How this instrument works
A transit is a shadow play measured in light, not position. When a planet crosses in front of its star, it blocks a disk-shaped bite of the star's light equal to the ratio of their cross-sectional areas, not their radii directly. Because the area of a circle grows with the square of its radius, the fraction of starlight lost is (Rp ⁄ Rs)², and multiplying by 100 turns that fraction into the percentage a photometer actually reports.
The formula assumes both bodies present flat, uniform disks and that the planet's path crosses the star's centre, so the dip reaches its full depth at mid-transit. Real starlight is not uniform across the disk — limb darkening dims the edges relative to the centre — so an observed light curve is slightly rounded rather than perfectly flat-bottomed, and the measured minimum can differ a little from the geometric figure this sheet returns.
This is also why the transit method favours large planets on well-aligned orbits: gas giants blot out enough light to register clearly against a star's natural flicker and instrument noise, while Earth-sized worlds produce dips two orders of magnitude smaller. A grazing transit, where the planet only clips the star's limb instead of crossing its full face, never reaches the depth this formula predicts, because the planet's silhouette against the disk never fully forms.
- Enter the planet's radius in Planet radius, in kilometres — Jupiter's is 71,492 km, Earth's is 6,371 km, for scale.
- Enter the host star's radius in Star radius, in kilometres — the Sun's is 696,000 km.
- Read Transit depth, % — the fractional drop in the star's measured brightness at mid-transit, already expressed as a percentage.
- Compare the figure to your instrument's noise floor: ground-based photometry typically resolves dips above roughly 0.1%, space telescopes well below that.
Worked example — a Jupiter-sized planet crossing a Sun-sized star
Set Planet radius to 71,492 km — Jupiter's equatorial radius — and Star radius to 696,000 km, the Sun's radius. The ratio Rp ⁄ Rs works out to 0.10272; squared it is 0.010551; multiplied by 100 the instrument reads Transit depth, % = 1.05511%. A Jupiter-sized planet crossing a Sun-sized star dims the star's measured brightness by a little over one percent at mid-transit, a periodic, repeatable signature exactly like the ones Kepler and TESS scan light curves to find.
Halve the star's radius to 348,000 km, roughly the size of a K-dwarf, while keeping the same Jupiter-sized planet, and the depth quadruples to 4.22043%, since the area ratio scales as the inverse square of the star's radius. Shrink the planet instead, to Earth's 6,371 km around the original Sun-sized star, and the depth falls to 0.00838% — about 125 times shallower than the Jupiter case, which is precisely why Earth-sized worlds demand far more sensitive photometry than gas giants do.
Questions
Why is the depth proportional to the square of the radius ratio?
Because a transit blocks starlight in proportion to blocked area, not blocked width. Both the planet's silhouette and the star's disk are circles, so their areas scale as radius squared; the area ratio, and therefore the fraction of light lost, is (Rp ⁄ Rs)². Double a planet's radius and the transit gets four times deeper, not two.
How much shallower is an Earth-sized transit than a Jupiter-sized one?
About 125 times shallower for the same host star. An Earth-radius planet (6,371 km) crossing a Sun-sized star (696,000 km) gives a depth of roughly 0.00838%, versus 1.05511% for a Jupiter-radius planet at the same star — the gap is the square of the radius ratio, about 11.2² ≈ 125.
Does the size of the host star change the answer?
Yes, strongly — depth scales as 1 ⁄ Rs². Swap a Sun-sized star (696,000 km) for one half that radius (348,000 km) and the same Jupiter-sized planet's transit depth quadruples, from 1.05511% to 4.22043%, one reason small, cool stars are favourite hunting grounds for transit surveys.
What does this formula leave out that a real light curve shows?
Limb darkening and transit geometry. A star's edge is dimmer than its centre, so the transit floor is not perfectly flat and the true minimum can differ slightly from (Rp ⁄ Rs)² × 100. A grazing transit, where the planet's path only clips the star's limb, never reaches this depth at all, because the planet never fully silhouettes against the disk.
Why does the formula not care which length unit is used?
Because it is a ratio: Rp ⁄ Rs cancels the units, so kilometres, miles, or solar radii would all give the identical percentage if applied consistently. This instrument's Planet radius and Star radius fields are fixed to kilometres, so simply enter both radii in km, such as Jupiter's 71,492 km or the Sun's 696,000 km.
Why report the result as a percentage instead of parts per million?
Percent is simply a more readable scale for the deep transits typical of gas giants: 1.05511% and 10,551 ppm describe the identical dip. Surveys hunting smaller planets often switch to ppm — an Earth-sized planet's 0.00838% reads as a cleaner 83.8 ppm.