Relativistic Velocity Calculator
Add two velocities u and v in the same direction using Einstein’s velocity-addition formula.
Definition
The relativistic (or Einstein) velocity-addition formula tells us how to add two velocities when at least one of them is an appreciable fraction of the speed of light, ensuring the combined velocity never exceeds c.
Formula
w = (u + v) / (1 + uv/c²)
where:
• u, v are the velocities being added (same direction)
• c = 299 792 458 m/s (exact)
• w is the resulting velocity as measured in the same inertial frame
How to Calculate (Step-by-Step)
- Enter the two velocities u and v in metres per second.
- Click “Calculate Relativistic Sum”.
- Read the resulting velocity w and its fraction of the speed of light.
FAQs
Why can’t we just add velocities classically?
At everyday speeds the difference is negligible, but near light-speed the classical addition would allow superluminal speeds, violating special relativity.
What if the velocities are in opposite directions?
Give one velocity a negative sign; the formula still works.
Does the formula work for any units?
Yes, as long as u, v, and c are expressed in the same unit.