Kinetic Energy Calculator — energy of motion (½mv²)

How it works

Kinetic energy is the energy of motion — the work needed to accelerate an object from rest to its current speed. It depends on mass and on the square of velocity:

KE = ½ × m × v²

where m is the mass and v is the speed. In SI units, kilograms and metres per second give an energy in joules (J). Because velocity is squared, speed matters far more than mass: double the speed and the kinetic energy quadruples; triple it and the energy is nine times as large.

The square also means direction is irrelevant — a velocity of −5 and +5 give the same kinetic energy. The value is always zero or positive, and it is zero only when the object is at rest. This calculator is unit-agnostic, so any consistent mass and velocity units work.

Worked example

An 80 kg object moving at 10 m/s has KE = ½ × 80 × 10² = ½ × 80 × 100 = 4000 J (4.0 kJ), the OpenStax example. A 75 kg person walking at 1.5 m/s carries only ½ × 75 × 1.5² = 84.4 J, but the same person cycling at 13.5 m/s has ½ × 75 × 13.5² ≈ 6834 J — about 80 times more, because the speed rose ninefold in the square.

Frequently asked questions

What is the formula for kinetic energy?

Kinetic energy is one-half the mass times the velocity squared: KE = ½mv². It equals the work done to bring an object from rest up to its speed, and it is measured in joules when mass is in kilograms and speed in metres per second.

Why is velocity squared in the formula?

Because the work needed to speed something up grows with the square of the speed — each extra unit of velocity takes more energy than the last. This is why stopping distances and collision damage rise so steeply with speed: doubling speed quadruples the kinetic energy that must be dissipated.

Does the direction of motion affect kinetic energy?

No. Squaring the velocity removes the sign, so an object moving left at 5 m/s has exactly the same kinetic energy as one moving right at 5 m/s. Kinetic energy is a scalar — it has magnitude but no direction.

What units does kinetic energy use?

The SI unit is the joule (J): one joule is 1 kg·m²/s². Using kilograms for mass and metres per second for velocity gives joules directly. This calculator treats the inputs as plain numbers, so keep the units consistent.

How is kinetic energy different from momentum?

Both describe motion, but kinetic energy (½mv²) is a scalar measured in joules, while momentum (mv) is a vector measured in kg·m/s. Kinetic energy depends on the square of speed; momentum depends on speed to the first power and keeps its direction.

How does kinetic energy relate to potential energy?

They are interchangeable forms of mechanical energy. A falling object trades gravitational potential energy (mgh) for kinetic energy (½mv²) as it speeds up; a ball thrown upward does the reverse. In the absence of friction, their sum stays constant — the conservation of energy.