workshop or in a first-year problem set, the classical formula is exact to more decimal places than you will ever measure.

And it is not a vector. Kinetic energy has no direction, which sounds like a technicality and is not. Momentum has direction and can cancel: two identical cars closing head on at the same speed have zero total momentum. Their total kinetic energy is very much not zero, and it has to go somewhere. That is the whole reason a head-on collision is so much worse than the closing speed suggests, and why crumple zones are designed around absorbing energy rather than around balancing momentum. Our momentum calculator handles the other half of that story.

Frequently asked questions

How do I calculate kinetic energy?

Multiply half the mass by the speed squared. A 1,500 kg car at 13.41 m/s (30 mph) carries half of 1500 times 13.41 squared, which is 134.9 kJ. Mass goes in kilograms and speed in metres per second to get joules, and this page converts from pounds, miles per hour or anything else you enter.

Why does doubling speed quadruple kinetic energy?

Because speed appears squared in the formula and mass does not. Double the speed and you square the doubling, so the energy goes up by a factor of four; triple it and the factor is nine. The practical version is that braking distance at a fixed braking force is proportional to energy, so stopping from 60 mph takes roughly four times the distance of stopping from 30, not twice.

What is the difference between kinetic energy and momentum?

Momentum is mass times velocity and has direction; kinetic energy is half mass times speed squared and has none. That difference decides real outcomes. Two identical cars closing head on at the same speed have zero total momentum, because the two velocities cancel, but their combined kinetic energy is large and has to go somewhere. It is the energy that does the damage, which is why crumple zones are designed to absorb energy.

How do I find speed from kinetic energy?

Rearrange to v equals the square root of twice the energy divided by the mass. Leave the speed box blank above and it does this for you. The square root is why halving an object's energy does not halve its speed: it drops it by a factor of about 1.41, which is the same relationship running backwards.

What is gravitational potential energy?

Mass times gravity times height, or mgh. The important feature is what the formula leaves out: the path. Carrying a box up a ramp and lifting it straight up store exactly the same energy, because only the change in height appears. It is also always measured relative to a reference you choose, so the meaningful question is never how much potential energy something has but how much it has compared with the floor or the ground.

Does mass affect how fast something falls?

No, and the formula shows why. Potential energy mgh becomes kinetic energy half mv squared, and setting them equal gives an impact speed of the square root of 2gh with the mass cancelling out completely. A hammer and a feather really do land together where there is no air to slow the feather down, which is what the Apollo 15 crew demonstrated on the Moon.

Does this formula work at very high speeds?

Up to about 10% of the speed of light it is accurate to more decimal places than you can measure. Beyond that the classical formula under-reports and the relativistic expression takes over, growing without limit as speed approaches c. That growth is the mathematical form of the rule that nothing with mass can reach light speed, since doing so would take infinite energy.

What units does kinetic energy use?

The joule, which is one kilogram metre squared per second squared. Larger amounts get kilojoules or megajoules, and this page also converts to calories, food Calories (which are kilocalories), foot-pounds and kilowatt-hours. A useful anchor: a 1,500 kg car at 60 mph carries about 540 kJ, which is roughly the energy in 129 food Calories, or about half a chocolate bar.

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