Exoplanet Transit Calculator (Depth, Duration and Probability)
How much a planet dims its star as it crosses the disc, how long the crossing lasts and how likely a random observer is to see it, from the sizes, the orbital period and the star's mass.
Results
The dashed line marks the value you entered.
What this tool does
A transiting planet blocks a fraction of the starlight equal to the square of the radius ratio: a Jupiter in front of a Sun-like star dims it by about 1 %, an Earth by only 0.008 % — which is why finding Earth-sized worlds needs space telescopes. The orbital distance follows from Kepler's third law, and the transit lasts a few hours for a close-in planet. Only orbits seen almost edge-on cause transits: the geometric chance is roughly the stellar radius divided by the orbital distance, about 10 % for a hot Jupiter and 0.5 % for an Earth-like orbit.
Formula
depth = (R_p ÷ R_s)² · a³ = G M P² ÷ 4π² · T = (P ÷ π) asin[ (R_s ÷ a) √((1 + k)² − b²) ÷ sin i ]
Variables
| Symbol | Meaning | Unit |
|---|---|---|
rs | Radius of the star (Sun = 1) | — |
rp | Radius of the planet | — |
un | Planet radius is given in | — |
pd | Orbital period of the planet | d |
sm | Mass of the star (Sun = 1) | — |
ib | Impact parameter (0 = across the middle of the star, 1 = grazing the edge) | — |
DP | Transit depth (dip in starlight) | % |
DU | Transit duration | h |
A | Orbital distance | AU |
PR | Chance that a random observer sees the transit | % |
K | Radius ratio, planet ÷ star | — |
Worked example
- Radius of the star (Sun = 1)1
- Radius of the planet1
- Planet radius is given in2
- Orbital period of the planet3.5 d
- Mass of the star (Sun = 1)1
- Impact parameter (0 = across the middle of the star, 1 = grazing the edge)0.3
- Transit depth (dip in starlight)1.0560 %
- Transit duration2.93 h
- Orbital distance0.0451 AU
- Chance that a random observer sees the transit10.31 %
- Radius ratio, planet ÷ star0.10276
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.