Time Dilation Calculator
Compute how much time slows down for a moving object traveling near the speed of light. Use it to explore relativistic time differences in spacecraft travel, particle accelerators, or GPS corrections.
About this calculator
Time dilation is a prediction of Einstein's Special Theory of Relativity: a moving clock ticks slower than a stationary one. The dilated (observed) time t' is related to the proper time t₀ (time measured by the moving observer) by the formula t' = t₀ / √(1 − v²/c²), where v is the object's velocity and c = 299,792,458 m/s is the speed of light. The denominator √(1 − v²/c²) is the inverse of the Lorentz factor γ. At everyday speeds, v²/c² is essentially zero, so t' ≈ t₀ — no noticeable effect. But as v approaches c, the denominator shrinks toward zero and t' grows dramatically. This is why muons created in the upper atmosphere survive long enough to reach Earth's surface, and why GPS satellites require relativistic corrections.
How to use
Suppose an astronaut travels for t₀ = 10 seconds (proper time) at v = 240,000,000 m/s (about 80% of the speed of light). Plug into the formula: t' = 10 / √(1 − (240,000,000)² / (299,792,458)²). First compute v²/c² = (2.4×10⁸)² / (2.998×10⁸)² ≈ 0.6401. Then √(1 − 0.6401) = √0.3599 ≈ 0.5999. So t' = 10 / 0.5999 ≈ 16.67 seconds. An outside observer sees 16.67 seconds pass while the astronaut experiences only 10.
Frequently asked questions
How does time dilation affect astronauts on long space missions?
Astronauts traveling at very high speeds experience time passing more slowly relative to observers on Earth. For missions within our solar system the effect is tiny — at 30 km/s (the ISS orbital speed), the dilation amounts to only microseconds per day. However, at speeds approaching the speed of light, the effect becomes dramatic: an astronaut could age just years while centuries pass on Earth. This is the basis of the 'twin paradox' thought experiment in Special Relativity.
What is the difference between proper time and dilated time in relativity?
Proper time (t₀) is the time measured by a clock that is co-moving with the object — it is the time experienced by the traveler themselves. Dilated time (t') is the longer time interval measured by a stationary observer watching the moving clock. The moving clock always ticks slower from the stationary observer's perspective. The ratio between them is the Lorentz factor γ = 1/√(1 − v²/c²).
Why do GPS satellites need to correct for time dilation?
GPS satellites orbit at about 14,000 km/h, which causes their onboard clocks to tick slightly slower due to Special Relativistic time dilation — losing about 7 microseconds per day. They also gain about 45 microseconds per day due to being higher in Earth's gravitational field (General Relativistic effect). The net gain of ~38 microseconds per day would cause GPS position errors of roughly 10 km per day if uncorrected, so the satellite clocks are pre-adjusted to account for both effects.