Lorentz Factor (Special Relativity) Calculator
Calculate the Lorentz factor γ for any velocity and find time dilation and length contraction.
⚡ Physics📐 γ = 1/√(1 - v²/c²)
Velocity as fraction of c (0-0.9999)
Or velocity in m/s (or 0)
Please enter valid values.
Formula & Reference
| Variable | Formula | Units |
|---|---|---|
| Lorentz Factor (Special Relativity) Calculator | γ = 1/√(1 - v²/c²) | γ (gamma) |
Step-by-Step Examples
Example 1
10% Speed of Light
v = 0.1c.
- γ = 1/√(1-0.01) = 1.005
- Barely relativistic
✓ γ = 1.005
Example 2
90% Speed of Light
v = 0.9c.
- γ = 2.294 | Time 2.3× slower | Length 43% of rest
✓ γ = 2.294
Example 3
99.99% c
v = 0.9999c.
- γ = 70.7 | Cosmic ray muons reach Earth via time dilation!
✓ γ = 70.7
Real-World Applications
Physics Students
Understand special relativity concretely.
Space Enthusiasts
Calculate time dilation for near-light travel.
Physics Teachers
Demonstrate relativistic effects.
Particle Physicists
Calculate relativistic particle properties.
Common Mistakes to Avoid
⚠️
Effects only near c
Significant above ~10% c, but technically exist at any speed. GPS satellites need relativistic corrections.
⚠️
Time dilation direction
The traveler ages LESS — moving clocks run slow.
Frequently Asked Questions
Cosmic ray muons? ▾
Created at ~0.999c, half-life 2.2 μs should decay in 660m, but γ≈22 extends life — they reach Earth's surface.
GPS and relativity? ▾
Satellites: -7 μs/day (SR time dilation) + 45 μs/day (GR, weaker gravity) = net +38 μs/day correction needed.
Mass at relativistic speeds? ▾
Relativistic mass m_rel = γm₀ increases. That's why you can't reach c — it takes infinite energy.