Donaldson R F Transit Depth & Duration Calculator
How much a planet dims its star, and for how long, as it crosses in front of it.
How this is worked out
As a planet crosses in front of its star, it blocks a fraction of the starlight equal to the ratio of their disc areas: depth = (Rplanet / Rstar)². How long that takes (the transit duration, from first to last contact) depends on how fast the planet crosses relative to the star's size, and how close to the star's centre the crossing happens (the "impact parameter", b — 0 for a transit straight across the middle, up to about 1 for a grazing transit just clipping the edge): T = (P/π) × sin&supminus;¹[(Rstar/a) × √((1+k)² − b²)], where k = Rplanet/Rstar, P is the orbital period and a is the orbital semi-major axis. This assumes a circular orbit and a near edge-on inclination (typical for the planets we can detect transiting at all).
Frequently asked questions
Why does a bigger impact parameter mean a shorter transit?
Because the planet's path across the star's disc is shorter the further off-centre it crosses (think of a chord nearer the edge of a circle being shorter than one through the middle) — at b close to 1 + k, the transit becomes grazing and vanishingly brief, and beyond that, it doesn't happen at all.
Why is transit depth useful for finding exoplanets?
It only depends on the two radii, not the planet's mass or composition, so even a rough brightness dip tells you the planet's size relative to its star directly — this is exactly how missions like Kepler and TESS find and characterise planets.
Related tools: Kepler's Third Law Calculator, Exoplanet Equilibrium Temperature Calculator, Habitable Zone Calculator.
Source / Last verified: Winn, J. N. (2010), "Transits and Occultations", in Exoplanets (ed. S. Seager), arXiv:1001.2010, the standard circular-orbit transit-duration formula (eq. 14, simplified form with sin i folded into the impact parameter) — read 1 October 2026. The default values on this page are HD 209458 b's commonly-published parameters; this tool reproduces its well-known transit depth (about 1.46%) and duration (about 3.07 hours), matching the commonly-cited observed figures for this planet (one of the first exoplanet transits ever detected).