Relativistic Length Contraction Calculator
Calculate the apparent length of an object moving at relativistic speed.
Based on Einstein's special theory of relativity.
Contracted Length
According to Einstein’s special theory of relativity, an object moving at velocity v relative to an observer appears shorter in the direction of motion:
L = L₀ × √(1 − v²/c²) = L₀ / γ
Where:
- L = Observed (contracted) length
- L₀ = Proper length (the object’s length in its own rest frame)
- v = Velocity relative to the observer
- c = Speed of light = 2.998 × 10⁸ m/s
- γ = Lorentz factor = 1/√(1 − v²/c²)
Key observations:
- Length contraction only occurs along the direction of motion
- Perpendicular dimensions are unchanged
- The effect is negligible at everyday speeds (even at 1% of c, contraction is only 0.005%)
- At 99% c: L = L₀/7.09 — object appears 7× shorter
- At 99.9% c: L = L₀/22.4 — object appears 22× shorter
Is this real? Yes. The contraction is not an optical illusion — it is a genuine geometric property of spacetime. Particle accelerator experiments confirm relativistic effects constantly.
Practical example: Protons in the Large Hadron Collider travel at 99.9999991% the speed of light. Their diameter in the direction of travel is contracted by a factor of γ ≈ 7,460 — from ~0.85 fm to only ~0.0001 fm in the lab frame.