Velocity Time Dilation
Lorentz factor and time dilation for motion at relativistic speeds.
Lorentz factor γ2.294157
Speed269813.21 km/s90.000000% of c
γ (Lorentz factor)2.29415734
Time dilationmoving clock runs at 43.588989% rate
Length contraction43.588989% of rest length
Kinetic energy factor1.2942e+0 × mc²
Twin paradox: time elapsed at this speed
Observer time
10.0000 yr
Traveler ages
4.3589 yr
Reference: γ by velocity
| v/c (β) | γ | Clock rate |
|---|---|---|
| 0.1c | 1.0050 | 99.4987% |
| 0.5c | 1.1547 | 86.6025% |
| 0.8c | 1.6667 | 60.0000% |
| 0.9c | 2.2942 | 43.5890% |
| 0.99c | 7.0888 | 14.1067% |
| 0.999c | 22.3663 | 4.4710% |
| 0.9999c | 70.7124 | 1.4142% |
| 0.99999c | 223.6074 | 0.4472% |
Special relativity
γ = 1/√(1−v²/c²). A moving clock ticks at 1/γ the rate of a stationary clock. For a round trip at constant speed, the traveler ages 2×τ while the Earth observer ages 2×t = 2×γτ. For accelerating rockets see the Relativistic Rocket Travel calculator.