Relativistic Time Dilation Calculator
Time dilation is one of the most striking predictions of special relativity: a clock moving at velocity v relative to a stationary observer ticks more slowly by the Lorentz factor gamma = 1 / sqrt(1 - v^2/c^2). If the moving clock measures a proper time t0 (the time elapsed on the moving clock), the stationary observer measures a dilated time t = gamma * t0, which is longer. This effect is real and measurable: muons created in the upper atmosphere survive long enough to reach Earth's surface only because their internal clock runs slowly in the Earth's rest frame. GPS satellites correct for both special and general relativistic time dilation to maintain accuracy. Enter the velocity as a fraction of the speed of light (beta = v/c) and the proper time elapsed.
Time dilation formula
gamma = 1 / sqrt(1 - beta^2)
t = gamma * t0
Where beta = v/c is the velocity as a fraction of the speed of light, t0 is the proper time (measured in the moving frame), and t is the coordinate time measured by the stationary observer. The dilated time t is always greater than or equal to t0.
Time dilation at various speeds
- v = 0.1c (beta = 0.1): gamma = 1.005, t = 1.005 t0 (0.5% dilation).
- v = 0.5c (beta = 0.5): gamma = 1.155, t = 1.155 t0 (15.5% dilation).
- v = 0.9c (beta = 0.9): gamma = 2.294, t = 2.294 t0 (129% dilation).
- v = 0.99c (beta = 0.99): gamma = 7.089, t = 7.089 t0 (609% dilation).
- v = 0.9999c: gamma = 70.71, t = 70.71 t0.
Time dilation: frequently asked questions
What is time dilation?
Time dilation is the phenomenon predicted by special relativity where a clock moving relative to an observer ticks more slowly than one at rest. The faster the relative motion, the greater the time dilation. The moving clock's elapsed time t0 relates to the stationary frame time t by t = t0 / sqrt(1 - v^2/c^2).
What is the Lorentz factor?
The Lorentz factor gamma = 1 / sqrt(1 - v^2/c^2) appears in all special relativity transformations. At v = 0, gamma = 1 (no effect). As v approaches c, gamma approaches infinity, meaning time effectively stops for the moving object as seen from the stationary frame.
Has time dilation been experimentally confirmed?
Yes. The Hafele-Keating experiment (1971) flew atomic clocks around the world on aircraft and measured the predicted time differences. GPS satellites run their clocks at a different rate to compensate for relativistic effects, without which GPS would accumulate errors of kilometers per day.
What does the twin paradox say about time dilation?
In the twin paradox, one twin travels at high speed and returns to find they have aged less than the stay-at-home twin. This is not a paradox but a real asymmetry: the traveling twin undergoes acceleration (turn-around), which breaks the symmetry and means their elapsed proper time is genuinely less.
At what speed does time dilation become significant?
Time dilation is negligible at everyday speeds. At 10% of c (0.1c), gamma is only about 1.005 so clocks slow by 0.5%. At 90% of c, gamma is about 2.29, so a 1-year journey takes about 2.29 years in the stationary frame. At 99% of c, gamma is about 7.09.
Official sources
- OpenStax University Physics Vol. 3: Time Dilation.
- NIST: Speed of Light in Vacuum (CODATA 2018).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.