Apply special relativity to find how a moving object’s length contracts and its Lorentz factor.
L = L0·√(1 − v²/c²), γ = 1/√(1 − v²/c²). L0 is the length measured in the object's own rest frame; the contracted length is what an observer seeing it move at speed v measures. Special relativity only — no acceleration or gravity.
Contracted length (m)
How to use this tool
Type the length measured in the object's rest frame — for example a spacecraft's length as measured by its crew.
Type v/c between 0 and just under 1. Everyday speeds give negligible contraction; the effect only matters near light speed.
The tool reports the length measured by an observer who sees the object moving, plus the Lorentz factor.
Contraction grows steeply near c: 40% at 0.8c, about 86.6% at 0.99c.
Formula & worked example
A 10 m rod moving at 0.8c has γ = 1.6667 and a contracted length of 6 m — 4 m (40%) shorter than its proper length.
Limitations — read this before you rely on it
Special relativity for uniform motion only. It assumes an inertial frame, a rigid rod along the direction of motion, and no gravitational fields; transverse dimensions do not contract.
Frequently asked questions
In the observer's frame, yes — its measured length is genuinely shorter. In its own rest frame it is unchanged. Length is frame-dependent in relativity, not an optical illusion.
In principle, but negligibly: a car at motorway speed contracts by far less than an atomic nucleus. The effect only matters at a sizeable fraction of light speed.
Only the dimension along the direction of motion. Width and height perpendicular to the motion are unchanged.
γ = 1/√(1 − v²/c²). It also governs time dilation and relativistic mass increase, and it blows up as v approaches c — which is why massive objects cannot reach light speed.
Yes: each inertial observer measures the other's rods as contracted. The apparent paradox is resolved because the two observers disagree about simultaneity.