Proper time is the time measured by a clock traveling with the moving object — the traveler's own clock. It is always shorter than or equal to the time measured by a stationary observer.

What is the Lorentz factor?

The Lorentz factor γ (gamma) equals 1 / sqrt(1 - v²/c²). At low speeds γ ≈ 1 and time dilation is negligible. As v approaches c, γ grows without bound and dilation becomes extreme.

What happens at exactly the speed of light?

The formula becomes undefined (division by zero) because no massive object can reach c. The calculator blocks inputs at or above 100% of c.

Does this apply to gravity (general relativity)?

No. This calculator only handles velocity-based dilation from special relativity. Gravitational time dilation requires a separate calculation involving the Schwarzschild metric.

Why is the traveler's time shorter?

From the stationary observer's frame, the moving clock runs slow. The traveler ages less than the observer over the same trip — this is the essence of the twin paradox.

Time Dilation Calculator

Calculate relativistic time dilation: enter a velocity and proper time to see how much time passes for a stationary observer vs. a traveler, plus the Lorentz factor.

Traveler Parameters

Velocity

Speed of light c = 299,792,458 m/s

Proper Time (traveler's clock)

Enter a velocity and time above,
then click Calculate.

Formula Reference

Lorentz Factor

γ = 1 / √(1 − v²/c²)

Dilated Time

t' = γ × t

Speed of Light

c = 299,792,458 m/s

Summary

This tool applies Einstein's special relativity equation t' = t / sqrt(1 - v²/c²) to compute time dilation. Enter a velocity as a fraction of the speed of light (or in m/s, km/s, or km/h) and a proper time interval. The calculator returns the Lorentz factor γ (gamma) and the dilated time measured by a stationary observer.

How it works

Enter the velocity of the traveler using any unit (% of c, m/s, km/s, or km/h).
Enter the proper time — the time elapsed on the traveler's clock.
Choose a time unit: seconds, minutes, hours, days, or years.
The Lorentz factor γ = 1 / sqrt(1 - v²/c²) is calculated first.
Dilated time t' = γ × t is displayed alongside the traveler's proper time.
The difference between observer time and traveler time is also shown.

Use cases

Understand how GPS satellites must correct for relativistic time shifts.
Explore thought experiments like the twin paradox.
Check homework problems in modern physics or special relativity courses.
Visualize how time slows as velocity approaches the speed of light.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu