--- title: Planet occurrence canonical_url: https://paxabyssi.com/wiki/Planet_occurrence markdown_url: https://paxabyssi.com/wiki/Planet_occurrence.md type: wiki-page revision_id: 509 revision_view: stable last_updated: 2026-09-27 license: CC BY-SA 4.0 license_url: https://creativecommons.org/licenses/by-sa/4.0/ science_status: - observed - model - sim summary: How common planets are, measured by counting the planets that surveys detect and correcting for the many they cannot. Most stars have at least one. categories: - Planetary systems - Exoplanets - Occurrence rates aliases: - How common are planets? - Planet occurrence rate - Occurrence rate - Eta Earth - Eta-Earth - Planets per star - Planet frequency infobox: type: physics_concept name: Planet occurrence rate sim_use: Pax Abyssi decides whether a star has planets with one probability, P(planets), read off a curve along the main sequence and multiplied by factors for companions, metallicity, population, evolutionary state and age (utils/archetype_generators/no_planets_share.py; config/architecture_probabilities.json). formulae: - name: Occurrence by inverse detection efficiency symbols: N_star stars searched; sum over the i planets found; p_tr,i the geometric chance the orbit transits; p_det,i the chance the pipeline would have caught it expression: f = (1 / N_star) * sum_i [ 1 / (p_tr,i * p_det,i) ] - name: Transit probability, circular orbit symbols: R_star stellar radius; a orbital semi-major axis (same units) expression: p_tr ~ R_star / a - name: Radial-velocity semi-amplitude, circular orbit symbols: m_p planet mass; i orbital inclination; M_J Jupiter's mass; P orbital period; M_star stellar mass expression: K = 28.4 m/s * (m_p sin i / M_J) * (P / 1 yr)^(-1/3) * (M_star / M_sun)^(-2/3) - name: Giant planets and stellar metallicity (Fischer and Valenti 2005) symbols: "[Fe/H] the star's iron abundance relative to the Sun, in dex; valid for -0.5 to +0.5" expression: P(giant) ~ 0.03 * 10^(2.0 [Fe/H]) validity: Every rate applies only inside the size and period window it was measured in. Adding windows together needs care, because planets cluster in systems rather than falling on stars independently. definition: The average number of planets per star, or the fraction of stars with at least one planet, inside a stated range of planet size or mass and orbital period, after correcting for the planets a survey could not have detected. key_quantities: confirmed_planets: as_of: 2026-09-25 value: 6372 source: NASA Exoplanet Archive giant_rate_percent: value: 26.6 (+7.5 / -5.4) source: Fernandes et al. 2019 window: 0.1 to 20 Jupiter masses, 0.1 to 100 AU planets_per_m_dwarf: value: 2.5 +/- 0.2 source: Dressing and Charbonneau 2015 window: 1 to 4 Earth radii, period below 200 d hot_jupiter_rate_percent: value: 0.43 +/- 0.05 (Kepler field) to 1.2 +/- 0.38 (nearby FGK stars) source: Fressin et al. 2013; Wright et al. 2012 cold_planets_microlensing: value: one or more bound planets per star source: Cassan et al. 2012 window: about 5 Earth masses to 10 Jupiter masses, 0.5 to 10 AU cool_jupiter_rate_percent: value: "6.7" source: Wittenmyer et al. 2020 window: mass above 0.3 Jupiter masses, period above 100 d eta_earth_conservative_hz: value: 0.37 to 0.60 planets per star source: Bryson et al. 2021 window: 0.5 to 1.5 Earth radii, stars of 4,800 to 6,300 K inner_planet_host_fraction_percent: value: F2V 32, G2V 57, mid-K 96 source: He, Ford and Ragozzine 2021 window: 0.5 to 10 Earth radii, 3 to 300 d sun_like_stars_with_kepler_like_systems_percent: value: 30 +/- 3 source: Zhu et al. 2018 window: radius above 1 Earth radius, period below 400 d misconceptions: - Kepler's early finding that roughly half of Sun-like stars have planets refers to one window of size and period. Stars that looked empty to Kepler can still hold cold giants, small planets or distant ones. - A planets-per-star figure and a fraction-of-stars figure are different numbers. Thirty per cent of Sun-like stars host Kepler-like systems averaging three planets each, so the planets-per-star rate in that window is about 0.9. worked_example: An observer far away sees Earth transit the Sun from only about 0.47% of random directions (R_sun / 1 AU = 696,000 km / 149.6 million km). Earth pulls the Sun back and forth at 9 cm/s; Jupiter at 12.5 m/s. related: - https://paxabyssi.com/wiki/Habitable_zone.md - https://paxabyssi.com/wiki/Super-Earth.md - https://paxabyssi.com/wiki/Mini-Neptune.md - https://paxabyssi.com/wiki/Radius_valley.md - https://paxabyssi.com/wiki/Star_system_generation.md - https://paxabyssi.com/wiki/Orbit.md --- # Planet occurrence > Source: https://paxabyssi.com/wiki/Planet_occurrence > > Licence: [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/). Text by Pax Abyssi Wiki contributors; history at https://paxabyssi.com/wiki/Planet_occurrence/history > > Revision 509, 27 September 2026 **Planet occurrence** is the astronomer's word for how common planets are: the average number of planets per star, or the fraction of stars that have any, inside a stated range of planet size and orbital period. It is never a raw count. Every survey method misses most of the planets that exist, so each rate is a detection count divided by the survey's sensitivity. Thirty years after the first planet was found around a Sun-like star [1], and with 6,372 planets confirmed as of 25 September 2026 [2], the answer is clear in outline: planets are the rule, most stars have several, and the kinds of planet a star gets depend strongly on its mass and its metal content. ## What a rate means Surveys see planets through narrow windows. A transit survey such as Kepler catches a planet only when its orbit happens to be edge-on, crossing the face of its star; for a circular orbit the chance of that alignment is roughly the star's radius divided by the orbit's size, $$ p_\mathrm{tr} \approx \frac{R_\star}{a}. $$ For Earth around the Sun that is 696,000 km divided by 149.6 million km, about 0.47 per cent, one viewing direction in 215. The radial-velocity method, which measures the star's wobble, has the opposite bias: it favours heavy planets close in. The star's speed amplitude is $$ K = 28.4\ \mathrm{m\,s^{-1}} \left(\frac{m_p \sin i}{M_\mathrm{J}}\right)\left(\frac{P}{1\ \mathrm{yr}}\right)^{-1/3}\left(\frac{M_\star}{M_\odot}\right)^{-2/3}, $$ which gives 12.5 m/s for Jupiter tugging on the Sun and 9 cm/s for Earth, a signal at the edge of what the best spectrographs can reach. To turn detections into a rate, each planet found is weighted by how unlikely it was to be found: $$ f = \frac{1}{N_\star}\sum_{i} \frac{1}{p_{\mathrm{tr},i}\,p_{\mathrm{det},i}}, $$ where $N_\star$ is the number of stars searched and $p_{\mathrm{det},i}$ is the measured chance that the survey's software would have flagged that planet. A single Earth-like detection in a transit survey therefore stands for about 200 planets that were not aligned. Two kinds of number come out, and they are easily confused. A *planets-per-star* rate counts planets; a *host fraction* counts stars with at least one. Planets clump into systems, so the two do not convert simply. If planets fell on stars independently, a mean of $\lambda$ planets per star would leave a fraction $e^{-\lambda}$ of stars empty. Kepler's close-in planets do not behave like that: about 30 per cent of Sun-like stars host a Kepler-like system of planets larger than Earth inside 400 days, and those systems average three planets each [3]. That is 0.9 planets per star in the window, but only 30 per cent of stars, where independent placement would have given 59. ## How we know Each method covers a different patch of the mass and distance plane, and the full picture is stitched together from all of them. - **Transits.** Kepler watched about 150,000 stars for four years and produced most of the statistics for small planets inside about one AU. It found that planets between Earth and Neptune in size, which the Solar System lacks, are the commonest kind close to stars, and that their radii split in two with a gap near 1.5 to 2 Earth radii [4]. TESS extends the same census to bright, nearby stars of every type. - **Radial velocity.** Decades-long wobble surveys of nearby stars measure giant planets out to a few AU and the frequency of planets around M dwarfs [5] [6]. - **Microlensing.** When a star passes in front of a more distant one, its gravity briefly magnifies the background light, and a planet adds a blip. The method is most sensitive at 0.5 to 10 AU, beyond the reach of the other two, and it found that cold planets are common too [7]. - **Direct imaging** sees young giant planets tens of AU from their stars. About 9 per cent of stars heavier than 1.5 solar masses have a planet of 5 to 13 Jupiter masses at 10 to 100 AU, and such planets are rarer around Sun-like stars [8]. (Image pending: Log-log chart of planet mass against orbital distance with shaded regions for transit, radial-velocity, microlensing and imaging surveys and the Solar System planets plotted as points) *Figure 1.* Diagram: each survey method sees a different window of planet mass and orbital distance. Most of the Solar System would be invisible to Kepler. ## What the surveys found **Small planets are everywhere close in.** Around Sun-like stars the fraction hosting at least one planet of 0.5 to 10 Earth radii within 300 days rises steeply toward cooler stars: 32 per cent for an F2 dwarf, 57 per cent for a G2 dwarf like the Sun and about 96 per cent for a mid-K dwarf [9]. M dwarfs are richer still, with 2.5 ± 0.2 planets of 1 to 4 Earth radii per star inside 200 days [10], and a radial-velocity survey of 238 M dwarfs finds 1.44 ± 0.20 planets per star between 1 and 1,000 Earth masses inside 1,000 days, which implies that nearly every M dwarf has one [6]. At the hot end the trend continues: a search of 20,257 A stars with TESS found no reliable small close-in planet, which puts sub-Neptunes around A stars at fewer than about 9 per 1,000 stars, several times rarer than around the Sun's kind [11]. **Hot Jupiters are rare.