Special Relativity Calculator

How it works

1. 1Enter a velocity as a percentage of the speed of light (0–99.999%). The tool converts it to m/s using c = 299,792,458 m/s.
2. 2The Lorentz factor γ = 1 ÷ √(1 − v²/c²) is computed first; all other effects scale from γ.
3. 3Time dilation (Δt = γ·Δt₀), length contraction (L = L₀ ÷ γ), and relativistic mass (m = γ·m₀) are derived from γ and shown instantly.

Use cases

• Physics students verifying time-dilation and length-contraction worked examples.
• Science communicators illustrating why GPS satellites need relativistic corrections.
• Educators building intuition about why nothing with mass can reach light speed.

Frequently asked questions

What is the Lorentz factor γ?

γ = 1 ÷ √(1 − v²/c²), where v is the speed and c ≈ 3×10⁸ m/s. At everyday speeds γ ≈ 1 and effects are negligible. At 80% of c, γ = 1 ÷ √(1 − 0.64) = 1 ÷ 0.6 ≈ 1.667.

How does time dilation work?

A moving clock ticks slower: Δt = γ·Δt₀, where Δt₀ is the proper time. At 0.8c, γ ≈ 1.667, so a 1 s proper interval is observed as ≈ 1.667 s by a stationary observer.

What is length contraction and why does 1 m become less than 1 m?

A moving rod is measured shorter: L = L₀ ÷ γ. At 0.8c, γ ≈ 1.667, so a 1 m rod measures ≈ 0.6 m. The effect is real but only perceptible near light speed — at 10 km/h, γ differs from 1 by less than 10⁻¹⁴.