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Time Dilation Calculator

Find how time slows at relativistic speeds.

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.

Worked example

A traveller experiences 10 seconds on board at β = 0.8. β² = 0.64 and 1 − 0.64 = 0.36, whose square root is 0.6. So γ = 1 / 0.6 = 1.6667. The observer at rest measures 10 × 1.6667 = 16.6667 s.

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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.

About this calculator

This calculator applies special relativity's time dilation formula, Δt' = γ·Δt, where γ is the Lorentz factor 1/√(1−v²/c²). As an object's speed v approaches the speed of light c, γ grows without bound, meaning a clock moving relative to a stationary observer ticks slower from that observer's point of view — a real, measured effect, not an illusion of perspective.

Particle physicists use this to explain why fast-moving muons created in the upper atmosphere survive long enough to reach the ground despite their short rest-frame lifetime, and satellite engineers must correct GPS clocks for exactly this effect (combined with gravitational time dilation) to keep positioning accurate to within meters. Physics students working through the twin paradox, astrophysics enthusiasts, and engineers dealing with high-precision timing systems all use this calculator to see how dramatically time stretches as speed approaches light speed.

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Comments (1)

  • Editorial team

    Here is a feel for the numbers: at 0.99 of light speed, γ is about 7.09, so 10 years on the moving clock (enter about 315,576,000 s) is roughly 70.9 years for a stationary observer. Enter speed as a fraction of c, not in km/s: divide by 299,792 km/s first. This covers the speed effect only; gravity changes clock rates separately. What speed or scenario are you exploring?

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