Relativity
Time dilation
The time seen by a stationary observer for a clock moving at v.
The Formula
t = t0 / sqrt(1 - v^2/c^2)
The time seen by a stationary observer for a clock moving at v.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| t | Dilated time | seconds | The time measured by the stationary observer. |
| t0 | Proper time | seconds | The time measured by the moving clock. |
| v | Velocity | metres per second | The speed of the moving clock. |
| c | Speed of light | metres per second | 299,792,458 metres per second. |
What Each Symbol Means
tseconds
Dilated time
The time measured by the stationary observer.
t0seconds
Proper time
The time measured by the moving clock.
vmetres per second
Velocity
The speed of the moving clock.
cmetres per second
Speed of light
299,792,458 metres per second.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate time dilation page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Time Dilation, filed under Science. Every number the guide produces comes from substituting into this one line.