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 perspective, it blocks some starlight — 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 / 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) around an M-dwarf (R = 0.3 R☉): δ ≈ 3.7%!

Kepler’s legacy: NASA’s Kepler mission (2009–2018) monitored over 150,000 stars continuously, detecting thousands of planet candidates. Its successor, TESS (2018–present), surveys nearly the entire sky looking for transiting planets around nearby stars. The photometric precision required is remarkable — detecting a 100 ppm signal with noise is exceptionally difficult.