Online Tool Store
Time Dilation Calculator
Calculate special-relativistic time dilation from velocity, and gravitational dilation from a mass and distance, with the Lorentz factor shown.
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Math & Science
Time Dilation Calculator
Frontend preview — no upload or external service.
Dilation result
At 0.87c the Lorentz factor is 2.03: one year aboard the ship corresponds to 2.03 years for the stationary observer.
How the Time Dilation Calculator works
- Enter a velocity as a fraction of the speed of light, or a mass and radius for the gravitational case.
- Enter the elapsed proper time you want converted.
- Read the Lorentz factor as well as the result — it is the quantity that makes the effect intuitive.
The method
Time dilation follows from the Lorentz factor, which stays near 1 until velocity approaches a substantial fraction of light speed and then rises sharply.
γ = 1 / √(1 - v²/c²); dilated time = γ x proper time
At 0.1c, γ is 1.005 — half a percent. At 0.87c it is 2.03, and at 0.99c it is 7.09. The effect is negligible until it suddenly is not.
FAQ
Why is GPS often cited as an example?
Because satellite clocks experience both effects at once: they run slow from their velocity and fast from weaker gravity, with the gravitational effect winning. Without correcting for both, positions would drift by kilometres a day.
Does either effect apply at everyday speeds?
Yes, but immeasurably for most purposes — an aircraft passenger gains tens of nanoseconds on a long flight. It is real and has been measured with atomic clocks.
Which observer's time is 'correct'?
Both. Each measures proper time along their own path, and there is no privileged clock. The difference only becomes comparable when the paths meet again.
How we compare
| Feature | Online Tool Store | A graphing calculator | A stats package |
|---|---|---|---|
| Lorentz factor shown | ✓ | ✗ | ✓ |
| Both velocity and gravity | ✓ | ✗ | Sometimes |
| No install | ✓ | ✓ | ✗ |
| Explains the GPS case | ✓ | ✗ | ✗ |
Time Dilation Calculator leads with the Lorentz factor, since it is the number that shows why the effect is invisible below about a tenth of light speed.