Length Contraction Calculator
Length contraction is a consequence of special relativity: objects moving at relativistic speeds appear contracted along the direction of motion when measured in the rest frame of the observer. The contracted length is L = L0 * sqrt(1 - v^2/c^2), where L0 is the proper length measured in the object's own rest frame, and v is its velocity relative to the observer. At v = 0.9c, an object with a proper length of 1 meter contracts to about 0.436 meters. The effect is negligible at everyday speeds but becomes dramatic approaching the speed of light. Enter the proper length and velocity as a fraction of c to calculate the contracted length and Lorentz factor.
Length contraction formula
L = L0 * sqrt(1 - beta^2) = L0 / gamma
gamma = 1 / sqrt(1 - beta^2)
L0 is the proper length (rest length). Beta = v/c. The contracted length L is always less than or equal to L0. Contraction occurs only in the direction of motion; transverse dimensions are unaffected.
Length contraction at various speeds
- beta = 0.1 (10% of c): L = 0.995 L0 (0.5% contraction).
- beta = 0.5 (50% of c): L = 0.866 L0 (13.4% contraction).
- beta = 0.9 (90% of c): L = 0.436 L0 (56.4% contraction).
- beta = 0.99 (99% of c): L = 0.141 L0 (85.9% contraction).
- beta = 0.9999: L = 0.01414 L0 (98.6% contraction).
Length contraction: frequently asked questions
What is length contraction?
Length contraction (also called Lorentz contraction) is the phenomenon in special relativity where an object moving at velocity v relative to an observer appears shorter along the direction of motion by a factor of 1/gamma. The contracted length is L = L0 / gamma = L0 * sqrt(1 - v^2/c^2), where L0 is the proper (rest) length.
Does the object actually shrink, or does it just appear shorter?
The contraction is a real physical effect of the geometry of spacetime, not an optical illusion. Measurements made simultaneously in the moving frame and the rest frame genuinely disagree on the object's length because simultaneity is relative. The proper length L0 remains the length in the object's rest frame.
Is length contraction symmetric between two observers?
Yes, it is symmetric. Observer A moving past stationary observer B measures B's rulers as contracted, and B measures A's rulers as contracted. This is consistent because measurements involve events that are not simultaneous in both frames.
In what direction does length contraction occur?
Contraction occurs only along the direction of motion. Dimensions perpendicular to the velocity are unchanged. A moving sphere does not become a sphere of different size; it becomes an oblate ellipsoid compressed along the direction of travel.
Has length contraction been experimentally verified?
Length contraction is consistent with all precision tests of special relativity. The relativistic beaming of light and Terrell rotation (apparent rotation of fast-moving objects) are related effects observed in astrophysics and confirmed in high-energy particle physics experiments at facilities like CERN.
Official sources
- OpenStax University Physics Vol. 3: Length Contraction.
- NIST: Speed of Light in Vacuum.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.