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Time Dilation Calculator

Calculate relativistic time dilation with Δt = Δt₀ / √(1 − v²/c²) — how much time stretches for a fast-moving clock as seen by a stationary observer. Also shows the Lorentz factor γ.

 

Formula

$$ \Delta t = \dfrac{\Delta t_0}{\sqrt{1 - v^2/c^2}} = \gamma\,\Delta t_0 \qquad \gamma = \dfrac{1}{\sqrt{1-v^2/c^2}} $$
c = 299,792,458 m/s

Worked example

A clock moving at 0.9c (2.7×10⁸ m/s) has γ ≈ 2.29, so 1 second of its proper time is seen as \( \Delta t = 2.29 \times 1 = 2.29\ \text{s} \) by a stationary observer — the moving clock runs slow.

How it works

Special relativity says moving clocks run slow. A time interval Δt₀ measured on a clock moving at speed v appears stretched to Δt = γΔt₀ for a stationary observer, where the Lorentz factor γ = 1/√(1−v²/c²).

At everyday speeds γ ≈ 1 and the effect is negligible, but it grows without limit as v approaches the speed of light. Enter speed in m/s (the speed of light is 2.998×10⁸ m/s); the calculator returns the dilated time and γ.

Frequently asked questions

What is time dilation?

Time dilation is the slowing of a clock as observed from a frame in which the clock is moving. The faster it moves, the more its time stretches relative to a stationary observer.

What is the time dilation formula?

Δt = Δt₀ / √(1 − v²/c²) = γΔt₀, where Δt₀ is the proper time, v the speed and c the speed of light.

What is the Lorentz factor?

γ = 1/√(1−v²/c²). It equals 1 at rest and rises toward infinity as v approaches c. It multiplies the proper time to give the dilated time.

Is time dilation real?

Yes. It is confirmed by fast-moving muons reaching the ground, atomic clocks flown on aircraft, and the corrections GPS satellites must apply to keep accurate time.

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