Kinetic Energy Calculator

How to Use the Kinetic Energy Calculator

The Kinetic Energy Calculator computes the energy of a moving object based on its mass and velocity. Kinetic energy is one of the most fundamental concepts in physics, governing everything from car crashes and sports to molecular motion and orbital mechanics.

The Kinetic Energy Formula

KE = ½ × m × v², where KE is kinetic energy in joules (J), m is mass in kilograms (kg), and v is velocity in meters per second (m/s). The squared velocity term means that doubling speed quadruples the kinetic energy. A car at 60 mph has four times the kinetic energy of one at 30 mph.

Practical Examples

A 1,500 kg car at 100 km/h (27.8 m/s): KE = 0.5 × 1500 × 27.8² = 579,630 J ≈ 580 kJ. A 0.145 kg baseball at 145 km/h (40.3 m/s): KE = 0.5 × 0.145 × 40.3² = 117.7 J. A 70 kg runner at 10 m/s: KE = 0.5 × 70 × 100 = 3,500 J.

Work-Energy Theorem

The net work done on an object equals the change in its kinetic energy: W = ΔKE = KE_final - KE_initial. To stop the 1,500 kg car from 100 km/h, brakes must do 580 kJ of work, converting kinetic energy into heat. This principle is fundamental to understanding braking distances and collision physics.

Kinetic vs. Potential Energy

Kinetic energy is energy of motion. Potential energy is stored energy due to position or configuration. A ball at the top of a hill has gravitational potential energy (PE = mgh). As it rolls down, PE converts to KE. At the bottom, nearly all energy is kinetic. This conversion is perfectly reversible in an ideal system.

Frequently Asked Questions

Q: Why does kinetic energy depend on velocity squared?

A: This comes from the work-energy theorem. Work = Force × Distance. An accelerating object covers more distance at higher speeds during the same time interval. The additional distance means more work is done, resulting in a squared relationship. This is why high-speed crashes are so much more destructive.

Q: What is the kinetic energy of a bullet?

A: A typical 9mm bullet (8g at 370 m/s) has KE = 0.5 × 0.008 × 370² = 548 J. A rifle round (10g at 900 m/s) has KE = 4,050 J. Despite their small mass, bullets carry significant kinetic energy due to their extreme velocity. Energy is the key factor in ballistic performance.

Q: How does kinetic energy relate to momentum?

A: Momentum (p = mv) and kinetic energy (KE = ½mv²) are related: KE = p²/(2m). A heavy slow object can have the same momentum as a light fast object, but the lighter object has more kinetic energy. Momentum is conserved in collisions; kinetic energy is conserved only in elastic collisions.