Gravity slows time. Clocks on Earth’s surface lose about 0.7 nanoseconds per second compared with deep space, and GPS satellites must correct for running about 45 µs a day fast because they sit higher in Earth’s gravity well.
How to use the Gravitational Time Dilation Calculator
- Time far from the mass Δt_f
- Mass M
- Distance of clock 1 from the centre
- Distance of clock 2 from the centre
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the time elapsed far away, the mass of the body (in Earth masses) and the distances from its centre (in Earth radii) of two clocks.
Inputs explained
| Field | What to enter |
|---|---|
| Time far from the mass Δt_f | Units: days, years, s, h |
| Mass M | Units: M⊕, M☉, kg |
| Distance of clock 1 from the centre | Units: R⊕, km, m |
| Distance of clock 2 from the centre | Units: R⊕, km, m |
What each result means
- Time on clock 1 = [Time far from the mass Δt_f]×[f1]
- Clock 1 lags the distant clock by = [Time far from the mass Δt_f]×(1 – [f1])×1e6
- Clock 2 runs ahead of clock 1 by = [Time far from the mass Δt_f]×([f2] – [f1])×1e6
Example values
How the main result changes when Time far from the mass Δt_f changes and everything else stays at the example values above:
| Time far from the mass Δt_f (days) | Time on clock 1 (days) |
|---|---|
| 0.5 | 0.5 |
| 0.75 | 0.75 |
| 1 | 1 |
| 1.25 | 1.25 |
| 1.5 | 1.5 |
| 2 | 2 |
Formula
Δt₀ = Δt_f·√(1 − 2GM/(rc²))
Worked example
Inputs — Time far from the mass Δt_f: 1 days; Mass M: 1 M⊕; Distance of clock 1 from the centre: 1 R⊕; Distance of clock 2 from the centre: 4.17 R⊕.
Results — Time on clock 1 = 0.999999999304 days; Clock 1 lags the distant clock by = 60.145732 µs; Clock 2 runs ahead of clock 1 by = 45.722296 µs.
Key terms
- Proper time
- Time measured by a clock in its own frame.
Frequently asked questions
Does time really run slower in gravity?
Yes – confirmed by atomic clocks at different heights.
How much faster do GPS clocks run?
About 45 µs/day from gravity, minus 7 µs/day from their speed.
What happens at the event horizon?
The factor reaches zero – time appears to stop for distant observers.
Is the effect noticeable on Earth?
Only with precise clocks: ~1 part in 10¹⁶ per metre of height.