Lorentz Factor Calculator
Lorentz factor γ from a speed (as a fraction of c, km/s or m/s), with relativistic length contraction, mass-energy and kinetic energy per kilogram.
How it works
γ = 1 ÷ √(1 − v²/c²)
The Lorentz factor is the multiplier in every special-relativity formula: time dilation, length contraction, relativistic momentum and energy. It stays near 1 at everyday speeds — a jet airliner has γ = 1.0000000000004 — and climbs steeply as v approaches c, reaching 7 at 99% and about 7,000 for protons in the LHC. Kinetic energy is (γ − 1)mc², which is why nothing massive can be pushed to c.
Worked example
v = 0.9c: γ = 1/√(1 − 0.81) = 2.294. A 10-year trip on board takes 22.9 years on Earth.
Frequently asked questions
What γ do GPS satellites have?
At 3.9 km/s, γ − 1 ≈ 8 × 10⁻¹¹ — tiny, but it shifts the clocks by 7 µs a day, which GPS must correct.
Is γ ever below 1?
No — for any real speed it is at least 1.
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This calculator is for educational purposes. Double-check important results before acting on them.