Time Dilation Calculator
Calculate relativistic time dilation at any speed.
Enter velocity in km/s, mph, or as a percentage of the speed of light and see how time slows for a moving observer.
Time dilation is a real, measured effect predicted by Einstein’s special relativity (1905) and confirmed by countless experiments. A clock that moves fast runs slower than a stationary one. The faster you move, the slower your clock ticks relative to someone standing still.
This is not a trick of perception — clocks on GPS satellites, muons in particle accelerators, and atomic clocks on aircraft all confirm this effect.
The Lorentz Factor (γ):
γ = 1 / √(1 − β²)
Where β = v/c (velocity as a fraction of the speed of light).
The Lorentz factor is always ≥ 1. At rest, γ = 1 (no dilation). As v approaches c, γ approaches infinity.
Time Dilation Formula:
t_earth = t_ship × γ
Where:
- t_ship = time measured on the moving ship (proper time)
- t_earth = time measured by a stationary observer on Earth
- γ = Lorentz factor
So if 1 year passes on the ship at 90% c (γ ≈ 2.294), then 2.294 years pass on Earth.
Time Difference:
Δt = t_earth − t_ship = t_ship × (γ − 1)
This is the extra time that passes on Earth compared to the ship.
Reference Values:
| Velocity | γ (Lorentz Factor) | Earth time per 1 ship year |
|---|---|---|
| 10% c | 1.005 | 1.005 years |
| 50% c | 1.155 | 1.155 years |
| 90% c | 2.294 | 2.294 years |
| 99% c | 7.089 | 7.089 years |
| 99.9% c | 22.37 | 22.37 years |
| 99.99% c | 70.71 | 70.71 years |
Real-World Examples:
- GPS satellites orbit at ~14,000 km/h. Without relativistic corrections, GPS would drift by ~7 µs/day — causing position errors of ~2 km/day.
- Muons created in the upper atmosphere at ~99.7% c have a half-life of 2.2 µs, yet reach Earth’s surface 10+ km below — only possible because of time dilation.
- Astronauts on the ISS (28,000 km/h) age slightly slower — accumulating about 0.01 seconds less per year than people on Earth.
Important Note: This calculator uses special relativity only (constant velocity, no gravity). For gravitational time dilation (near massive objects) or accelerating frames, general relativity is needed.