Time Dilation Calculator

The Time Dilation Calculator applies Einstein's theory of special relativity to any speed you enter. It computes the Lorentz factor (γ), shows how much more slowly a moving clock ticks, how much a moving object shortens through length contraction, and how far apart a fast-moving space traveler and a person on Earth would age. An interactive clock-rate curve marks exactly where your speed sits between everyday motion and the speed of light.

What Is Time Dilation?

Time dilation is one of the most famous predictions of special relativity: time passes more slowly for an object in motion than for an observer at rest. A clock flying past you ticks slower than the one on your wrist, and the closer its speed gets to the speed of light c (299,792,458 m/s), the more extreme the slowing becomes. This is not an illusion or a mechanical fault — it is a genuine property of space and time, confirmed by atomic clocks flown on aircraft, particle lifetimes in accelerators, and the everyday timing corrections built into GPS satellites.

Time Dilation Formula

The whole effect is governed by a single quantity, the Lorentz factor γ, which depends only on how fast you move relative to light.

Here \( \Delta t_0 \) is the proper time measured by the moving clock, \( \Delta t \) is the longer time measured by the stationary observer, \( L_0 \) is the object's rest (proper) length, and \( L \) is its shorter length while moving. Because γ is always at least 1, moving clocks always run slow and moving objects always contract — never the reverse.

The Lorentz Factor at a Glance

A Worked Example

Suppose a spaceship travels at 0.9c for what its crew measures as one year of proper time. First find β = 0.9, then γ = 1 / √(1 − 0.9²) = 1 / √0.19 ≈ 2.294. Time dilation gives Δt = 2.294 × 1 year ≈ 2.29 years passing on Earth, so the crew returns about 1 year and 107 days younger than everyone at home. Meanwhile a 100 m ship contracts to 100 / 2.294 ≈ 43.6 m along its direction of travel, as measured from Earth.

Real-World Time Dilation

How to Use This Calculator

1. Enter a velocity: Type a speed and pick a unit — a fraction or percentage of light speed, km/s, m/s, km/h, or mph.
2. Set a traveler time and length (optional): Enter how long the traveler experiences the trip and the rest length of a moving object. Defaults are 1 year and 100 metres.
3. Click Calculate: The tool computes the Lorentz factor, the dilated Earth time, and the contracted length.
4. Read the results: See γ on the hero panel, your speed marked on the clock-rate curve, the twin age gap, the length ruler, and a full step-by-step breakdown.

Frequently Asked Questions

What is time dilation?

Time dilation is a prediction of Einstein's special relativity: a clock moving relative to an observer ticks more slowly than a clock at rest. The faster the relative speed, the greater the slowing. The effect is described by the Lorentz factor and becomes dramatic only as the speed approaches the speed of light.

What is the time dilation formula?

The dilated time is the moving clock's proper time multiplied by the Lorentz factor: Δt = γ × Δt₀, where γ = 1 / √(1 − v²/c²). Here v is the relative speed and c is the speed of light.

What is the Lorentz factor (gamma)?

The Lorentz factor γ equals 1 / √(1 − β²), where β is the speed as a fraction of light speed. It equals 1 at rest, about 2 at 87% of light speed, about 7 at 99%, and grows without limit as the speed approaches c.

How fast do you need to go for time dilation to matter?

Everyday speeds barely register: even the International Space Station at about 7.66 km/s dilates time by only around 10 milliseconds per year. Time dilation becomes noticeable only above roughly 10% of the speed of light, where the Lorentz factor rises above 1.005.

What is length contraction?

Length contraction is the companion effect to time dilation: an object in motion is measured as shorter along its direction of travel by the same Lorentz factor. Its contracted length equals its rest (proper) length divided by γ. At 87% of light speed a 100-metre ship measures about 50 metres.

What is the twin paradox?

In the twin paradox, one twin travels at high speed and returns younger than the twin who stayed home, because the traveller's clock ran slow. This calculator estimates that age gap: for every unit of time the traveller experiences, γ units pass on Earth.

Additional Resources

• Time Dilation - Wikipedia
• Lorentz Factor - Wikipedia