Relativity Calculator

Lorentz factor γ, time dilation and relativistic mass at a given velocity.

Formulas

γ = 1 / √(1 − v²/c²)
Time dilation: t = γ · t₀
Relativistic mass: m = γ · m₀
Length contraction: L = L₀ / γ

Physics behind special relativity

Einstein's special theory says the laws of physics are the same for all inertial observers and that the speed of light is the same in all inertial frames. Consequences: time runs slower, lengths contract, and relativistic mass grows as relative velocity approaches c. For everyday speeds, γ ≈ 1 and all corrections are negligible; for v = 0.8 c, γ = 5/3 ≈ 1.667.

Worked example

v = 0.8 c

γ = 1/√(1 − 0.64) = 1/√0.36 = 1/0.6 ≈ 1.6667
t = 1.6667 · 1 s ≈ 1.667 s
m = 1.6667 · 1 kg ≈ 1.667 kg

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FAQs

What is the Lorentz factor?

γ = 1/√(1 − v²/c²).

Can anything travel at c?

Only massless particles.