Time Dilation Calculator

Special Relativistic Time Dilation

According to Einstein's special relativity, a moving clock runs slower relative to a stationary observer. The effect becomes significant only at speeds approaching the speed of light. Proper time $t_0$ is measured in the object's rest frame; dilated time $t$ is what a stationary observer measures.

Formula

$$t = \frac{t_0}{\sqrt{1 - v^2/c^2}}$$

Here $v$ is velocity, $c$ is the speed of light, and the Lorentz factor $\gamma = 1/\sqrt{1 - v^2/c^2}$ scales proper time to dilated time. Enter velocity as a fraction of $c$ (for example, 0.5 means half the speed of light).

Practical Scale

At everyday speeds the effect is negligible. GPS satellites must correct for both special and general relativistic time shifts because they move fast and sit in weaker gravity. Particle accelerators routinely observe measurable dilation for subatomic particles.

Frequently Asked Questions

What is proper time?

Proper time is the time measured by a clock traveling with the object. It is the shortest time interval between two events that occur at the same place in the object's frame.

Why must velocity stay below the speed of light?

As $v$ approaches $c$, the denominator $\sqrt{1 - v^2/c^2}$ approaches zero and dilated time grows without bound. Objects with mass cannot reach $c$ in special relativity.

What is the Lorentz factor?

The Lorentz factor $\gamma$ tells how much time is stretched. At $v = 0.5c$, $\gamma \approx 1.155$, so 60 seconds of proper time becomes about 69 seconds for a stationary observer.

Is time dilation the same as gravitational time dilation?

No. This calculator covers special relativistic dilation from relative motion. General relativity adds a separate effect from gravity, which GPS systems also account for.

Can both observers disagree on whose clock is slow?

Each observer sees the other's clock run slow. The apparent paradox is resolved because the observers cannot compare clocks at a single location without accelerating, which breaks the symmetry.

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Time Dilation

Special Relativistic Time Dilation

Formula

Practical Scale

Frequently Asked Questions

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