Exoplanet Transit Depth Calculator

Calculate how much a star's brightness dips when a planet transits it, δ = (Rp/R★)², in fraction, percent, ppm, and millimagnitudes — or work backward from an observed depth to a planet radius — with a to-scale transit diagram and a synthetic light curve.

Exoplanet transit depth calculator

In the simplest model — a uniform stellar disk, planet crossing dead-center — the fractional brightness drop is just the ratio of the two disks' areas: δ = (R_p / R_star)². Real light curves deviate somewhat from this (limb darkening, grazing transits), but it's the right first estimate, and the one every more detailed model corrects.

Planet radius (R_p)

Stellar radius (R_star)

0.00838%83.791 ppm0.09098 mmag

R_p / R_star = 0.00915

Drawn to scale (planet size floor-clamped for visibility when necessary) — the dark disk's area relative to the star's is exactly δ.

Schematic shape (ingress/egress durations are illustrative, not derived from an orbital period) — but the vertical axis is real: it's zoomed in tightly around the true depth so the dip stays visible even at 84 ppm.

Almost every exoplanet discovered by transit surveys — Kepler, TESS, and the ground-based programs before them — was found the same way: not by seeing the planet, but by watching its star’s light dim, very slightly, on a regular schedule. How much it dims depends on exactly one ratio.

The formula

\delta = \left(\frac{R_p}{R_\star}\right)^2

Picture the planet and star as two flat disks, the planet centered directly in front of the star: the fraction of starlight blocked is just the ratio of their areas. Simple as it looks, this is the foundation every real transit-fitting pipeline builds on — the corrections for limb darkening, grazing geometry, and finite ingress time are all refinements to this one relation, not replacements for it.

Two worked examples worth remembering

A Jupiter-sized planet in front of a Sun-sized star blocks about 1.06% of its light (R♃/R☉ ≈ 0.103, squared ≈ 0.0106) — large enough that ground-based telescopes found the first transiting hot Jupiters decades before space-based photometry existed.
An Earth-sized planet in front of a Sun-sized star blocks only about 84 parts per million (R⊕/R☉ ≈ 0.00915, squared ≈ 8.4×10⁻⁵) — a signal so small it demands the kind of ultra-precise, space-based photometry Kepler was purpose-built to deliver.

Why smaller stars matter so much

Depth scales as 1/R★², so shrinking the host star helps enormously. The same Earth-sized planet in front of a star like TRAPPIST-1 (radius about 0.121 R☉, barely larger than Jupiter) produces a transit depth of roughly 0.57% — nearly 70 times deeper than the Sun-sized case, despite the planet being identical. This is exactly why red dwarf stars have been such productive hunting grounds for Earth-sized, potentially habitable planets: the same small rocky world that would be invisible around a Sun-like star becomes readily detectable around a small one.

Running it in reverse

Given a measured transit depth and an estimate of the host star’s radius (from its spectral type, or an independent measurement), the same relation inverts cleanly: R_p = R★√δ. This is literally how a transit survey turns “I see a 500 ppm dip” into “there’s a planet about 2.4 Earth radii out there” — the very first step in characterizing any newly discovered transiting world.

Reading the two visuals

The to-scale transit diagram draws the star and the transiting planet’s silhouette at their true relative sizes — for an Earth-Sun pair, the planet is barely a dot, which is exactly the point: it makes vivid just how subtle a signal these surveys are built to catch.
The synthetic light curve shows the schematic shape of a transit — flat, dip, flat — with a vertical axis zoomed in tightly around the true depth (labeled honestly, however tiny) so the dip stays visible even at 84 ppm, where a linearly-scaled plot would show nothing but a flat line.