Exoplanet Transit Depth Calculator

What transit depth tells you

The transit method finds exoplanets by watching a star fade very slightly when a planet passes in front of it. That tiny brightness loss is called the transit depth. Even before you model the full light curve, the depth already tells you something physically important: how large the planet looks compared with the face of its star. If the planet blocks a larger fraction of the stellar disk, the dip is deeper. If the star is larger, the same planet covers less area and the dip becomes shallower. This is why transit depth is one of the first numbers astronomers check when they want a quick estimate of planet size or detectability.

This calculator is a clean first-order tool for that job. You enter the radius of the star and the radius of the planet, and the page returns the expected fractional dip in starlight for the simplest area-ratio model. That makes it useful for classroom exercises, back-of-the-envelope observing plans, catalog sanity checks, and quick comparisons between targets. It is especially helpful when you want intuition. A 2 Earth-radius planet can be quite hard to see around a Sun-sized star, but far easier around a smaller dwarf star. The basic calculation shows that contrast immediately.

What the two inputs mean

The first field is Star Radius R★ in solar radii. A value of 1 means a Sun-sized star. A value of 0.5 means the star's radius is half that of the Sun, which is common for smaller stars. A value above 1 represents a larger star, such as an inflated main-sequence star or subgiant. This number matters because the star sets the size of the background disk. A bigger star spreads the planet's silhouette over more surface area, so the observed dip gets smaller. When you compare targets, stellar radius is often the fastest way to see why some transits are easy and others are barely detectable.

The second field is Planet Radius Rₚ in Earth radii. A value of 1 is Earth-sized, 2 is a rough super-Earth scale, around 4 is a mini-Neptune, and about 11.2 is Jupiter-sized. Transit depth depends on radius, not mass, so this calculator does not care whether the planet is rocky or gaseous except through how large it is. One very common input mistake is entering a diameter instead of a radius. Another is copying a value reported in Jupiter radii into a field that expects Earth radii. Because the result is squared, those mistakes can make the output wrong by a large factor.

The formula behind the calculator

For a simple, central transit with no extra complications, the expected depth is approximately the ratio of the planet's blocked area to the star's visible area. Area scales with the square of radius, so the formula becomes the squared radius ratio. In words, the dip is about how much of the stellar disk the planet covers.

The JavaScript on this page converts the star radius from solar radii into meters and the planet radius from Earth radii into meters before taking the ratio. That conversion is important because the numerator and denominator must be in the same unit. The script uses 1 solar radius = 6.9634 × 10⁸ meters and 1 Earth radius = 6.371 × 10⁶ meters. Once the units match, they cancel, leaving a dimensionless fraction that can be shown as a percentage. If you see a value such as 0.0335%, that means the star is predicted to dim by 0.0335 percent during the transit in this simplified model.

In a broader mathematical sense, a calculator is just a function that maps inputs to an output. The following preserved MathML expression shows that abstract idea. Here, the transit depth page is a very specific case where the function happens to be the squared ratio of two radii.

Many science tools also combine weighted terms, correction factors, or multiple sources of uncertainty. That broader pattern is reflected in the preserved summation below. The transit-depth calculator itself does not sum several components, but seeing the notation is still a useful reminder that more detailed astrophysical models often add limb darkening, dilution, or instrumental effects on top of the core geometry.

For this page, though, the key physical message is simple and powerful: depth follows area ratio. Double the planet radius and the depth becomes four times larger. Double the star radius and the depth becomes four times smaller.

Worked example

Suppose the star radius is 1 solar radius and the planet radius is 2 Earth radii. The script converts those values into meters and then forms the ratio. The planet radius becomes 2 × 6.371 × 10⁶ m = 1.2742 × 10⁷ m. The star radius becomes 6.9634 × 10⁸ m. Their ratio is about 0.0183. Squaring that gives about 3.35 × 10^-4. As a percentage, the predicted transit depth is about 0.0335%.

That number is small, but it is not meaningless. It corresponds to roughly 335 parts per million, which is the scale of signal that precision photometry can measure. The example is useful because it calibrates intuition. A planet that is only twice Earth's radius still produces a very shallow dip around a Sun-sized star. Now compare the same 2 Earth-radius planet around a 0.5 solar-radius star. Because the star is half as large, the depth becomes four times larger, or roughly 0.134%. The planet did not change, but the host star made the observation much more favorable.

How to interpret the result

The result box shows the depth both as a percentage and in scientific notation. The percentage is best for quick intuition: it tells you how much the star dims in ordinary terms. The scientific notation is convenient when the dip is extremely small, which is common for Earth-sized planets around Sun-like stars. As a rough guide, values below about 0.01% are subtle; values around 0.1% are noticeably deeper; and values near 1% are large, classic transit signals often associated with big planets or small host stars. The exact observing difficulty depends on noise, cadence, stellar activity, and telescope quality, but the percentage gives you the right first reaction.

If the output seems surprising, do two quick checks. First, ask whether you entered radii rather than diameters. Second, ask whether the direction makes sense. Increasing the planet radius should always increase the transit depth. Increasing the star radius should always decrease it. If either trend is violated in your mental test, it usually means a unit or interpretation error slipped into the inputs. This kind of sanity check is valuable because the squared relationship makes even modest input mistakes look dramatic in the final number.

Common scenarios at a glance

The table below gives a few benchmark cases that help frame the calculator's output. These are not special to the code; they are just familiar examples that make the scale of transit signals easier to remember.

Benchmark cases like these are useful because they help you read the result in context instead of as an isolated decimal. When you are browsing target lists, a quick depth estimate can tell you whether a candidate is likely to be an easy classroom demonstration or a demanding precision problem.

Assumptions and limits

This calculator intentionally uses the simplest widely taught model. That is a strength when you want speed and clarity, but it also means the answer is an approximation rather than a full light-curve fit. Real stars are not perfectly uniform disks. Their edges can appear dimmer than their centers because of limb darkening. A transit can also be grazing rather than central, which changes the exact shape and interpretation of the light curve. Nearby stars in the photometric aperture can dilute the signal and make the observed dip shallower than the true planet-to-star area ratio would suggest.

• Limb darkening: the stellar surface is not equally bright everywhere, so detailed models adjust the shape and depth slightly.
• Geometry: the simple formula assumes a clean projected overlap and is most intuitive for non-grazing transits.
• Contaminating light: unresolved companion stars or background sources reduce the apparent depth.
• Starspots and activity: active stars can create brightness changes that mimic or distort transits.
• Input uncertainty: stellar radius errors feed directly into the inferred transit depth and any planet-size interpretation built on it.

Even with those caveats, the formula remains extremely useful. It captures the dominant geometry and gives the right scaling behavior. That is why it appears so often in introductory exoplanet work. If you later move on to fitting real data, you can treat this page as the conceptual starting point. It gives you a baseline expectation before you add the finer astrophysical details.

Using the result in practice

People use a transit-depth estimate in several ways. You might compare two target stars and ask which host makes the same planet easier to detect. You might check whether a reported planet radius is consistent with a measured dip and known stellar radius. You might plan an observing project and decide whether the expected signal is comfortably above your noise floor. You can also turn the relationship around conceptually: if you already measured the depth and trust the star radius, then the planet radius scales with the square root of that depth. This page performs the forward calculation, but the physical link runs both ways.

That is also why the optional mini-game below is tied so closely to the calculator. Every successful round reinforces the same lesson the formula teaches: the size ratio matters, and the signal changes quickly because the ratio is squared. Once that intuition clicks, the result box stops looking like a random decimal and starts feeling like a physical measurement of how much sky the planet covers.