Kinetic Energy Calculator

Physics guide

What is kinetic energy and how is it calculated?

Kinetic energy is the energy a body possesses because it is moving. Any object with mass that is in motion carries kinetic energy. It is a scalar quantity, meaning it has magnitude but no direction, and it is always zero or positive since mass and velocity squared are always non-negative.

The kinetic energy formula

The formula for kinetic energy was derived by Gaspard-Gustave de Coriolis in the 1820s from Newton's laws of motion:

Where KE is kinetic energy in joules, m is mass in kilograms, and v is velocity in meters per second. The "½" factor arises from integration of Newton's second law over a displacement: applying a constant force to accelerate a mass from rest produces work equal to exactly half the product of mass and velocity squared.

Solving for the three variables

The same equation can be rearranged to find any of the three variables when the other two are known:

The calculator detects which field you left empty and applies the correct rearrangement automatically. All inputs are converted to SI units (kg and m/s) before calculation, and the result is converted back to your chosen output unit.

Why velocity matters more than mass

Because velocity is squared in the formula, doubling an object's speed quadruples its kinetic energy, while doubling its mass only doubles the kinetic energy. This is why vehicle collision physics emphasizes speed limits so strongly: a car traveling at 120 km/h carries four times the kinetic energy of the same car at 60 km/h.

Real-world examples

• Baseball pitch (145 g at 144 km/h): KE = ½ × 0.145 × 40² = 116 J. Enough to shatter an unprotected hand if stopped abruptly.
• Rifle bullet (10 g at 900 m/s): KE = ½ × 0.010 × 900² = 4050 J. Despite the tiny mass, the enormous velocity gives a bullet tremendous stopping power.
• Olympic sprinter (80 kg at 10 m/s): KE = ½ × 80 × 100 = 4000 J, roughly equivalent to the bullet. The mass compensates for the lower speed.
• Commercial airliner (300,000 kg at 250 m/s): KE = ½ × 300,000 × 62,500 = 9.375 × 10⁹ J = 9.375 GJ. More energy than a large city uses in a second.

The work-energy theorem

The work-energy theorem states that the net work done on an object equals the change in its kinetic energy:

This relationship is at the heart of classical mechanics. When you brake a car, the friction force does negative work, reducing the kinetic energy to zero. The amount of energy that must be dissipated as heat equals the initial kinetic energy, which is why stopping distance increases with the square of speed.

Units of kinetic energy

The SI unit of energy is the joule (J). One joule is the energy transferred when a force of one newton acts over a distance of one meter. Other useful units include:

• Kilojoule (kJ): 1000 J. Used for engineering and vehicle calculations.
• Kilowatt-hour (kWh): 3.6 million J. The unit on your electricity bill.
• Calorie (cal) and kilocalorie (kcal): Used in nutrition. One food calorie (kcal) = 4184 J.
• Electronvolt (eV): Tiny unit used in atomic and nuclear physics. 1 eV = 1.602 × 10^-19 J.
• BTU: British Thermal Unit, used in HVAC and engineering in the US. 1 BTU = 1055 J.

Relativistic kinetic energy

At everyday speeds, the classical formula KE = ½mv² is accurate to many decimal places. However, as objects approach a significant fraction of the speed of light, Einstein's special relativity becomes important. The relativistic kinetic energy is:

For speeds below 10% of the speed of light (30,000 km/s), the classical formula gives results accurate to within 1%. This calculator uses the classical formula, which is valid for all everyday objects including aircraft, spacecraft (in orbit), and even most scientific projectiles.

Disclaimer

This calculator uses classical (Newtonian) mechanics and is accurate for all objects moving well below the speed of light. Results are rounded to six significant figures. Always verify critical engineering calculations with a qualified engineer.