# Time Dilation Calculator

Calculate relativistic time dilation with the Lorentz factor γ = 1/√(1-v²/c²). Find dilated time, time difference, and velocity as % of light speed.

## What this calculates

Time dilation is one of the most remarkable predictions of Einstein's special relativity: time passes more slowly for objects moving at high speeds relative to a stationary observer. The effect is described by the Lorentz factor γ = 1/√(1 - v²/c²), where v is velocity and c is the speed of light. This calculator shows how much time slows down at any speed.

## Inputs

- **Proper Time (t₀)** (s) — min 0 — Time as measured by the moving observer (in their own reference frame).
- **Velocity Input** — options: Fraction of c (0 to 1), m/s — Choose how to enter the velocity.
- **Velocity** — min 0 — Speed of the moving reference frame. Must be less than the speed of light.

## Outputs

- **Dilated Time (t')** (s) — Time measured by stationary observer: t' = γt₀
- **Lorentz Factor (γ)** — γ = 1/√(1 - v²/c²)
- **Time Difference** (s) — Extra time elapsed for stationary observer: t' - t₀
- **Velocity** (% of c) — Speed as a percentage of the speed of light

## Details

According to special relativity, a clock moving at velocity v relative to a stationary observer ticks more slowly. If the moving clock measures a time interval t₀ (proper time), the stationary observer measures t’ = γt₀, where γ = 1/√(1 - v²/c²). At everyday speeds, γ is indistinguishably close to 1. But at 90% of light speed, γ ≈ 2.29, meaning one second on the moving clock corresponds to 2.29 seconds for the stationary observer.

Time dilation is not a theoretical curiosity — it has been confirmed experimentally many times. Muons created in the upper atmosphere by cosmic rays live long enough to reach Earth’s surface only because time dilation extends their short 2.2 µs half-life. GPS satellites must correct for both special relativistic time dilation (clocks run slower due to orbital speed) and general relativistic effects (clocks run faster due to weaker gravity at altitude).

At 99% of c, γ ≈ 7.09: one year on the spacecraft equals 7 years on Earth. At 99.99% of c, γ ≈ 70.7. As v approaches c, γ approaches infinity, meaning time essentially stops for a photon from its own perspective. No massive object can reach c because the energy required also approaches infinity.

## Frequently Asked Questions

**Q: What is time dilation?**

A: Time dilation is the phenomenon where time passes more slowly for an object moving at high speed relative to a stationary observer. It is a direct consequence of Einstein's special relativity and has been confirmed by numerous experiments, including observations of cosmic ray muons and precision atomic clocks on aircraft.

**Q: What is the Lorentz factor?**

A: The Lorentz factor γ = 1/√(1 - v²/c²) quantifies relativistic effects. At v = 0, γ = 1 (no effect). At v = 0.5c, γ ≈ 1.155. At v = 0.9c, γ ≈ 2.294. At v = 0.99c, γ ≈ 7.089. It approaches infinity as v approaches c.

**Q: What is the twin paradox?**

A: The twin paradox involves one twin traveling at high speed and returning to find the other twin has aged more. If the traveling twin moves at 0.9c for 10 years (their time), 22.9 years pass on Earth. This is not a paradox: the asymmetry comes from the traveling twin accelerating and decelerating, breaking the symmetry between the two frames.

**Q: Is time dilation actually real?**

A: Yes. Time dilation has been measured with extraordinary precision. In 1971, Hafele and Keating flew atomic clocks on aircraft and measured nanosecond differences matching predictions. GPS satellites must compensate for 38 microseconds/day of combined relativistic effects, or positioning would drift by about 10 km daily.

**Q: Why can nothing travel at the speed of light?**

A: As an object approaches the speed of light, the Lorentz factor γ approaches infinity. The relativistic kinetic energy (γ - 1)mc² also approaches infinity, meaning infinite energy would be required. Only massless particles (photons, gluons) travel at exactly c. Massive particles can approach but never reach c.

---

Source: https://vastcalc.com/calculators/physics/time-dilation
Category: Physics
Last updated: 2026-04-21