Exoplanet Transit Depth Calculator

Background.

Seen from another star, Earth crossing the face of the Sun would dim it by about 84 parts per million, a drop of roughly one part in twelve thousand that lasts around thirteen hours when the crossing passes near the centre of the disc. Catching dips that small is what NASA's Kepler mission was designed for, and the reason it had to work from space.

The size of the dip is geometry. An opaque planet hides a circle of area πR_p² on a stellar disc of area πR_star², so the share of light lost is the square of the ratio of their radii: δ = (R_p/R_star)². You can run that forward, from two radii to a depth, or backward from a depth read off a light curve to the planet's size, which is how transit surveys actually turn a dip into a planet. Either way you get the depth in ppm, percent, as a plain fraction and as a magnitude drop, together with the planet's radius in Earth radii, Jupiter radii and kilometres.

Because the star's radius enters squared, small stars make small planets easy to see. The same Earth in front of a red dwarf a tenth the Sun's size produces a dip of 8,405 ppm, close to 1%, within reach of ground-based telescopes. Jupiter across the Sun gives 1.056%, which is why the first transiting planets found were giants.

The geometric depth is not exactly what a telescope records. Stars are brighter at the centre of their disc than at the edge, so a planet crossing the middle blocks more light than its area alone implies, while a planet that only clips the edge blocks less. Keep both in mind before comparing the number with real data.

What is exoplanet transit depth calculator?

Transit depth is the fractional drop in a star's brightness while a planet passes in front of it, measured against the star's normal out-of-transit light. It is dimensionless, a ratio of two areas, and is usually written in parts per million (10,000 ppm is 1%) or as a change in magnitude. What a light curve fixes directly is the radius ratio k = R_p/R_star. Converting that into a planet size in kilometres needs the star's radius from another source, typically spectroscopy combined with a parallax distance, or asteroseismology. Depth carries no information about mass: a bloated gas giant and a dense rocky world of the same radius cast identical dips, and it takes a radial-velocity mass to tell them apart.

How to use this calculator.

1. 01Choose a direction under "What do you want to find?": the transit depth from two radii, or the planet's radius from a depth you have measured or read in a paper.
2. 02Enter the star's radius in solar radii; both directions need it. A Sun-like star is about 1 and a late M dwarf about 0.1–0.15. Use the catalogue value for the actual host star where one exists rather than a typical value for its spectral type.
3. 03For depth from radii, enter the planet's radius in Earth radii. Neptune is about 3.86 and Jupiter 11.209. The planet has to be smaller than the star, and 1 R☉ is about 109 R⊕.
4. 04For planet size from depth, enter the depth in ppm; a percentage converts by multiplying by 10,000, so a 0.5% transit is 5,000 ppm. Depths of 1,000,000 ppm or more are rejected.
5. 05Read the radius ratio next to the depth, then the conventions note beneath the results. It gains a warning when the transiting body is more than half the star's radius, a size that points to an eclipsing star rather than a planet.

The formula.

The model is a dark disc passing in front of a uniformly bright one. With k = R_p/R_star, the depth is δ = k², and inverting gives R_p = √δ × R_star. Winn's review of transit physics writes it as δ ≈ k², the approximation covering the planet's own light, which is negligible for nearly all planets in visible light. Since δ is a ratio of areas the units cancel, but the planet is entered in Earth radii and the star in solar radii, so each is converted to metres first using the IAU 2015 Resolution B3 nominal values: 6.3781 × 10⁶ m for Earth's equatorial radius, 6.957 × 10⁸ m for the Sun, and 7.1492 × 10⁷ m for Jupiter's equatorial radius. Equatorial radii are the usual choice in transit work; Earth's polar radius of 6.3568 × 10⁶ m would give 83.49 ppm across the Sun instead of 84.05.

The magnitude version, Δm = −2.5 log₁₀(1 − δ), is Pogson's relation applied to the light that remains, 1 − δ. For shallow transits it is almost linear, Δm ≈ 1.0857 δ, the factor being 2.5 ÷ ln 10, so 84.05 ppm corresponds to 91.26 micromagnitudes.

Depth rises with the square of the planet's radius and falls with the square of the star's: halve the star and the same planet's dip is four times deeper. On the inverse route the square root softens errors in the depth, so a 4% error in δ becomes a 2% error in planet radius, while an error in the stellar radius carries straight through to the planet one for one.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Winn, J. N. (2010), "Transits and Occultations", in Exoplanets (ed. S. Seager), University of Arizona Press; arXiv:1001.2010, full text retrieved 2026-07-29. §2.4 gives the transit depth as δ_tra ≈ k² with k = R_p/R_star. §2.5 states that limb darkening causes "the flux decline during a transit to be larger than k² when the planet is near the center of the star" — the source of this page's statement about the DIRECTION of the correction. §4.2 gives the benchmarks "The loss of light is only 1% for a Sun-like star crossed by a Jupiter-sized planet" and "0.01% for an Earth-sized planet", which this calculator returns as 1.056% and 0.008405%. Peer-reviewed book chapter; open-access preprint.
2. [2]Charbonneau, D., Brown, T. M., Latham, D. W. and Mayor, M. (2000), "Detection of Planetary Transits Across a Sun-like Star", Astrophysical Journal Letters 529, L45; arXiv:astro-ph/9911436, abstract retrieved 2026-07-29. The first detection of an exoplanet transit (HD 209458 b). Reports a planet radius of 1.27 ± 0.02 R_Jup for an assumed stellar radius of 1.1 R☉, and notes that "the detailed shape of the transit curve due to both the limb darkening of the star and the finite size of the planet is clearly evident". Used here as the second, independent authority for the SIZE of the limb-darkening correction: those two radii give a geometric depth of 1.408% against the 1.7% depth measured. Peer-reviewed; open-access preprint.
3. [3]Prša, A., et al. (2016), "Nominal Values for Selected Solar and Planetary Quantities: IAU 2015 Resolution B3", Astronomical Journal 152, 41; arXiv:1510.07674, full text retrieved 2026-07-29. Table 1 gives the nominal terrestrial equatorial radius 6.3781 × 10⁶ m and polar radius 6.3568 × 10⁶ m, the nominal jovian equatorial radius 7.1492 × 10⁷ m and polar radius 6.6854 × 10⁷ m, and the nominal solar radius 6.957 × 10⁸ m — every radius conversion on this page. The resolution states these are conversion factors rather than the true planetary properties. Peer-reviewed; open-access preprint.
4. [4]Kepler mission documentation (NASA/ESA mission summary, eoPortal Directory entry for Kepler, retrieved 2026-07-29): "A Sun-Earth-like transit produces an apparent change in brightness of the star of 84 ppm (parts per million) with a duration of 13 hours, if it crosses near the center of the star." Used only as an external cross-check on the 84.05 ppm this page computes from the IAU nominal radii. Mission-documentation aggregator rather than a peer-reviewed paper; flagged as such, and no calculation depends on it.
5. [5]Koch, D. G., et al. (2010), "Kepler Mission Design, Realized Photometric Performance, and Early Science", Astrophysical Journal Letters 713, L79. The mission-design paper behind the 84 ppm Earth-analogue benchmark and Kepler's photometric requirement. Peer-reviewed; the CfA-hosted copy of the earlier SPIE design paper could not be reached on 2026-07-29 (connection refused), so this is cited bibliographically and no figure is taken from it that is not independently computed here.