Time Dilation Calculator (Special Relativity)
Time dilation calculator: how much time passes for a stationary observer while a clock moves at a given fraction of light speed, with the Lorentz factor.
t = t₀√(1 − v²/c²)
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
t = t₀ ÷ √(1 − v²/c²). At 80 % of light speed γ = 1.667: one year on board is 1.667 years on Earth.
Formula
t = t₀√(1 − v²/c²)
| Symbol | Quantity | Units |
|---|---|---|
| t₀ | Proper time (moving clock) | s, ms, µs, ns, min, h, d, wk, yr |
| v | Speed | m/s, km/h, mph, kn, ft/s, c |
| t | Time for the observer at rest | s, ms, µs, ns, min, h, d, wk, yr |
Worked example
Given: t₀ = 1 yr · v = 0.8 c
t = t₀√(1 − v²/c²)
Result: t = 1.66667 yr
Time for the observer at rest for different values of Proper time (moving clock)
| t₀ · Proper time (moving clock) | t · Time for the observer at rest |
|---|---|
| 0.5 yr | 0.83333 yr |
| 0.75 yr | 1.25 yr |
| 0.9 yr | 1.5 yr |
| 1 yr | 1.6667 yr |
| 1.1 yr | 1.8333 yr |
| 1.25 yr | 2.0833 yr |
| 1.5 yr | 2.5 yr |
| 2 yr | 3.3333 yr |
Other values as in the worked example.
Frequently asked questions
1 year at 0.8 c?
1.667 years for the observer at rest.
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