# Time Dilation Calculator

URL: https://speedycalculator.com/calculators/physics/time-dilation/
Last updated: 2026-10-25

> The time dilation calculator shows how much more slowly time passes for a fast-moving clock according to special relativity, using the Lorentz factor γ = 1 ÷ √(1 − v²/c²).

## Inputs

- Speed as fraction of light speed
- Time for the traveller (years, days, hours)

## Results

- Lorentz factor γ
- Time for a stationary observer
- Length contraction

## Formula

```
γ = 1 ÷ √(1 − v² ÷ c²)
Δt = γ × Δt₀
```

## Explanation

At everyday speeds the effect is tiny, but GPS satellites must correct for it, and at near light speed it becomes dramatic.

### How to use the Time Dilation Calculator

- **Speed as fraction of light speed**
- **Time for the traveller**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

The Lorentz factor multiplies the moving clock’s elapsed time to give the time measured by a stationary observer.

### Inputs explained

FieldWhat to enterSpeed as fraction of light speedA numberTime for the travellerUnits: years, days, hours

### What each result means

- **Lorentz factor γ** = 1÷sqrt(1 - [Speed as fraction of light speed]^2)
- **Time for a stationary observer** = [Lorentz factor γ] × [Time for the traveller]
- **Length contraction** = 1÷[Lorentz factor γ] × 100

## Worked example

Inputs — Speed as fraction of light speed: 0.9; Time for the traveller: 1 years.

Results — **Lorentz factor γ = 2.294157**; Time for a stationary observer = 2.2942 years; Length contraction = 43.589 % of rest length.

## FAQ

**Is time dilation real?**
Yes, it has been measured with atomic clocks on aircraft and in particle accelerators.

**Why can nothing reach light speed?**
γ becomes infinite, requiring infinite energy.

**What formula does the Time Dilation Calculator use?**
γ = 1 ÷ √(1 − v² ÷ c²).