Calculate the relative velocity of an object observed from a moving frame of reference using special relativity.
Velocities
Relative Velocity
About this calculator
Overview
In special relativity, velocities do not simply add up (u + v). As speeds approach the speed of light (c), the formula guarantees that no object exceeds c relative to any inertial frame.
💡
Pro Tips
Formula: w = (u + v) / (1 + (u * v) / c²)
u: Velocity of object relative to frame A
v: Velocity of frame A relative to frame B
w: Velocity of object relative to frame B
c: Speed of light (~300,000 km/s)
Velocities must be in the same units (e.g., c, m/s, or km/s). Inputs as fraction of c usually easier.
!
Fun Facts
"If you shine a flashlight forward from a spaceship moving at 0.5c, the light still moves away at exactly 1.0c, not 1.5c."
"At low speeds (much less than c), this formula simplifies to the classical Galilean addition (u + v)."
"This consequence of relativity ensures the speed of light is the universal speed limit."
