Relativistic Length Contraction Calculator
Compute how much a fast-moving object shortens along its direction of motion according to special relativity.
m
Velocity unit
Length seen by a stationary observer
49.9956 %
contractedObserved length
50%
Length lost
50%
- 1
Speed fraction β = v/c
β = 0.866 = 0.866β is the velocity as a fraction of the speed of light. - 2
Lorentz factor γ = 1 ÷ √(1 − β²)
1 ÷ √(1 − 0.866²) = 1.999824 - 3
Contracted length L = L0 ÷ γ
100 m ÷ 1.999824 = 50.0044
How does this calculator work?
A moving object shortens along its motion by the Lorentz factor: L = L0·√(1 − v²/c²) = L0/γ. Enter the rest (proper) length and the velocity (as m/s or a fraction of c). The contraction is tiny at low speeds and grows sharply as v nears the speed of light, where L approaches zero.
Formula
How this is calculated
Enter the proper length L0 — the length of the object measured in its own rest frame — and the velocity v relative to the observer. The velocity can be given directly in meters per second or as a fraction of the speed of light (β = v/c) using the unit selector; the calculator converts β to m/s by multiplying by c = 2.99792458×10⁸ m/s.
The Lorentz factor γ = 1/√(1 − v²/c²) quantifies relativistic effects. The contracted length seen by the stationary observer is L = L0/γ = L0·√(1 − β²). Contraction occurs only along the direction of motion; dimensions perpendicular to the motion are unchanged. The percent contraction is (1 − L/L0)·100, which equals (1 − 1/γ)·100.
The effect is negligible at everyday speeds and becomes dramatic only as v approaches c, where γ diverges and L → 0. The velocity must be strictly less than c; at or above c the formula is undefined (the square root of a non-positive number), so the calculator requires |β| < 1. L0 must be non-negative.
Frequently asked questions
Length contraction is a real, measurable difference between frames: an observer moving relative to the object measures it as shorter, while in the object's own rest frame its length is unchanged. Both descriptions are correct in their respective frames.
Only along the direction of relative motion. Dimensions perpendicular to the velocity are not affected, so a fast sphere appears flattened into the motion direction.
At v = c the term 1 − v²/c² becomes zero, making γ infinite and L zero, and beyond c it is negative, giving an imaginary Lorentz factor. Massive objects cannot reach c, so the model requires v < c.
Also known as
TG we-Calculate Editorial Team. (2026). Relativistic Length Contraction Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/length-contraction-calculator
TG we-Calculate Editorial Team. "Relativistic Length Contraction Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/length-contraction-calculator.
TG we-Calculate Editorial Team, "Relativistic Length Contraction Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/length-contraction-calculator
@misc{wecalculate_length_contraction_calculator, title = {Relativistic Length Contraction Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/length-contraction-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?