Kinetic Energy Calculator
Calculate kinetic energy, mass or velocity from KE = ½mv², with momentum and stopping distance alongside.
How to use this calculator
- 1Pick which quantity you want — the input for it disappears.
- 2Enter the other two in SI units: kilograms, metres per second, joules.
- 3Check the scaling table to see how sharply energy rises with speed at your chosen mass.
How the calculation works
KE = ½mv² m = 2KE ÷ v² v = √(2KE ÷ m) p = mv- KE
- Kinetic energy in joules
- m
- Mass in kilograms
- v
- Speed in metres per second
- p
- Momentum in kg·m/s
The v² term is the whole story: energy grows with the square of speed while momentum grows linearly. A car at 60 mph has twice the momentum of one at 30 mph but four times the kinetic energy — and it is energy that has to be dissipated by the brakes or the crumple zone.
This is the classical formula, valid well below light speed. Above roughly 10% of c the relativistic form is needed, and this calculator refuses rather than returning a quietly wrong answer.
Kinetic energy is a scalar and always positive; momentum is a vector and has direction. That difference is why momentum is conserved in every collision while kinetic energy is only conserved in perfectly elastic ones.
Worked example
A 1,500 kg car at 20 m/s (72 km/h)
- 1.KE = ½ × 1,500 × 20² = ½ × 1,500 × 400.
- 2.= 750 × 400 = 300,000 J, or 300 kJ.
- 3.Momentum: 1,500 × 20 = 30,000 kg·m/s.
- 4.At double the speed (40 m/s) the energy would be ½ × 1,500 × 1,600 = 1,200,000 J — four times as much for twice the speed.
Result: 300,000 J (300 kJ)
Why the square matters so much
Kinetic energy is proportional to the square of speed, and almost every counterintuitive fact about motion follows from that single exponent. Doubling speed quadruples energy. Tripling it multiplies energy by nine. Because braking has to dissipate all of that energy, and brakes dissipate it at a roughly constant rate, stopping distance grows with the square of speed too — which is why the difference between 30 and 60 mph is far more than double in practice.
The same relationship explains why a small increase in speed produces a disproportionate increase in collision severity, and why wind loading, projectile damage and drag losses all escalate faster than the speed itself.
Energy against momentum
Both describe motion and both involve mass and velocity, but they behave differently and answer different questions.
- Momentum, p = mv — a vector, scaling linearly with speed. Conserved in every collision without exception, which makes it the tool for working out what happens after objects hit each other.
- Kinetic energy, KE = ½mv² — a scalar, scaling with speed squared. Conserved only in perfectly elastic collisions — in real ones some becomes heat, sound and deformation, which is precisely what a crumple zone is designed to maximise.
- Why both are needed — a heavy slow object and a light fast one can have equal momentum but wildly different energies. The first is harder to stop in the sense of requiring impulse; the second does more damage on impact.
Where the classical formula stops working
½mv² is an approximation that happens to be extraordinarily accurate at everyday speeds. It is the low-velocity limit of the relativistic expression, and the error grows with the square of v/c. Below about 10% of light speed the discrepancy is under roughly one percent, which is why it is entirely safe for vehicles, projectiles and spacecraft.
Above that, the relativistic form takes over and kinetic energy grows without bound as speed approaches c — which is the reason nothing with mass can reach light speed. This calculator refuses to run above 10% of c rather than returning a classical answer that would be quietly and increasingly wrong.
What this assumes, and where it stops
Assumptions
- Speeds are far below the speed of light, so the classical formula applies.
- Mass is constant — this does not model a rocket losing propellant.
- Values are in SI units: kilograms, metres per second and joules.
Limitations
- Classical only. Above about 10% of light speed the relativistic formula is required, and the calculator refuses rather than returning a wrong figure.
- Translational kinetic energy only. A rotating object also carries rotational kinetic energy (½Iω²), which is not included.
- Does not model where the energy goes in a collision — that depends on how elastic the impact is.
Common questions
Why does doubling my speed quadruple the energy?
Because the formula squares velocity. At twice the speed, v² is four times larger, so the kinetic energy is four times larger for the same mass. This is the direct reason stopping distances grow so sharply with speed — the brakes have four times as much energy to convert into heat.
What is the difference between kinetic energy and momentum?
Momentum is mass times velocity and scales linearly; kinetic energy is half mass times velocity squared and scales quadratically. Momentum is a vector conserved in every collision; kinetic energy is a scalar conserved only in perfectly elastic ones. A truck at walking pace and a bullet can share a momentum value while differing enormously in energy.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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