How this instrument works
The first stage is ordinary kinematics: at a constant cruise speed v, covering a distance d takes t = d ⁄ v. Feed in Distance in light-years and Speed as a fraction of light speed, and dividing one by the other hands back the Earth-frame travel time directly in years, because a light-year is by definition the distance light — moving at v = 1 — covers in exactly one year. No unit juggling is needed; the light-year and the fraction-of-c speed were built to cancel cleanly against each other.
The second stage is special relativity, not an afterthought. A clock moving at speed v relative to Earth runs slow by the Lorentz factor, so the proper time it accumulates is t_ship = t_Earth × √(1 − v²). At the crawl of everyday speeds this correction is unmeasurably close to 1, which is why nobody notices it on a plane. Push v toward a real fraction of light speed and the square root starts pulling away from 1 in earnest — the crew's own calendar falls visibly behind the one kept by mission control back on Earth, and the gap is not an illusion of instruments but a genuine difference in how much time each observer's clock ticks through.
The model assumes v is held constant for the whole crossing, so it skips the years a real ship would spend accelerating up to cruise speed and decelerating back down at the far end — no engine, chemical, fusion, or a laser-driven sail, can jump a payload to a fixed fraction of c instantly. That makes the readout a clean idealization of the cruise phase, useful for comparing propulsion concepts and for building intuition about how much dilation a given speed actually buys, but not a full mission timeline with burn phases included.
- Enter Distance, light-years — how far the destination sits, measured in the distance light itself covers in a year. The default, 4.24, is the distance to Proxima Centauri b.
- Enter Speed, fraction of light speed — the ship's constant cruise speed written as a decimal of c, so 0.1 means 10% of light speed. The value must stay below 1.
- Read Travel time, Earth-frame years — how many years pass for an observer who stays behind, found from distance divided by speed.
- Read Travel time, ship-frame years (time dilation) — the shorter duration the crew's own clocks and calendars actually log for the same trip.
- Raise Speed, fraction of light speed toward 1 and watch the two readouts pull apart: Earth-frame time keeps falling smoothly while ship-frame time collapses toward zero.
Worked example — reaching Proxima Centauri b at 10% of light speed
Set Distance, light-years to 4.24, the measured distance to Proxima Centauri b, and Speed, fraction of light speed to 0.1 — an enormously fast cruise speed by any engineering standard available today, but a round number for comparing propulsion ideas. The first formula gives the Earth-frame answer directly: t_Earth = 4.24 ⁄ 0.1 = 42.4 years. Mission control, watching from the solar system, waits 42.4 years for word that the ship has arrived.
The second formula asks what the crew's own clocks recorded over that same crossing: t_ship = 42.4 × √(1 − 0.1²) = 42.4 × √0.99 = 42.1874673333 years, which rounds to about 42.19 years. At only 10% of light speed the Lorentz factor is barely below 1, so the gap between the two readings is small — roughly 78 days — but it is not zero, and it is not a rounding artifact: relativity guarantees the travelling clock reads less elapsed time than the stationary one for any v greater than zero, and this instrument reports the exact difference rather than an approximation of it.
Questions
Why does the ship-frame time come out shorter than the Earth-frame time?
Because a clock in motion relative to an observer ticks slower than that observer's own clock — a direct consequence of special relativity's Lorentz factor, √(1 − v²). Earth-frame time is what a stationary observer's calendar shows; ship-frame time is what the travelling crew's own clocks and biology actually log, and the two can only ever match when v = 0.
Why must Speed, fraction of light speed stay below 1?
Because 1 − v² would go negative for any v at or above the speed of light, leaving the square root undefined — the formula itself refuses an answer, mirroring the physical fact that no object with mass can reach or exceed c. The instrument enforces v < 1 for exactly this reason.
Does the calculator include the years spent accelerating up to cruise speed?
No. It assumes the ship travels the entire distance at a constant Speed, fraction of light speed, so it leaves out however long a real engine would need to reach that speed and later slow back down. Treat the readout as the cruise-phase idealization, not a full launch-to-arrival mission timeline.
How much faster would the trip to Proxima Centauri b need to be for a human lifetime?
At 50% of light speed the same 4.24 light-year distance takes 8.48 Earth-frame years and about 7.34 ship-frame years — well inside a career. At 99% of light speed, Earth still counts roughly 4.28 years, but the crew ages only about 0.6 of a year, the regime where dilation becomes dramatic rather than marginal.
Has any real spacecraft come close to these speeds?
Not remotely. NASA's Parker Solar Probe, the fastest object ever built, reaches roughly 190 km/s at closest solar approach — about 0.06% of light speed — a small fraction even of the 10% cruise speed in this page's own worked example. Reaching a genuine double-digit percentage of c stays a proposed capability, not a demonstrated one.
Is a 10% or 20% light-speed cruise actually being planned by anyone?
Conceptually, yes. The Breakthrough Starshot initiative has proposed pushing gram-scale light-sail probes toward roughly 20% of light speed with ground-based lasers, aiming at the Alpha Centauri system that includes Proxima Centauri b. No such sail has flown; the project remains in the research and engineering-feasibility stage.