Kinetic Energy Calculator

What is kinetic energy?

Kinetic energy is the energy a body has because it is moving. A parked lorry has none; the same lorry rolling along a road holds a large amount, and that is exactly the amount the brakes must turn into heat to stop it. In SI units energy is measured in joules (J). One joule is the work done by a force of one newton pushing something through one metre.

Two things decide how much kinetic energy a body carries: its mass and its speed. Speed counts for much more, because it appears in the formula squared. A light, fast object can easily outrank a heavy, slow one.

How to use the calculator

Use the Calculate buttons at the top of the form to say which quantity you are after. The form then shows just the two inputs that mode needs.

• Kinetic energy: enter the body mass and its velocity. The answer is listed in joules (switching to kilojoules or megajoules for big values), watt-hours, calories and foot-pounds.
• Mass: enter the energy and the velocity. The answer is given in kilograms and pounds, or in grams for light bodies and in tonnes and tons for heavy ones.
• Velocity: enter the energy and the mass. The answer is shown in m/s, km/s, miles/s and ft/s.

Every input has its own unit menu, so a mass in pounds and a speed in km/h can be entered directly. The calculator converts to SI units internally. All values must be greater than zero.

The kinetic energy formula

KE = ½ × m × v²m in kilograms, v in metres per second, KE in joules

Rearranging the same relationship gives the other two modes of the calculator:

m = 2 × KE ÷ v²

v = √(2 × KE ÷ m)

The expression is accurate for everyday speeds. Near the speed of light a relativistic formula is required, which this tool does not provide. It also covers straight-line (translational) motion only; a spinning wheel stores extra energy in its rotation.

Worked examples

Energy of a car. A 1,500 kg car moves at 25 m/s, which is 90 km/h. KE = ½ × 1,500 × 25² = ½ × 1,500 × 625 = 468,750 J. The calculator reports this as 468.75 kJ, which is about 130.2 Wh or 112 kcal.

Doubling the speed. At 50 m/s the same car holds ½ × 1,500 × 50² = 1,875,000 J, or 1.875 MJ. That is four times the energy for twice the speed, one reason stopping distances grow so fast on fast roads.

Finding a mass. A trolley travelling at 10 m/s carries 50 kJ. Then m = 2 × 50,000 ÷ 10² = 1,000 kg.

Finding a velocity. A 4 kg object holds 2,000 J. Then v = √(2 × 2,000 ÷ 4) = √1,000 ≈ 31.62 m/s, which is roughly 113.8 km/h.

Free fall. An object released from rest turns height into speed. After dropping 5 m it has v = √(2 × 9.80665 × 5) ≈ 9.9 m/s, whatever its mass. The potential energy calculator covers the energy side of that exchange.

The bullet is roughly twenty thousand times lighter than the cyclist, yet it carries more than half as much energy, because its speed is over a hundred times higher.

Energy and mass units

The mass menu has both tonne and ton. A tonne is the metric unit of 1,000 kg. A ton here means the US short ton of 2,000 lb, about 907 kg. They differ by almost ten percent, so check which one your source uses. The British long ton (2,240 lb) is not offered.

To use the energy results elsewhere, see the converters for joules to kilojoules and for speeds such as m/s to mph.

Common mistakes

• Forgetting to square the speed. Using v instead of v² understates the energy badly at high speed.
• Mixing units by hand. A speed in km/h must be divided by 3.6 before it goes into the formula; here the unit menu does that for you.
• Confusing weight with mass. Kilograms and pounds describe mass in this tool. A weight in newtons must first be divided by the gravitational acceleration.
• Assuming energy is conserved in a crash. Momentum is conserved in collisions, but kinetic energy is not: part of it becomes heat, sound and deformation. To estimate the resulting force, try the impact force calculator.

If you also need the speed-up that produced a given velocity, the acceleration calculator is the next step. More tools of this kind are collected on the physics calculators page.