Exoplanet Transit Depth Calculator

Background.

When a planet crosses in front of its star, the star dims by the fraction of its disc the planet covers. That fraction is the transit depth, and for a uniformly bright stellar disc it is exactly the square of the radius ratio: δ = (R_p/R_star)². This calculator runs that relation in both directions — depth from two radii, or planet radius from a measured depth — and reports the result in parts per million, as a percentage, as a raw fraction and as a magnitude drop.

The canonical number is worth internalising. Earth transiting the Sun, using the IAU's nominal equatorial radii of 6.3781 × 10⁶ m and 6.957 × 10⁸ m, gives a radius ratio of 0.009168 and a depth of **84.05 parts per million** — a brightness drop of about one part in twelve thousand, lasting roughly thirteen hours. NASA's Kepler mission literature quotes exactly 84 ppm for that case, and this page reproduces it from constants that never touched the mission documentation. Jupiter across the Sun gives 1.056%, more than a hundred times deeper, which is why the first transiting planet found was a hot Jupiter and why Earth analogues needed a purpose-built space telescope.

**The single most important thing to know about this formula is that it is not what a light curve measures.** Real stars are limb-darkened: brighter at the centre of the visible disc than at the edge. A planet crossing near the centre therefore blocks a disproportionately bright patch, and the observed depth at mid-transit is deeper than the geometric δ = k². Winn's review of transit physics states the direction explicitly — 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 size of the effect is not academic. For HD 209458 b, the first transiting planet ever detected, Charbonneau and colleagues reported a transit depth of 1.7% and derived a planet radius of 1.27 Jupiter radii assuming a 1.1-solar-radius star. Put those two radii into this calculator and the geometric depth is 1.41% — the depth they actually measured was about 21% larger. That gap is limb darkening, and it is why serious transit fitting uses a limb-darkened model rather than a bare square.

The second assumption is a central crossing. This page has no impact-parameter input, so it computes the depth for a planet passing over the middle of the disc. A grazing transit, where the planet only clips the edge, is shallower and produces a V-shaped rather than flat-bottomed light curve; inverting a grazing depth with this formula would underestimate the planet.

A few other things are deliberately excluded. The planet is treated as an opaque circular disc, so no rings, no atmospheric transmission and no thermal emission from the planet's own nightside. Real transit depths are wavelength-dependent both because limb darkening is and because a planet's atmosphere is more opaque in some bands than others — that wavelength dependence is the entire basis of transmission spectroscopy, and it means "the" transit depth of a planet is really a spectrum.

The radii used are the IAU 2015 Resolution B3 nominal values, which are exact declared conversion factors rather than measurements. One detail matters: B3 publishes both equatorial and polar radii for Earth and Jupiter, and this page uses the equatorial ones, as transit work conventionally does. It is not a rounding decision — Earth's polar radius would give 83.49 ppm instead of 84.05 ppm, a 0.7% difference that is larger than the photometric precision of a good space-based light curve.

Finally, the practical lesson the arithmetic teaches. Depth goes as the inverse square of the stellar radius, so shrinking the star helps enormously. The same Earth-size planet that produces 84 ppm across the Sun produces 8405 ppm — 0.84%, a hundred times deeper — across a star of 0.1 solar radii. That single fact is why ground-based and space-based small-planet searches point at M dwarfs.

What is exoplanet transit depth calculator?

A transit is the passage of a planet across the disc of its host star as seen from Earth, and the transit depth is the fractional loss of light while it happens. Because the planet blocks a solid, opaque disc of area πR_p² out of a stellar disc of area πR_star², the fraction blocked is the ratio of the two areas — the square of the ratio of the radii.

Depth is quoted in parts per million, in percent, or occasionally as a magnitude drop. The conversions are exact: 10 000 ppm is 1%, and Δm = −2.5 log₁₀(1 − δ). For small depths Δm ≈ 1.0857 δ, so 84 ppm is about 91 micromagnitudes.

What a transit measures directly is the radius RATIO, not the planet's radius. Turning a ratio into a physical size requires an independently determined stellar radius, which usually comes from spectroscopy plus a parallax, or from asteroseismology. That is why the stellar radius is a required input on both routes here and is echoed back in the results: every published exoplanet radius inherits the uncertainty of its host star's radius, and a revised stellar radius revises every planet in the system.

