Relativity Calculator

Written: 2002-03-30

This form will calculate Newtonian kinetic energy as well as relativistic mass, time dilation, and kinetic energy for an object of arbitrary mass and velocity. The defaults are for a 3500 pound automobile travelling at 60 miles per hour. Note that you can use scientific notation to enter large numbers, eg- 1E8 m/s for 100000000 m/s. Also note that for obvious reasons, the calculator cannot allow velocity figures equal to or greater than c.

Input Values

Mass (kg) Velocity (m/s)

Calculated Values

Relativistic mass (kg) Time dilation factor
Newtonian KE (J) Relativistic KE (J)
Newtonian momentum
(kg·m/s)		 Relativistic momentum
(kg·m/s)

The time dilation factor is rounded to 6 decimal places. It describes the rate at which a moving observer's perception of time is slowed down by relativistic time dilation. If the time dilation factor is 0.5, the moving observer will age half as quickly as the rest of us.

Notes:

  1. You will find that the time dilation factor rounds to unity for all velocities below 3E5 m/s (300 km/s, or 0.001c).

  2. You will find that at 2.5981E8 m/s, an object's relativistic kinetic energy is equal to the energy that would be yielded from total annihilation to energy. At velocities above this figure, its relativistic KE is greater than its annihilation energy.

  3. Rounding error is large when calculating relativistic KE for low-velocity objects, so the JavaScript code reverts to the Newtonian approximation for velocities below 0.001c.