Kinetic Energy Calculator

Kinetic energy is the energy that an object possesses because of its motion. Every moving object — from a thrown ball to a speeding car to an electron in an atom — carries kinetic energy. It is one of the two primary forms of mechanical energy (the other being potential energy).

The Kinetic Energy Formula

KE = ½ × m × v²

Where:

• KE = Kinetic energy (Joules, J)
• m = Mass of the object (kilograms, kg)
• v = Velocity of the object (meters per second, m/s)

Key Observations

• Kinetic energy increases with the square of velocity. Doubling speed quadruples kinetic energy.
• Kinetic energy increases linearly with mass. Doubling mass doubles kinetic energy.
• This is why vehicle speed is far more dangerous than vehicle mass in crash physics — a car at 100 km/h has 4× more kinetic energy than at 50 km/h.

Unit Conversions

Practical Examples

A 70 kg person running at 3 m/s (leisurely jog): KE = ½ × 70 × (3)² = ½ × 70 × 9 = 315 J

A 1,500 kg car at 100 km/h (27.78 m/s): KE = ½ × 1500 × (27.78)² = ½ × 1500 × 771.7 ≈ 578,775 J ≈ 579 kJ

A 9 mm bullet (8 g = 0.008 kg) at 370 m/s: KE = ½ × 0.008 × (370)² = ½ × 0.008 × 136,900 ≈ 547 J

Relation to Work

By the work-energy theorem, the net work done on an object equals its change in kinetic energy: W = ΔKE = ½m(v₂² − v₁²)

This relationship is fundamental to braking distance calculations — all of a vehicle’s kinetic energy must be dissipated as heat through the brakes to bring it to a stop.

At relativistic speeds. The classical formula KE = ½mv² is itself an approximation — accurate only when v is small compared to the speed of light. The correct expression from special relativity is KE = (γ − 1)mc², where γ = 1/√(1 − v²/c²) is the Lorentz factor. For everyday speeds the two formulas agree closely; the classical version is within 1% of the relativistic answer for v up to roughly 14% of c (about 42,000 km/s). Particle accelerators, GPS clock corrections, and cosmic-ray physics all need the relativistic form; cars and arrows do not.