Relative Velocity Calculator
Calculate relative velocity between two objects using classical subtraction or the relativistic Einstein addition formula for speeds near the speed of light.
Classical relative velocity is simple subtraction: if A moves at v₁ and B moves at v₂ (both relative to the ground, same direction positive), then A’s velocity relative to B is v₁ - v₂.
A car at 80 km/h and another at 50 km/h in the same direction: relative velocity = 30 km/h. In opposite directions: 80 + 50 = 130 km/h.
This works perfectly for everyday speeds. It breaks down at speeds approaching the speed of light.
Relativistic velocity addition
Einstein showed that velocities do not add linearly. If A moves at v₁ and B moves at v₂ relative to the ground:
v_rel = (v₁ - v₂) / (1 - v₁v₂/c²)
c = 2.998 × 10⁸ m/s (speed of light)
This formula has important consequences:
No combination of subluminal velocities can exceed c. If A moves at 0.9c and B moves at -0.9c (opposite directions), the Newtonian answer would be 1.8c. The relativistic result: (0.9c + 0.9c) / (1 + 0.81) = 1.8c/1.81 ≈ 0.994c.
Adding c to anything gives c: if A moves at c (a photon) and B moves at 0.99c in the same direction, A’s speed relative to B is (c - 0.99c)/(1 - 0.99c²/c²) = 0.01c/0.01 = c. The photon still moves at c relative to every observer.
When to use which formula
For speeds below ~1% of c (3,000 km/s), the relativistic correction is less than 0.01% and Newtonian is fine. Particle accelerators, cosmic ray physics, and GPS satellite corrections all require relativistic velocity addition.
Enter both velocities in m/s. Positive = one direction, negative = opposite.