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Calculators/Kinetic Energy
Classical Mechanics

Kinetic Energy Calculator

Calculate kinetic energy from mass and velocity — or solve for mass or velocity when KE is known. Multiple unit systems, instant step-by-step solution.

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Real-world examples

Kinetic energy equations

Kinetic energy
KE = ½mv²
Solve for mass
m = 2·KE / v²
Solve for velocity
v = √(2·KE / m)
Momentum
p = mv
KE from momentum
KE = p² / (2m)
Work-energy theorem
W = ΔKE = KE_f − KE_i

What is kinetic energy?

Kinetic energy is the energy an object possesses by virtue of its motion. Any object with mass that is moving has kinetic energy — a rolling ball, a flying plane, an orbiting satellite. The formula KE = ½mv² tells us that KE scales linearly with mass but quadratically with velocity — doubling the speed quadruples the kinetic energy.

This quadratic relationship with velocity is why car crash energy is so much greater at motorway speeds than at town speeds. A car at 70 mph doesn't have twice the kinetic energy of a car at 35 mph — it has four times as much.

For the full theory including the work-energy theorem and relativistic kinetic energy, see our article on Kinetic Energy.

Why does KE depend on v²?↓
Kinetic energy equals the work done to accelerate the object from rest. Work = F·d, acceleration = F/m, and the relationship between distance and velocity under constant acceleration gives d = v²/(2a). Combining these gives KE = ½mv². The v² term comes from kinematics, not from any special property of energy.
What is the difference between kinetic energy and momentum?↓
Momentum p = mv scales linearly with velocity. Kinetic energy KE = ½mv² scales quadratically. They measure different things: momentum is the "quantity of motion" and is conserved in all collisions; kinetic energy is only conserved in elastic collisions.
Can kinetic energy be negative?↓
No — kinetic energy is always zero or positive. Speed is always non-negative (it is the magnitude of velocity), so v² is always ≥ 0, and mass is always positive.

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