Length Contraction Calculator

What Is Length Contraction?

Length contraction is a prediction of special relativity: an object moving at high speed appears shorter along its direction of motion to a stationary observer. The effect becomes significant only when velocity approaches the speed of light.

Length Contraction Formula

$$L = \frac{L_0}{\gamma}$$

$L_0$ is the proper length measured in the object's rest frame, and $\gamma$ is the Lorentz factor:

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

At everyday speeds the contraction is negligible. At $v = 0.5c$, a 1 meter rod contracts to about 0.866 m.

Using This Calculator

Enter proper length and velocity as either m/s or a fraction of $c$. The tool computes contracted length, the Lorentz factor, and the percentage reduction.

Frequently Asked Questions

What is proper length?

Proper length is the length of an object measured in the frame where the object is at rest. It is the longest possible measured length for that object.

Does length contract in all directions?

No. Length contraction applies only along the direction of motion. Dimensions perpendicular to motion are unchanged.

What happens at the speed of light?

Massive objects cannot reach $c$. As $v$ approaches $c$, $\gamma$ grows without bound and contracted length approaches zero.

Is length contraction real or just appearance?

It is a physically measurable effect in relativity. Different inertial observers consistently measure different lengths for the same moving object.

Why use fraction of c?

Expressing velocity as $\beta = v/c$ makes relativistic formulas simpler and avoids very large numbers when working near light speed.

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What Is Length Contraction?

Length Contraction Formula

Using This Calculator

Frequently Asked Questions

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