Quick answer
Time dilation is t = t₀ ÷ √(1 − v²/c²). A clock moving at 90% of the speed of light runs slow by a factor γ = 2.294, so 10 units of proper time correspond to 22.94 units for a stationary observer.
Enter the speed (as a percentage of c, or in m/s) and the proper time on the moving clock. The calculator returns the dilated time and the Lorentz factor.
Related tools: Time Converter: Convert seconds, minutes, hours, days, weeks, months and years. Speed Distance Time Calculator: Solve distance, speed or time. Time Duration Calculator: Elapsed time between two clock times, including across midnight.
How to use the Time Dilation Calculator
- Choose speed given as: Percent of the speed of light and Meters per second.
- Enter speed (above 0).
- Enter proper time (on the moving clock) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Speed given as | Choose one: Percent of the speed of light; Meters per second | Starts at Percent of the speed of light |
| Speed | A number | > 0 |
| Proper time (on the moving clock) | A number | > 0 |
Formula and method
Formula
t = t₀ ÷ √(1 − v² ÷ c²)
IEEE-754 double precision; shown to the decimals indicated.
Special relativity; the speed must be below c.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Speed given as = Percent of the speed of light; Speed = 90; Proper time (on the moving clock) = 10.
| Result | Value |
|---|---|
| Dilated time | 22.941573 |
| Lorentz factor γ | 2.294157 |
Example 2
Inputs: Speed given as = Meters per second; Speed = 250000000.0; Proper time (on the moving clock) = 1.
| Result | Value |
|---|---|
| Dilated time | 1.811922 |
| Lorentz factor γ | 1.811922 |
Example 3
Inputs: Speed given as = Percent of the speed of light; Speed = 99.9; Proper time (on the moving clock) = 5.
| Result | Value |
|---|---|
| Dilated time | 111.83136 |
| Lorentz factor γ | 22.366272 |
The first line is the headline result (dilated time). Below it the time Dilation Calculator lists lorentz factor γ, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Small speeds
At everyday speeds γ is almost exactly 1; at 10% of c it is 1.005. Time dilation becomes large only above about 50% of c, where γ = 1.155.
Verified effects
Dilation has been measured with atomic clocks on aircraft and with muons, and GPS satellites must correct for it (together with gravitational effects). It is a symmetric effect between inertial observers; the twin paradox is resolved by acceleration.
How the result changes with proper time
Holding every other input at the first worked example, this table changes only proper time. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Proper time | Dilated time | Lorentz factor γ |
|---|---|---|
| 5 | 11.470787 | 2.294157 |
| 10 | 22.941573 | 2.294157 |
| 20 | 45.883147 | 2.294157 |
| 40 | 91.766294 | 2.294157 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Speed: entering "100" shows "The speed must be below the speed of light." beside that field and no result.
Choosing between the Time Dilation Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Time Converter](/converters/time-converter/) | value, from and to | Day (d) → Hour (h) |
| [Speed Distance Time Calculator](/science/speed-distance-time-calculator/) | Distance | |
| [Time Duration Calculator](/time/time-duration-calculator/) | start time and end time | Duration |
| [Time Card Calculator](/time/time-card-calculator/) | start times, end times and unpaid break per day | Total time |
| [Download Time Calculator](/technology/download-time-calculator/) | file size, size unit and connection speed | Time |
Assumptions and limitations
- Speed must be below the speed of light
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for speed to confirm this.
Frequently asked questions
Can speed exceed c?
No, the formula needs v < c.
What is proper time?
Time measured by the moving clock.
What is γ at 99%?
At 99% of the speed of light the Lorentz factor γ is about 7.09.
What does the Time Dilation Calculator calculate?
Dilated time for a clock moving at relativistic speed. It returns Dilated time and Lorentz factor γ.
What formula does the Time Dilation Calculator use?
t = t₀ ÷ √(1 − v² ÷ c²). Special relativity; the speed must be below c.
What do I need to enter in the time Dilation Calculator?
You enter Speed given as, Speed and Proper time (on the moving clock).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Speed must be below the speed of light.
What does the “Speed given as” option change?
It sets how the time Dilation is worked out. The choices are Percent of the speed of light and Meters per second.
What is an example of a time Dilation result?
With speed given as Percent of the speed of light, speed 90 and proper time (on the moving clock) 10, the dilated time is 22.941573.
Related calculators
- Time Converter — Convert seconds, minutes, hours, days, weeks, months and years.
- Speed Distance Time Calculator — Solve distance, speed or time.
- Time Duration Calculator — Elapsed time between two clock times, including across midnight.
- Time Card Calculator — Total hours, overtime and gross pay from daily start and end times.
- Download Time Calculator — Time to download a file at a given speed.
- Time From Now Calculator — Clock time after adding or subtracting minutes.
Sources
- CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.