Length Contraction Calculator
The contracted length of a moving object as seen by an observer it passes, with the Lorentz factor and the speed in ordinary units.
Special relativity: an object moving at speed v is measured shorter along its direction of motion by the Lorentz factor γ = 1 ÷ √(1 − v²/c²).
How the length contraction calculator works
Special relativity: an object moving at speed v is measured shorter along its direction of motion by the Lorentz factor γ = 1 ÷ √(1 − v²/c²). At everyday speeds γ is 1 to a dozen decimal places; at 0.9 c a 100 m ship measures 43.6 m. The object itself notices nothing — in its own frame it is the observer who is contracted.
Formula: L = L₀ ÷ γ; γ = 1 ÷ √(1 − β²); β = v ÷ c
Worked examples
| Inputs | Contracted length | Note |
|---|---|---|
| 100 m ship at 0.9 c | 43.589 | 43.59 m, γ = 2.294 |
| At 0.5 c | 86.6025 | 86.60 m |
| A meter rule at 0.99 c | 0.1411 | 0.141 m |
FAQFrequently asked questions
Does the object really get shorter?
In the observer’s frame, yes — it is a real measurement, not an illusion — but in the object’s own frame nothing changes. Length, like simultaneity, depends on the frame it is measured in.
Does it contract in every direction?
No, only along the direction of motion. Width and height are unchanged, so a fast-moving sphere measures as a flattened ellipsoid.
Why is there no effect at everyday speeds?
γ − 1 is about ½ β²; at an airliner’s 250 m/s, β is 8 × 10⁻⁷ and the contraction of a 70 m aircraft is a few hundred-billionths of a meter.
How does this relate to time dilation?
Same factor, opposite way: moving clocks run slow by γ while moving lengths shrink by γ. Together they keep the speed of light the same for everyone.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.