Calculate relativistic length contraction at any fraction of the speed of light with visual comparisons, Lorentz factor tables, and speed references.
Length contraction is one of the most counterintuitive predictions of Einstein's special relativity: an object moving at a significant fraction of the speed of light appears shorter along its direction of motion when measured by a stationary observer. The effect, also known as Lorentz-FitzGerald contraction, was first proposed independently by George FitzGerald and Hendrik Lorentz before Einstein's 1905 theory provided the full theoretical framework.
The contracted length follows the formula L = L₀/γ, where L₀ is the rest (proper) length and γ = 1/√(1 − v²/c²) is the Lorentz factor. At everyday speeds the effect is immeasurably small, but at 86.6% the speed of light the object contracts to exactly half its rest length. At 99.5% c, it would appear just one-tenth its original size.
This calculator computes the contracted length for any velocity and rest length, displays the Lorentz factor, provides visual comparison bars, and includes tables showing how contraction scales across a range of velocities from walking speed to near-light speed.
This calculator makes one of special relativity's most fascinating predictions tangible and visual. The comparison bars and speed tables build intuition about how dramatically space itself contracts at relativistic velocities, connecting abstract equations to physical reality. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.
Lorentz contraction: L = L₀ × √(1 − v²/c²) = L₀/γ, where L₀ is the rest (proper) length, v is velocity, c is the speed of light (299,792,458 m/s), and γ = 1/√(1 − v²/c²) is the Lorentz factor.
Result: Contracted length ≈ 50.0 m (γ = 2.0)
At 86.6% the speed of light, γ = 2.0, so a 100-meter object contracts to exactly 50 meters as seen by a stationary observer.
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A relativistic effect where objects moving at high speeds appear shorter in their direction of motion to a stationary observer. The effect is described by L = L₀/γ.
It is a real physical effect — the measured distance genuinely contracts. It is not an optical illusion but a consequence of the geometry of spacetime.
No. In your own reference frame, everything appears normal. Length contraction is only observed by someone in a different frame of reference measuring your length.
Below about 10% of the speed of light, contraction is less than 0.5%. It becomes dramatically noticeable above 50% c and extreme above 90% c.
Yes, indirectly. Muon lifetime experiments and particle accelerator measurements are consistent with Lorentz contraction. Directly measuring contracting objects is impractical at available speeds.
No. Length contraction occurs only along the direction of motion. Perpendicular dimensions are unaffected.