Add Relativistic Velocities

Name: Add Relativistic Velocities
Author: Jürgen Kummer

Calculator for the addition of two velocities close to the speed of light, which act in the same direction. Velocities in the usual areas of human life can be added up quite normally. If a train goes 100 km/h and you walk forwards on this train at 5 km/h, you have a velocity to the outside world of 105 km/h. At very high speeds this is no longer the case, since matter cannot reach or exceed the speed of light.

The relativistic velocity-addition formula is: v = ( v₁ + v₂ ) / ( 1 + v₁*v₂/c² )

Example: a (hypothetical) rocket flies through space at half the speed of light (50% c). From this a probe is launched also at half the speed of light in the direction of flight. This now moves at 80 percent of the speed of light.

The theory of relativity was developed by Albert Einstein, the special theory of relativity in 1905 and the general theory of relativity in 1916. The principle of relativistic speeds already arises from the special theory of relativity. This says something about the relativity of time, which results from the fact that the speed of light is absolute, independent of the location and speed of the observer. If you move at very high speeds close to the speed of light, then time passes more slowly; see time dilation. What does not change is the perception or measurement of the speed of light, regardless of whether it comes from within this movement or from outside. Velocities below this change according to the calculation above. This absoluteness of the speed of light also results in the famous formula of the theory of relativity, E = m c², according to which energy and mass can be converted into one another using a constant value.

Last updated on 06/30/2025. Author: Jürgen Kummer

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First velocity v₁:
Second velocity v₂:
Speed of light c:		m/s
Resulting velocity v: