Time Dilation Calculator (Special Relativity)
How much does time slow down at high speed?
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Time Dilation Calculator (Special Relativity) by TheCalcTools
How the Time Dilation Calculator (Special Relativity) works
Enter the speed as a percentage of the speed of light, a proper time and a rest length.
The Lorentz factor depends only on speed.
Moving clocks run slow by that factor, and lengths along the motion shrink by it.
The formula
Worked example
Using the default values shown in the calculator:
| Speed (% of the speed of light) | 87 |
|---|---|
| Proper time (years) | 1 |
| Rest length (m) | 100 |
- γ = 1 ÷ √(1 − 0.87²) = 2.028.
- One year on the moving clock is 2.028 years for a stationary observer.
- A 100 m ship measures 49.3 m long.
Result:
| Lorentz factor γ | 2.0282 |
|---|---|
| Time measured by a stationary observer (years) | 2.0282 |
| Contracted length (m) | 49.305 |
| Speed (km/s) | 260,819 |
Frequently asked questions
Is time dilation real?
Yes. It is measured routinely, for example in muon lifetimes and in the clocks aboard GPS satellites, which must be corrected for relativity.
Does it matter at everyday speeds?
The effect is negligible. At 100 km/h, γ differs from 1 by about 4 × 10⁻¹⁵.
Sources and further reading
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