Calculator Inputs
Plotly Graph
The chart shows how the Lorentz factor rises as speed approaches light speed.
Example Data Table
This example assumes one hour of proper time on the moving clock.
| Speed | Lorentz Factor γ | Observed Time for 1 Proper Hour | Extra Seconds Gained |
|---|---|---|---|
| 0.10c | 1.005038 | 1.005038 hours | 18.136 seconds |
| 0.25c | 1.032796 | 1.032796 hours | 118.064 seconds |
| 0.50c | 1.154701 | 1.154701 hours | 556.922 seconds |
| 0.75c | 1.511858 | 1.511858 hours | 1,842.688 seconds |
| 0.90c | 2.294157 | 2.294157 hours | 4,658.966 seconds |
| 0.99c | 7.088812 | 7.088812 hours | 21,919.723 seconds |
Formula Used
Here, v is velocity, c is the speed of light, γ is the Lorentz factor, τ is proper time, and t is the time measured by a stationary observer.
How to Use This Calculator
- Enter a velocity value and choose its unit.
- Add the proper time experienced by the moving clock.
- Optionally enter an observed time to reverse the calculation.
- Select your preferred output unit, decimal places, and graph detail.
- Press Calculate Time Dilation to show results above the form.
- Use the CSV or PDF buttons to export the result summary.
Frequently Asked Questions
1. What does the time dilation factor mean?
It is the Lorentz factor, usually written as γ. It tells you how much longer a stationary observer measures a moving clock interval compared with the proper time experienced by that moving clock.
2. Why does the factor stay near one at low speeds?
At everyday speeds, v is tiny compared with light speed. That makes v²/c² extremely small, so the square root term changes only a little and γ remains very close to one.
3. Can I enter speed as a fraction of light speed?
Yes. Choose the fraction or percent light speed option. The calculator converts that value internally, then applies the Lorentz equation using the same physical constant for every unit mode.
4. What is proper time in this tool?
Proper time is the interval measured by the clock traveling with the object. It is the shortest time between the two events in special relativity and acts as the base input for dilation calculations.
5. What happens if I enter an observed time too?
The calculator also reverses the relation. It estimates the proper time that would produce the observed interval at the selected speed, which is useful for checking scenarios from both directions.
6. Does this include gravitational time dilation?
No. This page covers special relativity only, where speed causes the effect. Gravitational time dilation requires general relativity and depends on gravitational potential, not just relative velocity.
7. Why can I not enter light speed or higher?
The Lorentz factor becomes undefined at exactly light speed and imaginary above it for massive objects. Physics therefore limits valid inputs here to velocities strictly below the speed of light.
8. What do the CSV and PDF downloads contain?
They export the result summary shown above the form. The PDF also adds the plotted chart, while the CSV stores the metric and value pairs for quick reuse in spreadsheets.