Kinetic Energy Calculator
Calculate kinetic energy (KE) from mass and velocity, or find mass or velocity from a known kinetic energy value.
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How to use this calculator
KE = kinetic energy (J), m = mass (kg), v = velocity (m/s). Kinetic energy grows with the square of speed — doubling speed quadruples energy.
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Enter mass and velocity to calculate kinetic energy.
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To find an unknown value, enter the two known values and set the unknown to 0.
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Results also include momentum (p = mv) and speed in km/h.
Frequently asked questions
How do I solve for mass or speed instead of energy?
Enter the two values you know and put 0 in the one you want. Mass 10 and energy 125 gives a speed of 5.0000 m/s, and speed 5 with energy 125 gives a mass of 10.0000 kg. Leaving all three non-zero is treated as a request for energy: the energy you typed is ignored and recomputed from mass and speed.
Why does it say "Enter at least two values"?
Because zero is the "solve for this" marker, a genuinely zero quantity cannot be used. A body with mass 10 kg at 0 m/s and 0 J of energy triggers the message instead of a result of 0 J. Kinetic energy at rest is simply 0 without needing a tool.
What units does it use?
Kilograms, metres per second and joules. The output also repeats energy in kilojoules, shows speed in km/h (multiplied by 3.6) and gives momentum in kg·m/s. If your speed is in km/h, divide by 3.6 first: 100 km/h is 27.78 m/s.
Can speed be negative?
Yes, as a direction. Mass 10 kg at -5 m/s still gives 125 J, because the speed is squared, but the momentum shows -50 kg·m/s. Mass and kinetic energy must be positive when entered as inputs; negative mass is rejected, as is negative energy when solving for speed or mass.
How does doubling speed change stopping distance?
With a constant braking force, the work needed to stop equals the kinetic energy, so stopping distance grows with the square of speed. A 1500 kg car at 100 km/h carries 578796.3 J in the tool, four times the 144699.075 J at 50 km/h, and so needs four times the braking distance.
Is kinetic energy the same as momentum?
No. Momentum p = mv scales linearly with speed, energy ½mv² with its square. They are related by KE = p² ÷ 2m. A 0.145 kg ball at 40 m/s has 116 J of energy and 5.8 kg·m/s of momentum.
Does it include rotation or relativity?
No. It treats the body as a point mass moving in a straight line at everyday speeds. A rolling wheel also stores rotational energy, and near the speed of light the ½mv² formula no longer applies.
Kinetic energy calculator — energy of motion from mass and speed
Why speed counts twice
Kinetic energy is KE = ½mv², with energy in joules, mass in kilograms and speed in metres per second. Because speed is squared, adding speed pays off quickly: tripling speed multiplies energy by nine. Mass enters only once, so doubling it merely doubles the energy. The joule is the SI unit, one kilogram-metre squared per second squared, and the tool also gives kilojoules so that vehicle-scale numbers stay readable. The speed line is printed in km/h as well, which saves a conversion when your data came from a speedometer.
Worked example: a 1500 kg car
At 27.78 m/s (100 km/h) the calculator returns 578796.3000 J, or 578.7963 kJ, and a momentum of 41670 kg·m/s. At 13.89 m/s (50 km/h) it returns 144699.0750 J. The ratio is 4.0000, as the squared speed predicts, even though the speed only halved. The momentum figures, 41670 and 20835 kg·m/s, differ only by a factor of two, which shows how differently the two quantities scale with speed.
Worked example: solving backwards
An object known to carry 125 J at 5 m/s must have a mass of 10.0000 kg. An object of mass 10 kg carrying the same 125 J must be moving at 5.0000 m/s. Set the unknown field to 0 and the calculator picks the right rearrangement: v = √(2KE ÷ m) or m = 2KE ÷ v². Negative energy has no physical meaning, so the tool refuses it, and a zero denominator cannot occur because the field you leave at 0 is the one being solved for.
A 1000 kg body at three speeds
Equal steps in speed do not give equal steps in energy.
| Speed | In km/h | Kinetic energy |
|---|---|---|
| 10 m/s | 36.00 | 50 kJ |
| 20 m/s | 72.00 | 200 kJ |
| 30 m/s | 108.00 | 450 kJ |
Energy and work
The work–energy theorem says the net work on an object equals the change in its kinetic energy. That is how the page connects to braking, throwing and lifting problems: calculate the energy, then divide by a force to get a distance. If a 1000 kg body at 30 m/s carries 450 kJ, a constant braking force of 9000 N must act over 50 m to bring it to rest. That is the work–energy theorem used in the direction most useful for road-safety and machinery problems.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →