Exoplanet Transit Depth & Duration Calculator

How it works

depth = (R_p ÷ R★)² · R_p = R★ × √depth · a = ∛(G M★ P² ÷ 4π²) · T₁₄ ≈ (P ÷ π) × (R★ + R_p) ÷ a · P(transit) ≈ R★ ÷ a

When a planet crosses the face of its star it blocks a fraction of the light equal to the ratio of the two disc areas, so the dip in brightness is simply the square of the radius ratio — a Jupiter across a Sun removes about 1%, an Earth about 0.008%. That is why the method finds small planets most easily around small stars and why the star's radius must be known to turn a depth into a planet size. The duration follows from geometry and Kepler's law: the planet's orbital speed and the chord it cuts across the stellar disc give the time from first to last contact. Repeating transits at a fixed period both confirm the signal and, through stacking, let missions dig well below the single-event noise.

Worked example

A Jupiter-size planet (11.2 R⊕) crossing a Sun-size star: (11.2 × 6,371 ÷ 695,700)² = 0.0105, a 1.05% or 10,500 ppm dip. On a 3.5-day orbit around a solar-mass star (a = 0.045 AU) the transit lasts about 3.0 hours, and with 200 ppm noise it is detected at S/N ≈ 53 in a single event. An Earth on the same orbit would dip only 84 ppm.

Frequently asked questions