Space Travel Time Calculator (ship and Earth time, constant g or constant speed)

Understanding the space travel time calculator — concept and principle

This calculator estimates how long a journey to a star takes on board a spaceship and as measured on Earth, either for constant acceleration with a flip and braking at the midpoint, or for constant cruising speed. It also gives the peak speed, Lorentz factor, time saved by the crew and round-trip time. It is a favourite of science-fiction fans and relativity students.

Time dilation at the fast midpoint lets the crew age 2.4 years less than people on Earth.

How it is calculated

Constant acceleration a, each half of distance d:

Earth time t = √((d/c)² + 2d/a)

Ship time T = (c/a) arcosh(a d/c² + 1)

Peak γ = a d/c² + 1

Constant speed v: Earth time = distance ÷ v; ship time = Earth time × √(1 − v²/c²)

With c = 1 light-year per year, 1 g ≈ 1.03 ly/yr².

The principle

Special relativity says moving clocks run slow by the factor γ. A ship accelerating at a steady 1 g gets closer and closer to light speed, so its clocks fall further behind Earth's. For long trips the crew's time grows only logarithmically with distance, while Earth time grows roughly with distance in light-years. Accelerating for half the trip and braking for the other half lets the ship arrive at rest.

Worked example

Default inputs: 4.37 light-years (Alpha Centauri), constant acceleration 1 g, flip at midpoint.

Each half = 2.185 ly; a = 1.0323 ly/yr².
Peak γ = 1.0323 × 2.185 + 1 = 3.25557; peak speed 95.16558449% of c.
Earth time = 2 × √(2.185² + 2 × 2.185 ÷ 1.0323) = 6 years.
Ship time = 2 × (1/1.0323) × arcosh(3.2556) = 3.58 years; time saved 2.42 years.
Round trip on board = 7.16 years.

Each point is the calculator re-run with only “Acceleration (g, for constant acceleration)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Acceleration (g, for constant acceleration)	Time on board (years)
0.25	7.89
0.5	5.38
0.75	4.25
1	3.58
1.25	3.12
1.5	2.79
2	2.32

How to read the result

Even the nearest star takes years on board at 1 g, and a round trip means Earth ages noticeably more than the crew. For distant galaxies the ship time can be surprisingly short, but Earth time is still at least the light travel time.

Common mistakes

Thinking the ship exceeds the speed of light.
Forgetting that Earth time can never be less than the distance in light-years (for a one-way trip).
Ignoring the enormous fuel requirement, which the calculation does not include.

Keep in mind: This is an idealised relativistic calculation. Real spacecraft could not sustain 1 g for years with any known propulsion.

Frequently asked questions

Why is the crew's time shorter?

Moving clocks run slow, and near light speed the effect is large.

How fast does a 1 g ship get on this trip?

About 95% of the speed of light at the midpoint.

Why 1.03 ly/yr²?

9.80665 m/s² expressed in light-years per year squared.

Is fuel included?

No. A real rocket would need an enormous mass ratio.

Sources: P. Gibbs and J. Baez, "The Relativistic Rocket", Usenet Physics FAQ · OpenStax, University Physics Volume 3 (2016), section 5.3 "Time Dilation"

Checked 9 Nov 2026. P. Gibbs and J. Baez, “The Relativistic Rocket”, Usenet Physics FAQ (UC Riverside mirror): t = √((d/c)² + 2d/a), T = (c/a) ch⁻¹(ad/c² + 1), γ = ad/c² + 1, g ≈ 1.03 ly/yr², stopping-trip table (nearest star 4.3 ly → 3.6 years). Constant-speed case: OpenStax, University Physics Volume 3 (2016), §5.3 time dilation. Standard gravity 9.80665 m/s² (standard value).

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