What is length contraction?

Length contraction (also called Lorentz contraction) is the phenomenon where an object moving relative to an observer is measured to be shorter along the axis of motion than its rest length. It is a direct consequence of Einstein's special theory of relativity and only becomes noticeable at velocities approaching the speed of light.

What is the Lorentz factor?

The Lorentz factor γ (gamma) equals 1 / √(1 − v²/c²). At low speeds γ ≈ 1 (no contraction). As velocity approaches c, γ grows toward infinity, meaning the contracted length shrinks toward zero.

Does length contraction only happen along the direction of motion?

Yes. Length contraction only affects the dimension parallel to the direction of motion. Dimensions perpendicular to the motion are unchanged.

Can velocity equal or exceed the speed of light?

No. According to special relativity, massive objects cannot reach or exceed c. Entering v/c = 1 or higher is physically impossible — the calculator will display an error for those values.

Is length contraction real or just an optical illusion?

It is a genuine physical effect, not merely an optical illusion. The contracted length is the actual length measured by an observer in the reference frame where the object is moving, consistent with the Lorentz transformation.

Length Contraction Calculator

Enter an object's rest length and its velocity as a fraction of the speed of light to instantly compute its relativistically contracted length.

Inputs

Rest Length (L₀)

Velocity (v/c) — fraction of speed of light

Enter a value between 0 (stationary) and <1 (just below c).

0c (stationary) 0.9999c (near light speed)

Results

Fill in the inputs and click Calculate to see results.

Quick Examples

Summary

Length contraction is a prediction of Einstein's special relativity: an object moving relative to an observer appears shorter along the direction of motion. This calculator applies the Lorentz transformation to find the contracted length L = L₀ × √(1 − v²/c²), where L₀ is the rest length and v/c is the velocity ratio. Results also include the Lorentz factor γ and the amount of contraction.

How it works

Enter the rest length of the object (the length measured when it is stationary).
Select the unit for the rest length (meters, kilometers, light-years, etc.).
Enter the velocity as a fraction of the speed of light (e.g. 0.9 for 90% of c).
The calculator computes the Lorentz factor γ = 1 / √(1 − v²/c²).
The contracted length L = L₀ / γ is displayed alongside the amount of contraction.

Use cases

Verify textbook special relativity homework answers.
Visualize how spacecraft length appears to shrink at high velocities.
Explore thought experiments involving near-light-speed travel.
Understand why particles in accelerators behave differently than classical predictions.
Teach or learn the Lorentz factor and its physical consequences.
Compare contracted lengths across different velocity scenarios.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu