Length Contraction

L = \frac{L_0}{\gamma} = L_0\sqrt{1 - \frac{v^2}{c^2}}

Moving objects are shortened in the direction of motion as measured by a stationary observer.

Variables

Contracted length

Allowed values: greater than 0

L₀

Proper length

Allowed values: greater than 0

Lorentz factor

Allowed values: 1 or more

unitless

Relative velocity

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

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 after Time Dilation and before Relativistic Momentum.
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 Length Contraction formula?

Length Contraction is written L = L₀/γ = L₀√(1 − v²/c²). Moving objects are shortened in the direction of motion as measured by a stationary observer. It belongs to Modern Physics, under Special Relativity.

What are the units in L = L₀/γ = L₀√(1 − v²/c²)?

In SI units, L is contracted length, measured in m; L₀ is proper length, measured in m; γ is lorentz factor (dimensionless); v is relative velocity, measured in m/s; c is speed of light, measured in m/s.