Time Dilation Calculator
Relativistic time dilation for speed and gravity, with GPS.
About this tool
Enter a speed as a percentage of light speed, in km/s or km/h, and a time at home, to see the Lorentz factor, how much the traveller ages and how much a moving clock loses per day. The second section compares an orbiting clock with one on Earth's surface; it's preset for GPS satellites.
Relativity and clocks
Special relativity says a moving clock runs slow by the Lorentz factor, γ = 1 ÷ √(1 − v² ÷ c²). At 80% of light speed γ is 1.667, so a traveller ages 6 years while 10 pass at home, the famous twin paradox, and lengths along the motion contract by the same factor. At everyday speeds γ differs from 1 by tiny amounts, yet atomic clocks on airliners have measured it. General relativity adds gravitational time dilation: clocks higher in a gravitational field run faster, by about GM/c² × (1/r₀ − 1/r). GPS satellites show both effects. Orbiting at 20,200 km and 3.87 km/s, their clocks lose about 7.2 µs a day from speed but gain about 45.7 µs from weaker gravity, a net 38.5 µs a day ahead of ground clocks. Light travels about 11 km in that time, so the system corrects for it. Honest limits: the gravity calculation uses the weak-field approximation, which is excellent for Earth orbits, and ignores Earth's rotation and orbital eccentricity. The light-year converter and the orbital period calculator are related.
Frequently asked questions
What is the Lorentz factor?
γ = 1 ÷ √(1 − v²/c²). It tells you how much time slows and length contracts at speed v.
How much does time slow at 80% of the speed of light?
By a factor of 1.667: 10 years at home is 6 years for the traveller.
Why do GPS satellites need relativity corrections?
Their clocks run about 38 microseconds a day fast (gravity effect minus speed effect), which would cause kilometres of position error.
Does gravity affect time?
Yes. Clocks deeper in a gravitational field run slower; at Earth's surface the effect is about 0.7 parts per billion compared with far away.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.