Lorentz Contraction (Length Contraction) Calculator

Compute relativistic length contraction from a proper length and speed (m/s or speed-of-light ratio beta), including the Lorentz factor gamma.

Input

Enter a proper length and speed to compute the relativistic length contraction. Speed can be given as the light-speed ratio beta or in m/s.

Proper length L0

Length of the object measured in its rest frame (meters)

Speed input mode

Choose whether to enter the light-speed ratio beta or a speed in m/s

Light-speed ratio beta

beta

Beta = v divided by c. Enter a value from 0 up to but below 1

Result

Contracted length L

0.43589m

Light-speed ratio beta = 0.9

Lorentz factor gamma

2.294157

Contraction ratio L over L0

0.43589

Shortening percentage

56.411011 percent

Shortening L0 minus L

0.56411 m

L = L0 times the square root of (1 minus beta squared) = L0 over gamma, with gamma = 1 over the square root of (1 minus beta squared) and beta = v over c (c is 299792458 m/s). Length shrinks only along the direction of motion.

How it works

The contracted length is L = L0 times the square root of (1 minus beta squared), which equals L0 divided by gamma. L0 is the proper length measured in the rest frame.
Beta is the speed-of-light ratio, beta = v divided by c, where c is the vacuum speed of light 299792458 m/s. Speed can be entered in m/s or as beta.
The Lorentz factor is gamma = 1 divided by the square root of (1 minus beta squared). It grows as the speed approaches light speed, and length shrinks only along the direction of motion.
Length contraction is undefined when beta reaches 1 or more, that is when the speed equals or exceeds the speed of light.

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