Time dilation calculator
Enter a speed and the time that passes on the moving clock. The calculator gives the Lorentz factor γ, the time that passes for an observer at rest, how far the moving clock falls behind and how short a moving object of a given length looks.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the speed and choose its unit: per cent of the speed of light, km/s, m/s or km/h.
- Enter the time measured on the moving clock and choose seconds to years.
- Optionally enter an object’s length at rest to see how long it looks while moving.
- Lorentz factor: γ = 1 ÷ √(1 − β²), with β = v ÷ c and c = 299,792,458 m/s.
- Time dilation: Δt = γ × t₀. The moving clock falls behind by (γ − 1) × t₀.
- Length contraction: L = L₀ ÷ γ.
Worked example
A ship travels at 90 % of c for 1 year by its own clock. γ = 1 ÷ √(1 − 0.81) = 2.294157, so 2.294157 years pass on Earth and the ship’s clock falls behind by 1.294157 years. A 100 m ship looks 43.589 m long from Earth.
At 60 % of c, γ = 1 ÷ √(1 − 0.36) = 1 ÷ 0.8 = 1.25: 10 hours on board are 12.5 hours at rest.
Tips
- Small speeds, tiny effects. At everyday speeds γ prints as 1; look at “falls behind by” to see the difference, computed in a form that keeps its precision.
- It is symmetric. Each observer sees the other’s clock run slow; the twin paradox is resolved by the travelling twin turning around.
- Nothing reaches c. For a speed of 100 % of c or more the calculator shows an error.
Frequently asked questions
What is time dilation?
In special relativity a clock moving relative to you runs slow. If the moving clock shows a time t₀, you measure Δt = γ × t₀, where γ = 1 ÷ √(1 − v²/c²). At 90 % of the speed of light γ = 2.294, so one year on board is 2.294 years for you.
What is the Lorentz factor?
γ = 1 ÷ √(1 − v²/c²). It is 1 at rest, 1.25 at 60 % of c, 2.294 at 90 % of c, and grows without limit as the speed approaches c. It sets the size of time dilation, length contraction and relativistic mass-energy.
What is length contraction?
An object moving past you is shorter along the direction of motion, L = L₀ ÷ γ, where L₀ is its length at rest. A 100 m ship at 90 % of c measures 43.589 m. Its width and height do not change.
Does time dilation affect satellites and astronauts?
Yes, but only slightly. At the International Space Station's 7.66 km/s, special relativity makes its clocks lose about 28 microseconds a day. Gravitational time dilation acts the other way and is not included in this calculator.