Time Dilation Calculator
Time is relative. This time dilation calculator lets you explore one of the most mind-bending predictions of Albert Einstein's special theory of relativity: when an object moves at a very high speed, time slows down for it relative to a stationary observer.
Time is Relative: Twin Astronauts
Imagine a pair of twins. One stays on Earth while the other boards a rocket and travels through space at a speed close to the speed of light. When the traveling twin returns, they find that far less time has passed for them than for their sibling on Earth. The stay-at-home twin has aged much more — even though both twins experienced time passing at a perfectly normal rate from their own perspective.
This is not science fiction. It is a measurable, experimentally confirmed phenomenon known as time dilation.
Time Dilation Equation
The time dilation formula is derived from the Lorentz transformation and reads:
Δt' = γ × Δt = Δt / √(1 − v²/c²)
Where:
- Δt — Proper time: the time interval measured by the traveling (moving) observer.
- Δt' — Dilated time: the time interval measured by the stationary observer. This is always longer than Δt.
- γ (gamma) — The Lorentz factor: a dimensionless number ≥ 1 that quantifies how much time is stretched.
- v — Speed of the moving observer.
- c — Speed of light: exactly 299,792,458 m/s (≈ 186,282 mi/s).
- β (beta) — Velocity as a fraction of the speed of light: β = v/c.
The Lorentz Factor (γ)
The Lorentz factor γ = 1 / √(1 − β²) is the key multiplier in time dilation. Its value depends entirely on the speed relative to the speed of light:
- At v = 0: γ = 1 (no time dilation)
- At v = 0.5c: γ ≈ 1.155 (15.5% more time for stationary observer)
- At v = 0.8c: γ ≈ 1.667 (67% more time)
- At v = 0.9c: γ ≈ 2.294 (time more than doubles)
- At v = 0.99c: γ ≈ 7.089 (time is 7× longer)
- At v = 0.999c: γ ≈ 22.37 (time is 22× longer)
- As v → c: γ → ∞ (time dilation becomes infinite)
How to Use This Calculator
- Enter the velocity of the traveling observer. You can input it in m/s, km/h, mph, ft/s, or as a fraction of the speed of light (e.g. 0.8 means 0.8c = 80% of c).
- Enter the proper time — the duration measured by the traveler. Choose your preferred unit: seconds, minutes, hours, days, or years.
- Click Calculate. The calculator will show you the Lorentz factor, the dilated time experienced by the stationary observer, and the time difference.
Measurement Systems
This calculator supports both the metric system (m/s, km/h) and the American (imperial) system (mph, ft/s), making it easy to input velocities regardless of which unit system you prefer. The results include a full velocity conversion table.
Real-World Examples
- GPS satellites orbit at about 14,000 km/h (≈ 3.9 km/s). At this speed, time dilation is tiny but measurable — about 7 microseconds per day — and must be accounted for to keep GPS accurate.
- Muons created in the upper atmosphere by cosmic rays travel at ~0.9997c. Without time dilation, they would decay before reaching Earth's surface. Because time runs slower for them, we detect them on the ground.
- Future space travel: A ship traveling at 0.9c for 1 year of on-board time would experience about 2.3 years passing on Earth. At 0.99c, over 7 Earth years would pass for every traveler year.
Frequently Asked Questions
Does time dilation affect only clocks?
No — it affects all physical processes, including biological aging, chemical reactions, and atomic decay. From the traveler's perspective, nothing is unusual; it is the outside world that appears to run faster.
Is time dilation the same as gravitational time dilation?
No. This calculator computes velocity-based time dilation from special relativity. Gravitational time dilation (as seen near massive objects like black holes) is described by general relativity and uses a different formula.
Why can't anything reach the speed of light?
As velocity approaches c, the Lorentz factor γ approaches infinity. An infinite amount of energy would be required to accelerate a massive object to c, making it physically impossible.
What is a "fraction of c"?
When you enter velocity as a fraction of c (e.g. 0.8), you are saying the object moves at 0.8 × 299,792,458 m/s ≈ 239,833,966 m/s. This notation is common in physics because relativistic effects only become significant when v is a substantial fraction of c.