Time Dilation Calculator
Time dilation is the special relativity result that a moving clock ticks more slowly. The effect is tiny at everyday speeds and dramatic once you get close to the speed of light.
Dilated time in seconds
2.2942
- Lorentz factor
- 2.2942
- Velocity in metres per second
- 269,813,212
- Extra seconds gained
- 1.2942
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
t = t0 / sqrt(1 - v^2/c^2), where the reciprocal of the root is the Lorentz factor
- t
- The time measured by the stationary observer
- t0
- The proper time, measured by the moving clock
- v
- The speed of the moving clock
- c
- The speed of light, 299,792,458 metres per second
How to check the result by hand
- 1
Divide the velocity by the speed of light
This fraction is often written as beta. At ninety percent of light speed beta is 0.9, which is the only number the rest of the formula needs.
- 2
Square beta and subtract it from one
0.9 squared is 0.81, and one minus 0.81 is 0.19. This is the quantity under the square root.
- 3
Take the square root
The square root of 0.19 is about 0.43589, and its reciprocal is the Lorentz factor.
- 4
Take the reciprocal
One divided by 0.43589 is 2.294157, which is the Lorentz factor at ninety percent of light speed.
- 5
Multiply the proper time by the factor
One second of proper time becomes 2.294157 seconds for the stationary observer, which is the dilation.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Time Dilation page.