Lorentz Factor

\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}

The factor by which time, length, and relativistic mass change for a moving object.

Variables

Lorentz factor

Allowed values: 1 or more

unitless

Relative velocity

m/s

Speed of light

Allowed values: greater than 0

m/s

Derivation

Derived from the postulates of special relativity and the invariance of the speed of light.

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

Relativity of Simultaneity (Special Relativity) shares Lorentz factor, Relative velocity, Speed of light
Relativistic Momentum (Special Relativity) shares Lorentz factor, Speed of light
Relativistic Total Energy (Special Relativity) shares Lorentz factor, Speed of light
Relativistic Kinetic Energy (Special Relativity) shares Lorentz factor, Speed of light
Proper Time (Special Relativity) shares Lorentz factor, Speed of light
Mass-Energy Equivalence (Special Relativity) shares Speed of light

Where this formula is listed

Modern Physics formulas, under Special Relativity, alongside Energy-Momentum Relation, Relativistic Velocity Addition and Relativistic Doppler Effect.
In the modern physics list it comes before Time Dilation.
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 Lorentz Factor formula?

Lorentz Factor is written γ = 1/√(1 − v²/c²). The factor by which time, length, and relativistic mass change for a moving object. It belongs to Modern Physics, under Special Relativity.

What are the units in γ = 1/√(1 − v²/c²)?

In SI units, γ is lorentz factor (dimensionless); v is relative velocity, measured in m/s; c is speed of light, measured in m/s.

How is the Lorentz Factor formula derived?

Derived from the postulates of special relativity and the invariance of the speed of light. The result is γ = 1/√(1 − v²/c²).