Time dilation calculator
This time dilation calculator shows how much slower a moving clock runs. Example: at 80 % of the speed of light γ = 1.66667, so 10 years on board are 16.6667 years on Earth.
Example: What is given: Proper time t₀ (time on the moving clock) · Enter speed in: Percent of the speed of light · Speed v 80 % von c · Proper time t₀ 10 · Time unit: Years → Result: γ = 1.66667 · observer time t = 16.6667 years. Source: Halliday/Resnick/Walker, Fundamentals of Physics, Kap. „Relativity“ (t = γ·t₀, γ = 1/√(1 − v²/c²)). Updated: .
How it is calculated
Time dilation means that a moving clock runs slower as seen by a stationary observer. It follows from Albert Einstein’s special theory of relativity (1905) and arises because the speed of light is the same for all observers. In everyday life the effect is tiny; close to the speed of light it becomes large.
Formula
t = γ · t₀ with the Lorentz factor γ = 1 / √(1 − v²/c²) and the speed of light c = 299,792,458 m/s. t₀ is the proper time on the moving clock, t the observer’s time. Rearranged: t₀ = t / γ.
Worked example
A spaceship travels at 80 % of the speed of light (β = 0.8). Then γ = 1 / √(1 − 0.8²) = 1.66667. If 10 years pass on board, 10 · 1.66667 = 16.6667 years have passed on Earth, which is 6.66667 years more. At 60 % of c, γ is only 1.25. A GPS satellite moving at 3.874 km/s loses about 7.21376 µs per day because of its motion (the gravitational effect from general relativity works the other way and is larger).
- γ only becomes noticeably larger than 1 from about 10 % of c (γ ≈ 1.005).
- As v → c, γ grows without limit; v = c is unreachable for objects with mass.
- The calculator treats uniform motion without gravity.
Frequently asked questions
What is the Lorentz factor?
The factor γ = 1 / √(1 − v²/c²) by which the time of the moving clock appears stretched. At 80 % of the speed of light γ = 1.66667.
Does an astronaut really age more slowly?
Yes, as measured from Earth: at γ = 1.66667 they age only 6 years in 10 Earth years. They notice nothing unusual themselves.
How fast must you go for the effect to be noticeable?
At 60 % of c, γ = 1.25, at 80 % already 1.66667. At everyday speeds the deviation is around 10⁻¹² and measurable only with atomic clocks.
Sources and legal basis
- Halliday/Resnick/Walker, Fundamentals of Physics, Kap. „Relativity“ (t = γ·t₀, γ = 1/√(1 − v²/c²))
- NIST CODATA 2022: Lichtgeschwindigkeit c = 299 792 458 m/s (exakt)
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