What is time dilation?

Time dilation is a consequence of special relativity: a clock moving relative to an observer ticks more slowly than a clock at rest relative to that observer. The faster the motion, the greater the effect. At everyday speeds the difference is immeasurably small; near the speed of light it becomes dramatic.

What is the Lorentz factor?

The Lorentz factor γ = 1 / √(1 − v²/c²) quantifies how much time, length, and momentum differ between frames. At rest γ = 1 (no effect). At 0.9c, γ ≈ 2.294 — meaning a stationary observer measures elapsed time as roughly 2.3 times what the traveler experiences.

Which clock runs slower?

The moving clock runs slower as measured by the stationary observer. If a traveler ages 1 year at 0.9c, an Earth observer measures 2.294 years on their own clock for the same journey. The traveler does not feel time slow down — they experience every second normally.

Proper time (Δt) is the time measured by a clock that travels with the moving object — the traveler's own wristwatch. Dilated time (Δt') is what a stationary observer measures for the same interval. The two are related by Δt' = γ × Δt.

What is gravitational time dilation?

Gravitational time dilation arises from general relativity: clocks in stronger gravitational fields run slower than clocks in weaker fields. GPS satellites must correct for both this effect and the velocity-based (special relativity) effect to stay accurate. This calculator covers only the velocity-based (special relativistic) case.

Can velocity ever reach or exceed c?

No. As v approaches c, γ approaches infinity — it would take infinite energy to reach c. The calculator will show a warning when v ≥ 0.9999c because the result is physically unbounded.

Time Dilation Relativity Calculator

Name: Time Dilation Relativity Calculator
Availability: InStock
Author: Nham Vu

Enter a velocity and proper time to calculate how much time passes for a stationary observer due to special relativistic time dilation.

Inputs

Proper Time (traveler's clock)

Duration experienced by the moving object

Velocity

Fraction of c m/s

× c

c = 299,792,458 m/s

Results appear here after you calculate.

Velocity vs. Time Dilation Reference Table

Velocity (v/c)	Lorentz Factor (γ)	Observer Time per Traveler Year	Extra Time per Year

Observer time = γ × traveler time. At 0.1c, the effect is negligible (<0.5%). Near c, it grows without bound.

Gravitational Time Dilation (General Relativity)

This calculator covers velocity-based time dilation from special relativity. A separate but related effect — gravitational time dilation — comes from general relativity: clocks deeper in a gravitational well (closer to a massive body) run slower than clocks farther away. GPS satellites experience both effects simultaneously. The velocity effect makes satellite clocks run ~7 μs/day slower; the gravitational effect makes them run ~45 μs/day faster — for a net +38 μs/day correction applied in GPS firmware.

Summary

Enter a velocity and proper time to calculate how much time passes for a stationary observer due to special relativistic time dilation.

How it works

Enter the proper time — the duration experienced by the moving traveler.
Select the time unit (seconds, minutes, hours, days, or years).
Enter the velocity as a fraction of the speed of light (e.g. 0.8 for 80% of c) or in m/s.
The calculator computes the Lorentz factor γ = 1 / √(1 − v²/c²).
Dilated time Δt' = γ × Δt is the duration measured by a stationary observer.

Use cases

Verify textbook special relativity problems and homework exercises.
Explore how close to the speed of light a spaceship must travel for meaningful time differences.
Calculate aging differences for twin paradox thought experiments.
Understand why muons created in the upper atmosphere reach Earth's surface.
Compare relativistic time effects across different velocities for physics courses.
Estimate onboard vs. mission-control elapsed time for hypothetical interstellar travel.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu