Exoplanet Transit Probability Calculator

Estimate the geometric probability that a planet's orbit happens to be aligned for a transit, P ≈ (R★+Rp)/a, with an advanced mode for eccentricity and argument of periapsis — plus a viewing-angle geometry diagram and a distance-versus-probability chart, pairing with the Transit Depth Calculator.

Exoplanet transit probability calculator

For a randomly oriented orbital plane, the chance we happen to see a transit at all is geometric, not astrophysical: P ≈ (R★+R_p)/a. It pairs with this site's Transit Depth Calculator — one answers "how likely are we to see it," the other "how big would the dip be if we did."

P_transit ≈ 0.46951%
About 1 in 213 randomly oriented orbits would show a transit
transit zone−a+a

Full range of orbital orientations (band exaggerated to stay visible — really just 0.46951% of this width)

Zoomed to the star's own scale — this band is to true proportion.

10⁻¹%10⁰%10¹%10⁻¹ AU10⁰ AU10¹ AUthis planet

Dashed line: the 1/a trend for this system's own star+planet size. Dots: real example systems, each with their own stellar radius — they don't sit exactly on the line because their stars aren't the same size as this one.

Most planets never transit their star, from any given vantage point — not because transits are rare events in time, but because seeing one requires pure geometric luck: the orbital plane has to happen to line up almost exactly edge-on to our line of sight. This calculator estimates exactly how lucky you’d need to be.

The formula

Ptransit≈R⋆+RpaP_{\rm transit} \approx \frac{R_\star + R_p}{a}

R★ and R_p are the star’s and planet’s radii, a the orbital semi-major axis. For a small planet this is often simplified to R★/a, since R_p barely changes the answer. Earth around the Sun: P ≈ 0.47% — roughly 1-in-213 odds that a random distant observer would ever catch Earth transiting. A hot Jupiter parked at 0.05 AU: P ≈ 10.3% — over twenty times more likely, purely from being so much closer to its star.

Why this pairs with transit depth

This calculator has a natural partner: this site’s Exoplanet Transit Depth Calculator. The two answer completely different questions about the same observation:

A hot Jupiter wins on both counts — likelier to transit and produces a deeper signal when it does — which is exactly why the first exoplanets ever found by the transit method were hot Jupiters, long before smaller, more distant worlds became detectable.

Why close-in planets and small stars help

Both effects compound in the same direction. Closer orbits (smaller a) directly raise P by simple geometry — that’s the entire content of the formula. Smaller host stars help too: not because P has a special sensitivity to stellar radius, but because a small star’s own habitable zone sits much closer in, dragging orbital distances down along with it. An Earth-sized planet at a red dwarf’s habitable-zone distance can have several times Earth’s own transit probability, entirely for this reason — part of why systems like TRAPPIST-1 have yielded so many transiting terrestrial planets at once.

Eccentricity and the argument of periapsis

For an eccentric orbit, the fuller relation is

Ptransit≈R⋆+Rpa⋅1+esin⁡ω1−e2P_{\rm transit} \approx \frac{R_\star + R_p}{a}\cdot\frac{1+e\sin\omega}{1-e^2}

ω, the argument of periapsis, ties the planet’s closest approach to a specific point in its orbit relative to our line of sight. A favorably oriented, highly eccentric orbit can multiply the circular-orbit probability several-fold; an unfavorably oriented one suppresses it just as much. HD 80606 b — a real hot Jupiter on a famously eccentric orbit (e ≈ 0.93) — is the textbook example: it does transit, and part of why astronomers were able to catch it is exactly this geometric boost from a favorable ω.

Reading the visuals