Length Contraction Calculator
In special relativity an object moving relative to an observer is measured shorter along its direction of motion, an effect called length contraction. The contracted length equals the proper length (the length in the object's own rest frame) times the square root of one minus the speed squared over the speed of light squared, or equivalently the proper length divided by the Lorentz factor. This calculator takes the proper length and the speed as a fraction of the speed of light (beta), and returns the contracted length, the Lorentz factor, the amount of contraction, and the actual speed in metres per second using the exact value c = 299,792,458 m/s. Contraction occurs only along the direction of motion.
Length contraction formula
Lorentz factor gamma = 1 / square root of (1 - beta^2)
Contracted length L = L0 * square root of (1 - beta^2)
Contraction amount = L0 - L
Speed (m/s) = beta * 299,792,458
beta is the speed as a fraction of the speed of light, so beta must be between 0 and 1 (not equal to 1). The speed of light c is exactly 299,792,458 metres per second.
Relativity context
- Length contraction applies only along the direction of relative motion.
- The Lorentz factor is 1 at rest and diverges as speed approaches that of light.
- Proper length is the length measured in the object's own rest frame.
- Effects are negligible at everyday speeds and significant only near light speed.
- The speed of light is a defined constant: exactly 299,792,458 m/s.
Length contraction: frequently asked questions
What is the length contraction formula?
The contracted length is the proper length times the square root of one minus the speed squared over the speed of light squared: L = L0 times sqrt(1 - v^2/c^2). Equivalently L = L0 divided by the Lorentz factor gamma. An object moving relative to an observer is measured shorter along its direction of motion.
What is the Lorentz factor?
The Lorentz factor gamma equals one divided by the square root of one minus beta squared, where beta is the speed as a fraction of the speed of light. Gamma is one at rest and grows without bound as the speed approaches that of light, which is why lengths contract and times dilate at high speed.
Why enter speed as a fraction of light speed?
Relativistic effects depend only on the ratio of speed to the speed of light, beta = v/c, so expressing speed as that fraction avoids huge numbers and rounding error. A beta of 0.5 means half the speed of light. The speed of light used is exactly 299,792,458 metres per second.
Does length contraction affect all directions?
No. Contraction occurs only along the direction of relative motion. Dimensions perpendicular to the motion are unchanged. So a fast-moving cube appears shortened along its travel axis but keeps its other two dimensions.
Is the contraction real or just apparent?
It is a genuine feature of how lengths are measured between frames in special relativity, not an optical illusion, though what a single observer would visually see also involves light travel time. Both observers consider their own measurements correct; there is no preferred frame.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.