Space Travel Calculator — Relativistic Time Dilation

Formula

How this is calculated

Einstein's special relativity predicts that a moving clock ticks more slowly than a stationary one — a phenomenon called time dilation. For a spacecraft travelling at speed v = β·c (where β is the fraction of the speed of light), the Lorentz factor γ = 1 / √(1 − β²) quantifies the stretching of time. From Earth, the trip to a star d light-years away takes t = d / β years. Passengers on the ship experience only τ = t / γ = d√(1 − β²) / β years — shorter by the factor γ.

At everyday speeds β is so tiny that γ ≈ 1 and the difference is immeasurable. But at 90% of c, γ ≈ 2.3; at 99% c, γ ≈ 7; and at 99.9% c, γ ≈ 22. The curve shown plots ship proper time against speed for the chosen distance, revealing how steeply time compresses as you approach c.

This calculator assumes constant-velocity travel (no acceleration phase). Real rocket trajectories involve an acceleration/deceleration arc that alters both the equations and energy requirements enormously; the travel times shown are therefore a lower-bound estimate for constant-speed coasting. Energy requirements are not shown — at relativistic speeds they grow without bound and currently far exceed any feasible propulsion concept.