Relativistic Velocity Addition

u = \frac{u' + v}{1 + \frac{u'v}{c^2}}

How velocities add in special relativity. Ensures no velocity exceeds c.

Variables

Velocity in S frame

m/s

Velocity in S' frame

m/s

Relative velocity of frames

m/s

Speed of light

Allowed values: greater than 0

m/s

Your notes

0/5000

Constants in this formula

Speed of Light in Vacuum

299,792,458. Exact by definition.

m/s

Other modern physics formulas with the same quantities

Time Dilation (Special Relativity) shares Speed of light
Length Contraction (Special Relativity) shares Speed of light
Relativistic Momentum (Special Relativity) shares Speed of light
Mass-Energy Equivalence (Special Relativity) shares Speed of light
Relativistic Total Energy (Special Relativity) shares Speed of light
Relativistic Kinetic Energy (Special Relativity) shares Speed of light

Where this formula is listed

Modern Physics formulas, under Special Relativity, alongside Energy-Momentum Relation, Relativistic Doppler Effect, Proper Time and Relativity of Simultaneity.
In the modern physics list it comes after Energy-Momentum Relation and before Relativistic Doppler Effect.
Modern Physics formula sheet, one of 41 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Relativistic Velocity Addition formula?

Relativistic Velocity Addition is written u = (u′ + v)/(1 + u′v/c²). How velocities add in special relativity. Ensures no velocity exceeds c. It belongs to Modern Physics, under Special Relativity.

What are the units in u = (u′ + v)/(1 + u′v/c²)?

In SI units, u is velocity in s frame, measured in m/s; u′ is velocity in s' frame, measured in m/s; v is relative velocity of frames, measured in m/s; c is speed of light, measured in m/s.