Kinetic Energy Calculator (½mv²)
Calculate kinetic energy, mass, or speed with KE = ½mv² — solve for any of the three, with a worked example.
Kinetic energy
Kinetic energy is the energy an object has because it's moving — the energy you'd have to put in to get it up to speed, and the energy it can release when it stops. It depends on mass and, crucially, on the square of speed.
KE = ½ · m · v²
Mass in kilograms and speed in metres per second give energy in joules. The v² term is the important part: doubling the speed quadruplesthe kinetic energy, which is why a small increase in speed makes such a big difference to braking distance and impact severity. This calculator solves for kinetic energy, mass, or speed.
Worked example
A 1000 kg car at 20 m/s (72 km/h) carries KE = ½ × 1000 × 20² = 200 000 J (200 kJ). Speed it up to 40 m/s and the energy jumps to ½ × 1000 × 1600 = 800 000 J — four times as much for twice the speed. Rearranged, to find the speed at a known energy, v = √(2·KE / m).
Related
Convert the result into other energy units with theenergy converter, or work out the force behind the motion with the force calculator.
Non-relativistic, and the energy has to go somewhere
The ½mv² form is a low-speed approximation. It stays accurate to well within a percent up to about 10% of the speed of light, so it covers anything mechanical you will meet, but it is not the general case. The more practical caveat is what happens on impact: this tells you the energy involved, not the force, because force depends on the stoppingdistance. The same kinetic energy absorbed over a metre of crumple zone and over a centimetre of rigid barrier produce wildly different forces.