Kinetic Energy Calculator

How to use this calculator

Enter the mass and speed to get kinetic energy and momentum. You can also start from the energy: enter kinetic energy and mass to find the speed, or kinetic energy and speed to find the mass. Momentum works as an input too — any two of the four values determine the other two.

Speeds can be typed in m/s, km/h, mph, ft/s or knots, and energy can be shown in joules, kilojoules, kilowatt-hours, calories, BTU, foot-pounds or electron-volts. Switching a unit after the calculation simply re-expresses the same quantity, which makes the calculator a quick way to compare, for example, the energy of a baseball pitch in joules and foot-pounds.

The formula

KE = ½ m v²

p = m v

KE = p² / (2m)

m: mass
v: speed
KE: kinetic energy
p: momentum

Kinetic energy is the work needed to accelerate a mass from rest to speed v. Because it grows with the square of speed, small increases in speed have outsized effects: going from 50 to 60 mph raises the energy of a car by 44%. Momentum, by contrast, is linear in speed and is the quantity conserved in collisions, while kinetic energy is conserved only in perfectly elastic ones.

Worked example

A 1,500 kg car travels at 72 km/h. How much kinetic energy must its brakes remove to stop it?

Convert speed: 72 km/h ÷ 3.6 = 20 m/s.
KE = ½ m v² = 0.5 × 1,500 × 20² = 300,000 J = 300 kJ.
Momentum p = m v = 1,500 × 20 = 30,000 kg·m/s.

The brakes must convert 300 kJ into heat. At 144 km/h (double the speed) the energy would be four times larger: 1.2 MJ.

Assumptions and limits

Speeds are much smaller than the speed of light; at more than about 10% of c use the relativistic formula.
The object is treated as a point mass moving in a straight line; rotational kinetic energy (of wheels, for instance) is not included.

Frequently asked questions

Why does kinetic energy depend on speed squared?

Work equals force times distance. Stopping from twice the speed takes twice as long at the same deceleration and covers four times the distance, so four times the work is required.

Can kinetic energy be negative?

No. Mass is positive and v² is never negative, so kinetic energy is zero or positive. Momentum carries a direction and can be negative.

How is kinetic energy related to stopping distance?

With constant braking force F, stopping distance d = KE / F. That is why stopping distance roughly quadruples when speed doubles.