Length Contraction Calculator

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Calculates the shortening of an object's length as measured by an observer moving relative to it (Special Relativity).

How To Use

How to use this calculator

Start with your values, or try a preset.

Step 1

Enter Proper Length (L₀) and Velocity (v) in the units shown.

Step 2

Read Lorentz Factor (γ) and Contracted Length (L) in the results panel. Results update as you change the inputs.

Step 3

Choose a preset to load an example, then adjust the values for your situation.

Worked Examples

See the inputs and their calculated results.

Proper Length (L₀): 10 m; Velocity (v): 0.1 c

Lorentz Factor (γ): 1.005037815; Contracted Length (L): 9.949874371 m

Proper Length (L₀): 10 m; Velocity (v): 0.5 c

Lorentz Factor (γ): 1.154700538; Contracted Length (L): 8.660254038 m

Proper Length (L₀): 10 m; Velocity (v): 0.8 c

Lorentz Factor (γ): 1.666666667; Contracted Length (L): 6 m

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