Time Dilation Calculator

How it is calculated

Special relativity says a moving clock runs slow as seen by a stationary observer: Δt' = γ × Δt, with the Lorentz factor γ = 1 / √(1 − β²) and β = v / c. Here Δt is the proper time in seconds, measured on the moving clock, and β is the speed as a fraction of the speed of light, so 0.8 means 80 percent of c. β must be at least 0 and below 1, and the time cannot be negative, otherwise there is no result. The dilated time is the time elapsed for the stationary observer. Rounded to four decimals, the effect is almost invisible at everyday speeds and grows quickly as β approaches 1.

Common mistakes

• Entering the speed in km/s or m/s instead of as a fraction of c; 0.8 means 0.8c, not 0.8 m/s.
• Entering β of 1 or more: the formula breaks down, since nothing with mass reaches the speed of light.
• Swapping the two times: the larger number is for the observer at rest, not the moving clock.
• Expecting a noticeable effect at everyday speeds, where γ is practically 1.
• Confusing time dilation with gravitational time dilation, which this tool does not include.