How the UFO Travel Calculator Works
This calculator estimates how long an interstellar trip takes at a constant cruising speed, both as measured by observers who stay behind — the "Earth-frame" time — and as experienced by the travelers themselves once special-relativistic time dilation is included. It combines two textbook equations: the ordinary distance/speed relationship t = d / v, and the Lorentz time-dilation factor γ = 1 / √(1 − v²/c²), where c is the speed of light (≈299,792.458 km/s).
Deriving the two travel times
The Earth-frame travel time is simply distance divided by speed: t = d / v — the same relationship used for a car trip, just at astronomical scale. Special relativity adds a second number: the time that passes for the crew onboard, called proper time (τ). A clock moving at speed v runs slow relative to a "stationary" observer by the Lorentz factor γ, so onboard time is τ = t / γ = t × √(1 − v²/c²). At everyday speeds γ is indistinguishable from 1 (no noticeable dilation), but as v approaches c, γ grows without bound and the onboard clock falls further and further behind the Earth-frame clock. For example, at 90% of light speed γ ≈ 2.294, so the crew ages less than half as much as observers back home.
Working with units
- Distance can be entered in light-years (best for interstellar scales), astronomical units (AU, best within a solar system), kilometers, or miles; the calculator converts everything to kilometers internally using 1 ly = 9.4607 × 10¹² km and 1 AU = 149,597,870.7 km.
- Speed can be entered directly as a percentage of the speed of light (%c), or in km/s, km/h, or mph; the speed of light used is c = 299,792.458 km/s (≈186,282 mi/s).
- Select "round trip" to double the one-way distance before computing travel time, useful for mission-planning round trips rather than one-way flybys.
Knowing the limits
This model only works for speeds strictly below c (0 < v < c); at v = c the Lorentz factor is undefined (division by zero), and faster-than-light travel has no accepted mechanism in relativity, so the calculator rejects such inputs. It also ignores acceleration and deceleration ramps, gravitational time dilation near stars or black holes, and relativistic length contraction of the distance as measured by the crew — refinements a full mission-trajectory model would need but which are beyond a simple constant-velocity estimate.