What is the kinetic energy formula?

Kinetic energy is calculated using KE = 0.5 x m x v squared, where m is mass in kilograms and v is velocity in metres per second. The result is in Joules. Doubling the speed quadruples the kinetic energy because velocity appears as a squared term in the formula.

Why does speed have a bigger effect on kinetic energy than mass?

Because velocity is squared in the formula while mass is linear. Doubling the mass doubles the kinetic energy, but doubling the speed multiplies it by four. This is why vehicle crash severity increases dramatically at higher speeds.

What is the unit of kinetic energy?

The SI unit of kinetic energy is the Joule (J), which equals one kilogram times metre squared per second squared (kg m2 s-2). For larger amounts, energy is commonly expressed in kilojoules (kJ, 1000 J) or kilowatt-hours (kWh, 3,600,000 J).

Kinetic Energy Calculator

This calculator uses the kinetic energy formula, KE = half m v squared, to solve for kinetic energy, mass, or speed depending on which quantity you want to find. Kinetic energy is the energy an object possesses due to its motion, measured in Joules. Any moving object with mass has kinetic energy, and the amount depends on both the mass of the object and the square of its velocity. Because velocity is squared, a small increase in speed produces a large increase in kinetic energy, which is why crash severity escalates rapidly with speed. You select what you want to solve for, enter the two known values, and the calculator returns the result. When solving for kinetic energy, you provide mass in kilograms and speed in m/s, and receive the energy in Joules, kilojoules, and kilowatt-hours. When solving for mass, you provide kinetic energy in Joules and speed in m/s. When solving for speed, you provide kinetic energy in Joules and mass in kilograms. This tool is useful for physics students, mechanical engineers sizing flywheels and braking systems, vehicle safety analysts, and sports scientists studying ball impact energy. The formula applies to translational (linear) kinetic energy only; a rotating object also has rotational kinetic energy not captured here.

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Solve for

Mass (m)

Speed (v)

m/s

Kinetic Energy (KE)

3,500 J

kinetic energy

Kilojoules3.50 kJ

Kilowatt-hours0.000972 kWh

How it works

The three rearrangements of the kinetic energy equation are: KE = ½mv² (energy), m = 2KE / v² (mass), and v = sqrt(2KE / m) (speed). Select the variable you want to find, enter the other two, and the calculator applies the correct formula. Energy in Joules is converted to kilojoules by dividing by 1,000, and to kilowatt-hours by dividing by 3,600,000.

Worked example

A 70 kg person running at 10 m/s has kinetic energy = 0.5 × 70 × 10² = 0.5 × 70 × 100 = 3,500 J = 3.50 kJ = 0.000972 kWh. These match the default values pre-filled above.

Related calculators

Potential Energy Calculator: gravitational PE = mgh, the energy stored in height.
Velocity Calculator: find the speed used in the KE formula.
Force Calculator: Newton's Second Law F = ma.
Free Fall Calculator: combine with KE to find the energy at impact.

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