Relativistic Rocket Calculator
How long would it take to travel to cosmic destinations using a constantly accelerating rocket? (Like in Project Hail Mary.)
Journey Parameters
Journey Results
Ship Time
3 years, 11 months
Earth Time
13 years, 2 months
Journey Details
- Distance:11.9 ly
- Acceleration:1.5g (14.71 m/s²)
- Mode:Brachistochrone
- Peak Velocity:99.52% c
- Peak Lorentz Factor (γ):10
- Time Dilation Ratio:3.37×
Rocket Mass Ratio
- One-way ratio (accel only):20.39 : 1
- Brachistochrone ratio (accel + decel):416 : 1
- = (20.39)² — ratios compound for accel + decel
This calculator uses the hyperbolic motion equations from special relativity to compute proper (ship) time and coordinate (Earth) time for a spacecraft maintaining constant proper acceleration.
The “infinite fuel” assumption means we ignore the rocket equation entirely — this calculator answers the pure physics question of what relativistic time dilation does to travel times at constant thrust. At 1g, a human-comfortable acceleration, you can reach the Andromeda Galaxy in about 28 years of ship time — while 2.5 million years pass on Earth.
Based on the Relativistic Rocket FAQ by John Baez, and Ask a Mathematician. if you find any mistakes.