Kinetic Energy Calculator
The kinetic energy formula is KE = ½ m v², and this kinetic energy calculator works out the answer the moment you enter a mass and a speed. You'll get the result in joules, kilojoules, and calories at once, so you don't have to convert by hand. It'll also solve in reverse: give it the energy and one other value, and it finds the missing mass or velocity. There's a live drawing that speeds up as you raise the velocity, so you can see why energy grows so fast.
- Solve for KE, mass, or v
- Joules & kilojoules
- Calories too
- Live motion view
- Formula shown
Last updated June 18, 2026 Method: KE = ½ m v² Reviewed by the Calcowa physics team
Enter positive values to see the result.
KE = ½ × 2 × 3² = 9 J
What is the kinetic energy formula?
Kinetic energy is the energy an object has because it's moving, and it's found with KE = ½ × m × v², where m is the mass in kilograms and v is the speed in meters per second. For a 2 kg object moving at 3 m/s, the kinetic energy is 9 joules.
The squared speed is the part that matters most. Because v is squared, speed counts far more than mass: double the speed and the energy quadruples, while doubling the mass only doubles it. That single fact explains why highway crashes are so much more violent than city ones, and why stopping distance balloons as you drive faster.
How do you calculate kinetic energy?
To calculate kinetic energy, square the speed, multiply by the mass, then halve it. Here's the full sequence:
- 1
Get mass and speed in SI unitsUse kilograms for mass and meters per second for speed.
- 2
Square the speedMultiply the speed by itself to get v squared.
- 3
Multiply by the massMultiply the squared speed by the mass in kilograms.
- 4
Halve the resultDivide by two, and the answer is in joules.
- 5
Convert if neededSwitch to kilojoules or calories if that's the unit you want.
A kinetic energy example, step by step
Take a 1,500 kg car moving at 13.4 m/s, which is about 30 mph. Square the speed to get roughly 179.6, multiply by the 1,500 kg mass for 269,400, then halve it.
KE = ½ × 1500 × 13.4² = 134,700 J
about 135 kilojoules, or 32,200 calories
Now bump that car to 70 mph and the energy jumps past 735 kJ, more than five times as much, even though the speed only doubled. Type the numbers into the calculator above to see it.
Finding mass or velocity from kinetic energy
Sometimes you know the energy and need a missing piece. To find the velocity, rearrange to v = √(2 × KE / m). To find the mass, use m = 2 × KE / v². Flip the calculator to its mass or velocity mode and it'll handle the algebra for you.
This is handy in physics homework and in real engineering, where you often know how much energy a system carries and want the speed it implies. It also ties into the Speed Converter when your speed starts out in mph or km/h and you need m/s first.
Kinetic energy of everyday things
Numbers feel abstract until you compare them. Here's the kinetic energy of some familiar objects, worked out with KE = ½ m v². Notice how the highway car carries over five times the energy of the city car, even though it's only going about twice as fast.
| Object | Kinetic energy | Good to know |
|---|---|---|
| Walking person (70 kg, 1.4 m/s) | 69 J | A relaxed strolling pace |
| Sprinter (70 kg, 10 m/s) | 3,500 J | Top human running speed |
| Car on a street (1,500 kg, 13.4 m/s) | 135 kJ | About 30 mph |
| Car on the highway (1,500 kg, 31.3 m/s) | 735 kJ | About 70 mph, over 5x the energy |
| Baseball pitch (0.145 kg, 40 m/s) | 116 J | A fast 90 mph fastball |
Frequently asked questions
Is kinetic energy a vector or a scalar?
Kinetic energy is a scalar, so it has size but no direction. It's always positive or zero, no matter which way the object moves, because the speed gets squared in the formula. Momentum, by contrast, is a vector that does point in the direction of travel.
The kinetic energy formula is KE = ½ × m × v², where m is mass in kilograms and v is speed in meters per second. The answer comes out in joules. Because the speed is squared, doubling the speed gives you four times the kinetic energy, which is why crashes get so much worse at higher speeds.
To calculate kinetic energy, square the speed, multiply by the mass, then halve the result. For a 2 kg object moving at 3 m/s, that's ½ × 2 × 9 = 9 joules. This kinetic energy calculator does all three steps the moment you type the numbers, and it shows the working too.
Rearrange the formula. To find mass, use m = 2 × KE / v². To find velocity, use v = √(2 × KE / m). Switch the calculator to the mass or velocity mode and it'll do the rearranged math for you, so you don't have to.
Kinetic energy is measured in joules (J) in the SI system, where 1 joule equals 1 kg·m²/s². You'll also see kilojoules (kJ) for larger values and, in some textbooks, the calorie or foot-pound. This calculator shows joules alongside kilojoules and calories so you've got the unit you need.
Kinetic energy is the energy of motion, while potential energy is stored energy waiting to be released, like a ball held up high. They trade back and forth: a roller coaster swaps potential energy for kinetic as it drops, then back again as it climbs. The total stays the same if there's no friction.
It comes from the physics of work and acceleration. The work needed to speed something up grows with the square of the final speed, so the energy it carries does too. That squared term is the reason a small jump in speed makes such a big difference to stopping distance and impact force.
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