Length Contraction Relativity Calculator
Calculate how much an object shrinks along its direction of motion at relativistic speeds using the Lorentz contraction formula.
Enter Parameters
Enter a value between 0 and 1 (e.g. 0.9 = 90% of c)
Reference: Common Velocities
| Scenario | Speed | v / c | γ (Lorentz factor) | Length ratio (L / L₀) |
|---|
c = 299,792,458 m/s. Length contracts only along the axis of motion.
Summary
Calculate how much an object shrinks along its direction of motion at relativistic speeds using the Lorentz contraction formula.
How it works
- Enter the proper (rest) length of the object and choose a unit.
- Enter the velocity as a fraction of c (e.g. 0.9 for 90% the speed of light) or in m/s.
- The calculator applies L = L₀ × √(1 − v²/c²) and displays the contracted length.
- The Lorentz factor γ = 1 / √(1 − v²/c²) and percent contraction are shown alongside.
- A reference table lists γ and length ratios for common benchmark velocities.
Use cases
- Verify special-relativity homework problems involving Lorentz contraction.
- Understand how a 100-meter spaceship would appear to a stationary observer at 0.99c.
- Explore the relationship between velocity and length contraction for physics courses.
- Compare Lorentz factors across ISS orbital speed, particle accelerator speeds, and hypothetical near-light travel.
Frequently Asked Questions
Last updated: 2026-07-23 ·
Reviewed by Nham Vu