physics

Time Dilation Calculator

Calculate time dilation due to relative motion using special relativity. Moving clocks run slower by the Lorentz factor.

Reviewed by Christopher FloiedUpdated April 16, 2026

This free online time dilation calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Proper Time (s)

Velocity (m/s)

How to Use This Calculator

Enter your input values

Fill in all required input fields for the Time Dilation Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

Read the results

The Time Dilation Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Time Dilation Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

•Use the Time Dilation Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
•Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
•Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
•Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Time Dilation Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate time dilation due to relative motion using special relativity. Moving clocks run slower by the Lorentz factor. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Time Dilation Calculator

The Time Dilation Calculator computes how time slows for moving objects according to special relativity. At everyday speeds, the effect is imperceptibly small, but at speeds approaching light, it becomes dramatic. This isn't theoretical — GPS satellites must correct for time dilation (both special and general relativistic) to provide accurate positions. At 99% of light speed, 1 second for the traveler equals ~7 seconds for stationary observers.

The Math Behind It

Time dilation is a direct consequence of Einstein's special relativity postulates: 1. Laws of physics are the same in all inertial frames 2. Speed of light is constant in all inertial frames **Lorentz factor**: γ = 1/√(1-v²/c²) - v = 0: γ = 1 (no dilation) - v = 0.5c: γ = 1.155 - v = 0.9c: γ = 2.294 - v = 0.99c: γ = 7.089 - v = 0.999c: γ = 22.366 - v → c: γ → ∞ **Experimental verification**: - Muons from cosmic rays survive longer than their half-life predicts - Atomic clocks on fast aircraft show time differences - GPS satellites require relativistic corrections (~38 microseconds/day) - Particle accelerator experiments confirm predictions to high precision **Twin paradox**: If one twin travels at high speed and returns, they age less than the stationary twin. This seems paradoxical but is resolved by noting the traveling twin undergoes acceleration (breaking symmetry).

Formula Reference

Time Dilation

t = t₀ / √(1 - v²/c²)

Variables: t₀ = proper time, v = velocity, c = speed of light

Worked Examples

Example 1: Space Travel

1 year at 0.9c (2.697×10⁸ m/s)

Step 1:v²/c² = 0.81

Step 2:γ = 1/√(0.19) = 2.294

Step 3:Dilated time = 1 × 2.294 = 2.29 years

1 year for the traveler equals 2.29 years for stationary observers.

Example 2: Everyday Speed

1 second at 1000 m/s (aircraft)

Step 1:v²/c² = 1.11×10⁻¹¹

Step 2:γ ≈ 1 + 5.56×10⁻¹²

Step 3:Difference: 5.56 ps per second

Only 5.56 picoseconds difference — detectable by atomic clocks.

Common Mistakes & Tips

!Forgetting v must be less than c.
!Confusing proper time (moving clock) with dilated time (observer).
!Applying to accelerating frames (requires general relativity).

Related Concepts

E = mc²

Another consequence of special relativity.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

E = mc² Calculator

Frequently Asked Questions

Why haven't I noticed time dilation?

At everyday speeds, γ is ~1.000000000001. You'd need to travel at a significant fraction of light speed for noticeable effects.

Is time dilation real?

Absolutely. GPS satellites would drift by kilometers per day if relativistic corrections weren't applied. Particle physics experiments routinely rely on it.