Relativistic Velocity Addition Calculator
Add velocities using relativistic formula
About this calculator
The Relativistic Velocity Addition Calculator computes the combined velocity when two objects are moving at very high speeds, approaching the speed of light. Unlike classical physics where velocities simply add together, Einstein's special relativity requires a more complex formula that accounts for time dilation and length contraction effects. This calculator is essential for physicists, students, and researchers working with particle accelerators, cosmic ray studies, or theoretical physics problems involving near-light-speed scenarios.
How to use
Enter the first velocity and second velocity in the input fields, specifying units (m/s, km/s, or as a fraction of light speed). The calculator will automatically apply Einstein's relativistic velocity addition formula: v = (v₁ + v₂)/(1 + v₁v₂/c²). The result shows the combined velocity, which will always be less than the speed of light.
Frequently asked questions
When do I need relativistic velocity addition?
Use this formula when either velocity exceeds about 10% of light speed (30,000 km/s). Below this threshold, classical addition gives acceptable approximations.
Why can't the result exceed light speed?
Einstein's formula ensures the combined velocity never surpasses light speed, reflecting the universal speed limit imposed by special relativity.
What units can I use for input velocities?
You can input velocities in meters per second, kilometers per second, or as fractions of light speed (c) for convenience.