Lorentz Factor Calculator
Enter a speed to compute the Lorentz factor γ = 1/√(1 − v²/c²) of special relativity.
Input Data
Results
At a glance:The Lorentz factor γ = 1/√(1 − β²) with β = v/c appears in every special-relativistic formula. It measures how much moving clocks slow (time dilation Δt = γ·Δτ), lengths contract (L = L₀/γ), and momenta grow (p = γmv). At v = 0, γ = 1 (Newtonian limit); as v → c, γ → ∞, which is why massive objects cannot reach light speed. For example v = 0.8c gives γ = 1.667; v = 0.99c gives γ ≈ 7.09. The factor also enters E = γmc² and the relativistic Doppler shift. This tool computes γ from v (any units, vs c ≈ 299792458 m/s).
Formula
γ = 1/√(1 − v²/c²)
β = v/c
$$\gamma = \dfrac{1}{\sqrt{1 - (v/c)^2}}$$How to Use
- Enter the speed v (m/s).
- The calculator returns γ = 1/√(1 − v²/c²).
Case Studies
Particle accelerator
v = 0.99c.
γ = 1/√(1−0.9801) = 1/√0.0199 ≈ 7.09.
Its mass-energy is ~7× its rest energy; lifetime dilated 7×.
FAQ
Why does γ blow up near c?
The denominator √(1 − v²/c²) → 0 as v → c, so γ → ∞. Infinite energy would be needed to accelerate a massive object to c.
What is γ at everyday speeds?
Tiny: for v = 30 km/s (Earth orbit), γ − 1 ≈ 5×10⁻⁹ — negligible. Relativistic effects matter only when v is a sizable fraction of c.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.