Exoplanet Transit Depth Calculator

The transit method is the most productive way to detect exoplanets. When a planet passes in front of its star from our line of sight, it blocks a little of the starlight. That dip is the transit.

Transit depth formula:

δ = (R_planet / R_star)²

This is the fraction of stellar flux blocked.

In parts per million (ppm):

δ_ppm = δ × 10⁶

Transit duration (for a circular orbit with impact parameter b = 0):

t_dur = (P / π) × arcsin((R_star + R_planet) / a)

A more complete formula including planet radius and impact parameter b:

t_dur ≈ (P × R_star / (π × a)) × √((1 + k)² - b²)

Where k = R_planet/R_star and b is the impact parameter (0 = central transit, 1 = grazing).

Real-world transit signals:

• Jupiter transiting Sun: δ ≈ (71,492 / 695,700)² ≈ 1.05% (10,500 ppm)
• Earth transiting Sun: δ ≈ (6,371 / 695,700)² ≈ 0.0084% (84 ppm)
• A hot Jupiter (R = 1.2 R_Jup, Jupiter radii) around an M-dwarf (R = 0.3 R☉): δ ≈ 16.9%. A sixth of the star blotted out, which is why small red stars are the easiest targets for finding big planets.

Kepler’s legacy: NASA’s Kepler mission (2009–2018) monitored over 150,000 stars continuously, detecting thousands of planet candidates. Its successor, TESS (Transiting Exoplanet Survey Satellite, 2018 onward), surveys nearly the entire sky looking for transiting planets around nearby stars. The photometric precision this demands is the whole difficulty. Pulling a 100 ppm dip out of a noisy light curve means measuring a star’s brightness to one part in ten thousand, repeatedly, from a moving platform.