Transit depth is one of three things a light curve gives you. The others are the orbital period, from the spacing of successive transits, and the transit duration and shape, which constrain the orbital inclination and the stellar density. Combining a transit radius with a radial-velocity mass gives a bulk density, and that is how a planet is classified as rocky, icy or gaseous.

What transit depth is not: it is not a measure of mass, it is not independent of wavelength, it is not what you read straight off a raw light curve without accounting for limb darkening, and on its own it cannot distinguish a genuine planet from an eclipsing binary blended with a brighter star — which is why every transit candidate requires follow-up validation.

How to use this calculator.

1. 01Choose the forward route (two radii → depth) or the inverse (depth → planet radius).
2. 02Enter the stellar radius in solar radii. This is required in both routes, because the depth is a ratio to the stellar disc and every inferred planet radius depends on it.
3. 03Enter either the planet radius in Earth radii, or the observed depth in parts per million.
4. 04Read the depth in ppm, percent and magnitudes, and read the radius ratio k — that ratio is the quantity a light curve actually constrains.
5. 05Before comparing with a measured light curve, read the conventions note. It states that a limb-darkened star shows a deeper drop than this geometric value, and by roughly how much.
6. 06If you are inverting a real measurement, remember the answer is only as good as the stellar radius you supplied — a 5% error there is a 5% error in the planet.

The formula.

The derivation is one line of geometry. A planet of radius R_p projects an opaque disc of area πR_p² onto a stellar disc of area πR_star². If the star's surface brightness were uniform, the fraction of light removed would be the ratio of those areas, πR_p²/πR_star² = (R_p/R_star)² = k². Winn's review states it as δ_tra ≈ k², with the approximation sign covering the planet's own (usually negligible) emission. Inverting gives R_p = √δ × R_star, which is what transit surveys do: they measure a depth, adopt a stellar radius from spectroscopy or asteroseismology, and infer a planet size.

The magnitude form is Δm = −2.5 log₁₀(1 − δ), the standard Pogson relation applied to a flux ratio of (1 − δ). For small depths the logarithm linearises to Δm ≈ 1.0857 δ, so Earth's 84.05 ppm across the Sun is 91.26 micromagnitudes and Jupiter's 1.056% is 11.53 millimagnitudes.

Units and dimensions. Planet radius in Earth radii, stellar radius in solar radii, depth in ppm, percent and as a bare fraction, magnitudes dimensionless. The depth itself is dimensionless — a ratio of areas — and the test suite guards this by doubling both radii and confirming the depth does not change. It also checks the two scalings that matter: depth goes as the square of the planet radius, and as the inverse square of the stellar radius.

Rounding stage. No intermediate rounding: forty significant digits internally, rounded once at the return boundary to twelve significant digits. Fixed decimal places were rejected because depths span from about 10⁻² for a hot Jupiter to below 10⁻⁹ for an asteroid-sized body, and a small depth would round to a flat zero rather than to a small number.

Significant figures. Three at most, and usually fewer. The geometric depth is exact arithmetic, but it is not what a light curve shows: limb darkening alone changed HD 209458 b's measured depth from the geometric 1.41% to an observed 1.7%. Quoting five digits of a geometric transit depth implies a correspondence with observation that does not exist.

Invalid-domain behaviour. A zero, negative or missing stellar radius raises a field error in both routes, because the ratio is undefined without it. A zero or negative planet radius raises an error in the forward route — a planet with no radius blocks no light and produces no transit to measure. In the inverse route a depth of zero or below raises an error, and so does any depth of 1 000 000 ppm or more: at δ = 1 the star vanishes entirely, the magnitude drop −2.5 log₁₀(1 − δ) diverges, and the transiting body would have to be at least as large as the star. One condition attaches a warning rather than an error: a radius ratio above 0.5 means the transiting body is more than half the star's radius, which is the regime of eclipsing binaries rather than planets, and where the assumptions of an opaque dark disc and a negligible companion luminosity fail together. That one-half edge is a presentation convention chosen for this page, not a published threshold.

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 engine 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.