Relativistic Kinetic Energy Calculator

How it is calculated

The tool uses γ = 1 / √(1 − β²) and KE = (γ − 1) × m × c². m is the rest mass in kilograms, β = v/c is the speed as a fraction of the speed of light (a number from 0 up to but not including 1), and c = 299,792,458 m/s. γ is the Lorentz factor, shown to four decimals, and the kinetic energy is in joules.

You enter β, not a speed in m/s: for a speed in m/s, divide by 299,792,458 first. Mass must be above zero, β must be at least 0 and below 1; β = 1 or more returns nothing because γ would be infinite or undefined. At low speeds the result approaches the classical ½mv².

Common mistakes

• Typing a speed such as 180000000 into the β field. It needs the fraction v/c, so 180,000,000 m/s is about 0.6.
• Entering the mass in grams or in electronvolt units. The mass must be in kilograms.
• Entering β as a percentage (60 instead of 0.6). Values of 1 or more return no result.
• Confusing kinetic energy with total energy. Total energy is γmc², which includes the rest energy mc²; the tool gives only the part above rest energy.
• Expecting the classical formula to be close at high speed. At β = 0.6 the classical value is already about 28% off.