Calculate relativistic travel times to nearby stars with constant acceleration or cruise speed. Includes time dilation, ship vs Earth time, and interstellar destination table.
How long would it take to reach Earth's nearest stellar neighbors? The answer depends dramatically on the propulsion technology. At a constant 1g acceleration (comfortable Earth-like gravity) with a midpoint flip-and-decelerate profile, you could reach Proxima Centauri in just 3.5 years of ship time — even though 5.9 years pass on Earth. Welcome to relativistic time dilation.
Einstein's special relativity guarantees that time passes more slowly for the traveler. At high fractions of light speed, a crew could cross the entire Milky Way in a single human lifetime (ship time), though millions of years would pass on Earth. The Lorentz factor γ = 1/√(1−v²/c²) quantifies this effect: at 99% of light speed, γ = 7.09, meaning 7 years pass on Earth for every 1 year on the ship.
This calculator models two flight profiles: constant acceleration with midpoint turnaround (most realistic for a fusion or antimatter drive), and constant cruise speed. The interstellar destinations table shows travel times to 9 major targets from Proxima Centauri to the Andromeda Galaxy.
Science fiction writers need realistic travel times. Physics students explore relativistic mechanics. Space enthusiasts compare propulsion scenarios. This calculator handles the relativistic math for constant acceleration — a problem that requires hyperbolic functions most people can't solve by hand. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.
Constant acceleration (relativistic): τ = (c/a)×acosh(a×d/(2c²)+1) for half-trip. Earth time: t = (c/a)×sinh(a×τ/c). Peak v = c×tanh(a×τ/c). Time dilation: γ = 1/√(1−v²/c²).
Result: Earth time: 5.87 years, Ship time: 3.56 years, Peak: 95.3% c
Accelerating at 1g to the midpoint of the 4.24 ly trip to Proxima Centauri, then decelerating at 1g: 5.87 years pass on Earth but only 3.56 years for the crew, reaching 95.3% c at midpoint. γ = 3.3 at peak.
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Moving clocks tick slower. At speed v, ship time passes at rate 1/γ compared to Earth time, where γ = 1/√(1−v²/c²). At 99% c, γ ≈ 7 — 7 Earth years per 1 ship year.
To decelerate and arrive at rest. Without flipping, you'd fly past the destination at near light speed. The flip-and-brake profile gives constant artificial gravity the entire trip.
Relativistic rocket equation: mass ratio = e^(a×τ/c) for each half. For 1g to Proxima: ~3:1 mass ratio with perfect antimatter. Fusion drives would need far more mass.
At 1g constant acceleration, the crew could reach Andromeda (2.5M ly) in about 28 years of ship time — but 2.5 million years would pass on Earth.
Special relativity prohibits accelerating massive objects to or beyond c. Speculative concepts (Alcubierre drive, wormholes) require exotic matter not known to exist.
It explores the physics any advanced craft would face crossing interstellar distances — how long it takes at various speeds, what time dilation the occupants experience. Use the examples and notes as a quick consistency check before trusting any value.