Time Dilation Calculator Formula
Understand the math behind the time dilation calculator. Each variable explained with a worked example.
Formulas Used
Dilated Time (observer)
dilated_time = proper_time / sqrt(1 - pow(velocity_fraction, 2))Lorentz Factor (gamma)
lorentz_factor = 1 / sqrt(1 - pow(velocity_fraction, 2))Variables
| Variable | Description | Default |
|---|---|---|
proper_time | Proper Time (moving frame)(s) | 1 |
velocity_fraction | Velocity (fraction of c) | 0.9 |
How It Works
Time Dilation
Special relativity predicts that time passes more slowly for objects in relative motion.
Formula
t = t_0 / sqrt(1 - v²/c²) = gamma * t_0
where t_0 is the proper time (measured in the moving frame) and gamma = 1/sqrt(1 - v²/c²) is the Lorentz factor.
Worked Example
1 second of proper time at 90% the speed of light.
proper_time = 1velocity_fraction = 0.9
- 01gamma = 1 / sqrt(1 - 0.9²)
- 02gamma = 1 / sqrt(1 - 0.81)
- 03gamma = 1 / sqrt(0.19)
- 04gamma = 1 / 0.4359 = 2.294
- 05t = 1 * 2.294 = 2.294 s (observed from outside)
Ready to run the numbers?
Open Time Dilation Calculator