Relativistic Rocket Trip Calculator
A trip to another star under constant acceleration — accelerating to the halfway point and decelerating the rest — with the time that passes aboard, the time that passes on Earth, the peak speed and the peak time dilation.
A ship that accelerates at one g for the first half and brakes at one g for the second reaches Proxima Centauri in about 3.
How the relativistic rocket trip calculator works
A ship that accelerates at one g for the first half and brakes at one g for the second reaches Proxima Centauri in about 3.6 years of ship time — while nearly 6 pass on Earth. Push the distance to the galactic center and the crew ages about 20 years while Earth ages 27,000. Constant acceleration makes the relativistic rocket the only way to cross such distances in a lifetime, and the fuel it would need is the reason nobody has built one.
The formulas are exact special relativity for uniform proper acceleration.
Formula: per half: τ = (c/a) acosh(1 + a x / c²); t = √((x/c)² + 2x/a); γ_max = 1 + a x / c²
Worked examples
| Inputs | Ship time for the trip (years) | Note |
|---|---|---|
| Proxima Centauri at 1 g | 3.54 | 3.6 ship years, 5.9 Earth years |
| The galactic center | 19.757 | 20 years aboard, 26,000 on Earth |
| A flyby | 2.292 | faster, but you keep going |
FAQFrequently asked questions
How long to Proxima Centauri at 1 g?
About 3.6 years for the crew and 5.9 for Earth, accelerating halfway and braking the rest. Without braking, under three years aboard.
Why do ship and Earth disagree?
Time dilation: the moving clock runs slow by the Lorentz factor, which at the midpoint of a 1 g trip to Proxima is about 3.2. Over longer trips the gap becomes enormous.
Could a crew reach the galactic center?
In principle in about twenty years of their own time at 1 g — while 26,000 years pass at home. The fuel would be the mass of a small moon; the arithmetic is honest, the engineering is not available.
What does 1 g feel like aboard?
Exactly like standing on Earth, for the whole trip — the floor pointing backwards, then forwards after the turnaround. It is the most comfortable possible way to travel.
Why does the Newtonian estimate fail?
Because it would have the ship exceed light speed after about a year at 1 g. Relativity caps the speed and the acceleration goes into time dilation instead.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- NASA — the US space agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).