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Time Dilation Calculator
See how much a moving clock slows down in special relativity. Enter the speed as a fraction of light speed or in km/s and the time measured on the moving clock to get the Lorentz factor γ, the time that passes for a stationary observer and how much a moving object contracts.
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Enter your values to see the result.
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How to use the Time Dilation Calculator
- Enter the speed and choose its unit (fraction of c is easiest).
- Enter the proper time: the time on the moving clock.
- Optionally enter a proper length to see length contraction.
- Read γ, the dilated time and the difference, and compare speeds in the table.
Special relativity formulas
| Quantity | Formula | At 0.8c |
|---|---|---|
| Speed ratio | β = v / c | 0.8 |
| Lorentz factor | γ = 1 / √(1 − β²) | 1.6667 |
| Time dilation | Δt = γ Δτ | 1 year → 1.667 years |
| Length contraction | L = L₀ / γ | 100 m → 60 m |
| Low-speed approximation | γ ≈ 1 + β²/2 | (only for v ≪ c) |
Lorentz factor reference
| Speed | γ | 1 year on the moving clock = |
|---|---|---|
| 0.1c (29,979 km/s) | 1.0050 | 1.005 years |
| 0.5c | 1.1547 | 1.155 years |
| 0.8c | 1.6667 | 1.667 years |
| 0.9c | 2.2942 | 2.294 years |
| 0.99c | 7.0888 | 7.089 years |
| 0.999c | 22.366 | 22.37 years |
c = 299,792,458 m/s exactly. Proper time is always measured by the clock travelling with the object; every other inertial observer measures a longer interval.
Frequently asked questions
What is the time dilation formula?
Δt = γ × Δτ, where Δτ is the proper time on the moving clock, Δt is the time measured by a stationary observer and γ = 1 / √(1 − v²/c²) is the Lorentz factor.
What is the Lorentz factor?
γ = 1 / √(1 − β²) with β = v/c. It is 1 at rest, about 1.155 at 0.5c, exactly 5/3 ≈ 1.667 at 0.8c, about 2.294 at 0.9c and about 7.089 at 0.99c. It grows without limit as v approaches c.
What is length contraction?
An object moving at speed v is measured shorter along its direction of motion by a stationary observer: L = L₀ / γ. At 0.8c a 100 m spaceship is measured as 60 m long.
How much time dilation do GPS satellites experience?
Moving at about 3.87 km/s, a GPS satellite clock runs slow by roughly 7 microseconds per day from special relativity. Gravity makes it run fast by about 45 microseconds per day, so the net effect is about +38 microseconds per day. This calculator shows only the velocity part.
Why do muons from the upper atmosphere reach the ground?
Muons live about 2.2 microseconds in their own frame. At 0.998c, γ ≈ 15.8, so in Earth's frame they live about 35 microseconds and travel roughly 10 km instead of about 660 m.
Can anything reach the speed of light?
No object with mass can. As v approaches c, γ and the energy needed grow without limit, which is why the calculator only accepts speeds below c.
Does this include gravitational time dilation?
No. This tool covers special relativity (velocity) only. Gravitational time dilation from general relativity depends on the gravitational potential and needs a separate calculation.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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