# Time Dilation Formula Calculator

> An interactive calculator for exploring time dilation effects from Einstein's theory of special relativity.

## About This Site

This is a time dilation calculator that helps users understand how time passes differently for travelers moving at relativistic speeds compared to stationary observers. The calculator uses Einstein's time dilation formula to compute journey times, maximum velocities, energy requirements, and other relativistic effects.

## The Time Dilation Formula

t' = t / sqrt(1 - v²/c²)

Where:
- t' = time measured by the observer (on Earth)
- t = time experienced by the traveler
- v = velocity of the traveler
- c = speed of light (299,792,458 meters per second)

## Calculator Features

Users can input:
- Distance in light-years
- Acceleration in m/s²

The calculator outputs:
- Traveler's time (proper time experienced on the spacecraft)
- Observer's time (time passed on Earth)
- Maximum velocity (as a fraction of light speed)
- Total energy required for the journey

## Interactive Charts

The calculator generates 8 interactive visualizations:
1. Speed vs Time - Acceleration towards light speed
2. Distance vs Time - Distance covered over time
3. Traveler's vs Observer's Time - Time passage comparison
4. Energy Requirement vs Distance - Energy needs for relativistic travel
5. Doppler Shift vs Time - How light wavelengths change during travel
6. Velocity vs Distance - Speed at different distances
7. Lorentz Factor vs Time - Time dilation increase with speed
8. Proper vs Observer Distance - Distance measurement differences

## Educational Content

The site explains:
- What time dilation is
- Why time slows down at high speeds
- Real-world evidence (GPS satellites, atomic clock experiments)
- The Twin Paradox and how acceleration resolves it
- Gravitational time dilation

## Languages

Available in 8 languages:
- English (/en/)
- Spanish (/es/)
- German (/de/)
- French (/fr/)
- Italian (/it/)
- Brazilian Portuguese (/pt-BR/)
- Portuguese (Portugal) (/pt-PT/)
- Dutch (/nl/)

## Technical Details

- Static site with client-side calculations
- Uses Chart.js for visualizations
- No server-side processing required
- All physics calculations follow special relativity equations

## Contact

Created by Matthew Clarkson
Website: https://matthewclarkson.com.au