Relativistic Constant-Acceleration Travel Calculator
How long would it take to travel to distant cosmic destinations under constant acceleration? 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.
Relativistic Travel Calculator
v0.2Journey Parameters
Enter acceleration in multiples of g (9.81 m/s²)
Journey Results
Ship Time
3 years, 7 months
Earth Time
5 years, 10 months
Journey Details
- Distance:4.25 ly
- Acceleration:1g (9.81 m/s²)
- Mode:Brachistochrone
- Peak Velocity:94.96% c
- Peak Lorentz Factor (γ):3.192
- Time Dilation Ratio:1.66×
Rocket Mass Ratio
- One-way ratio (accel only):6.22 : 1
- Brachistochrone ratio (accel + decel):38.72 : 1
- = (6.22)² — ratios compound for accel + decel