Exoplanet Travel Planner Calculator

Enter the distance to an exoplanet and a constant acceleration to get the crew's travel time, Earth-frame elapsed time, peak speed, and time dilation using the relativistic rocket equation.

Quick Facts

Relativistic rocket equation
τ = (c⁄a)·cosh⁻¹(1 + a·d⁄c²)
Gives the crew's proper (onboard) time τ to cover distance d under constant proper acceleration a.
Speed of light
c = 299,792,458 m/s
Exact by definition; under this model the ship's speed always stays below c.
1 light-year
≈ 9.461 × 10¹⁵ m ≈ 63,241 AU
The distance light travels in one Julian year (365.25 days).
1 g constant thrust
9.80665 m/s²
A commonly assumed sustainable acceleration for a crewed "torch ship" — feels like Earth gravity onboard.

Your Results

Calculated
Ship (Proper) Time
-
Elapsed time on the crew's own clock
Earth-Frame Time
-
Elapsed time for observers at origin/destination
Peak Speed
-
Fraction of light speed at turnover/arrival
Time Dilation Factor
-
Lorentz factor γ at peak speed

Ready

Enter a distance and constant acceleration, then press Calculate.

The Relativistic Rocket Equation Behind This Calculator

Interstellar distances are so large that any realistic starship must spend a long time accelerating before it gets anywhere close to the destination — and it takes just as long to slow back down. This calculator uses the relativistic rocket equation, the standard result from special relativity for a vehicle under constant proper acceleration (the acceleration felt onboard, exactly what an accelerometer bolted to the deck would read). It returns both the crew's own elapsed time and the elapsed time back at the origin and destination, since the two are not the same once a ship spends years near the speed of light.

The formula: proper time, coordinate time, and peak speed

For a ship starting from rest and accelerating at a constant proper acceleration a over a distance d, special relativity gives the crew's proper time as τ = (c⁄a)·cosh⁻¹(1 + a·d⁄c²), and the time measured by observers in the starting frame as t = (c⁄a)·√[(1 + a·d⁄c²)² − 1]. The instantaneous Lorentz factor at the end of that leg is γ = 1 + a·d⁄c², and the speed reached is v = c·√(γ² − 1)⁄γ. For an "accelerate then decelerate" trip, the calculator runs this formula on half the total distance and doubles both times, so the ship reaches maximum speed exactly at the midpoint and arrives at rest. For a continuous-acceleration "flyby," it runs the formula once on the full distance, since the ship never stops thrusting.

Why the two clocks disagree, and what this model leaves out

Time dilation is not a measurement error — clocks moving at a large fraction of c genuinely tick more slowly relative to a "stationary" observer, and the effect compounds the longer the ship spends near that speed. That is why a multi-light-year trip can feel like only a few years to the crew even though it takes noticeably longer at the destination. The model assumes a rigid, idealized ship that can sustain a constant proper acceleration indefinitely with unlimited propellant; it ignores turnaround maneuvers, relativistic Doppler-shifted communications, interstellar dust drag, and the fact that no current propulsion technology can sustain 1 g for years. Treat the results as a physics benchmark for how relativity shapes interstellar travel times, not as an engineering flight plan.

Frequently Asked Questions

How long would a trip to Proxima Centauri b take at 1g?
Proxima Centauri b orbits our nearest neighboring star, about 4.24 light-years away. Using this calculator with a constant 1 g acceleration and an accelerate-then-decelerate profile (so the ship arrives at rest), the crew experiences roughly 3.6 years of ship time, while about 5.9 years pass at the origin and destination. The ship reaches a peak speed of nearly 95% of the speed of light at the journey's midpoint.
Why does the crew experience less time than observers back home?
This is relativistic time dilation. The faster an object moves relative to an observer, the slower its clock runs from that observer's point of view. A ship under constant acceleration spends much of the trip at a large fraction of the speed of light, so its onboard (proper) clock accumulates noticeably less time than clocks that stay behind at the origin or destination.
What does "constant acceleration" mean for a real spacecraft?
It means the engine keeps producing the same felt acceleration (measured onboard, e.g. a steady 1 g) for the whole boost phase, giving the crew Earth-like apparent gravity. No known propulsion system can sustain 1 g for years, so these numbers describe an idealized "torch ship" — useful for understanding the physics of interstellar travel, not a trip you could book today.
What is the difference between the two trip profiles?
"Accelerate then decelerate" burns the engine for the first half of the distance and flips around to brake for the second half, so the ship arrives at rest at the destination — the realistic choice for actually visiting a planet. "Continuous acceleration (flyby)" keeps thrusting the whole way and never slows down, which reaches the destination faster but flies past it at high speed rather than stopping.

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