** Giant planets orbiting in less than ten days, the first kind found around a Sun-like star [1], occur around 0.43 ± 0.05 per cent of stars in the Kepler field [12] and 1.2 ± 0.38 per cent of nearby F, G and K dwarfs in radial-velocity surveys [13]. The two samples were chosen differently and the gap between them is not fully explained. TESS finds 0.41 ± 0.10 per cent overall and 0.26 ± 0.11 per cent for A stars [14], and 0.27 ± 0.09 per cent for early M dwarfs [15]. **Cold giants are about ten times commoner than hot ones.** The Anglo-Australian Planet Search finds giant planets of more than 0.3 Jupiter masses on orbits longer than 100 days around 6.7 per cent of Sun-like stars, against 0.84 per cent for hot Jupiters in the same sample [5]. Combining Kepler and radial velocities, giant-planet occurrence rises with distance, peaks near 2 to 3 AU, close to where water freezes in a young planetary disc, and then declines; giant planets of 0.1 to 20 Jupiter masses anywhere between 0.1 and 100 AU number about 0.27 per Sun-like star [16]. Microlensing adds Neptune-mass and super-Earth planets at a few AU in large numbers, enough to conclude that stars have one or more bound planets as a rule [7]. **Metal-rich stars make giants.** The chance that a Sun-like star has a giant planet detectable by radial velocity grows as the square of its iron content, $$ P(\text{giant}) \approx 0.03 \times 10^{\,2.0\,[\mathrm{Fe/H}]}, $$ about 3 per cent at solar metallicity, 12 per cent at twice the Sun's iron (\[Fe/H] = +0.3) and 0.3 per cent at a third of it [17]. Small planets show no such dependence and form around stars across a wide range of metallicity [18]. **Planets come in correlated families.** Cold Jupiters are about three times more common around stars that host inner super-Earths, and about 90 per cent of cold-Jupiter hosts also have super-Earths closer in [19]. About half of hot-Jupiter systems, 51 ± 10 per cent, have a distant massive companion between 1 and 20 AU [20]. By these measures the Solar System, with nothing inside Mercury's orbit, is unusual: a population model fitted to Kepler finds fewer than about 8 per cent of planetary systems with no planet interior to Mercury [21]. ## Earth-like planets and eta-Earth The number most often asked for is **eta-Earth**, $\eta_\oplus$: the average number of rocky, roughly Earth-sized planets in the [habitable zone](https://paxabyssi.com/wiki/Habitable_zone.md) of a Sun-like star. Almost no such planets are detected directly, because a year-long orbit transits rarely and produces a tiny wobble, so eta-Earth is an extrapolation and its value depends on the definitions chosen. For planets of 0.5 to 1.5 Earth radii around stars of 4,800 to 6,300 K, the final Kepler data give 0.37 to 0.60 per star in the conservative habitable zone and 0.58 to 0.88 in the wider optimistic one, which would place the nearest such planet around a G or K dwarf about 6 parsecs away on average [22]. An earlier estimate for planets of 1 to 2 Earth radii with periods of 200 to 400 days found 5.7 per cent [23]. For M dwarfs the conservative figure is 0.16 Earth-size planets per star [10]. None of these numbers says anything about whether such planets are habitable in practice. > **How many planets are in the Milky Way?** > > Put the pieces together and the Galaxy holds at least as many planets as stars: microlensing alone implies one or more per star at 0.5 to 10 AU [7], and the close-in small planets of M dwarfs, which make up most stars, add two or more each [10]. With a stellar population usually quoted between 100 and 400 billion (see [Milky Way](https://paxabyssi.com/wiki/Milky_Way.md)), that is hundreds of billions of planets, the great majority of them sub-Neptunes and super-Earths around red dwarfs, a kind of world the Solar System does not contain. ## Notable numbers | Quantity | Value | Window | Source | | ---------------------------------------- | ------------- | ---------------------------------------- | ----------- | | Confirmed planets | 6,372 | all methods, as of 25 September 2026 | [2] | | Sun-like stars with a Kepler-like system | 30 ± 3 % | larger than 1 Earth radius, inside 400 d | [3] | | G2V stars with an inner planet | 57 % | 0.5 to 10 Earth radii, 3 to 300 d | [9] | | Small planets per M dwarf | 2.5 ± 0.2 | 1 to 4 Earth radii, inside 200 d | [10] | | Hot Jupiters, FGK stars | 0.43 to 1.2 % | period below 10 d | [12] [13] | | Cool Jupiters, Sun-like stars | 6.7 % | above 0.3 Jupiter masses, beyond 100 d | [5] | | Eta-Earth, conservative zone | 0.37 to 0.60 | 0.5 to 1.5 Earth radii, FGK stars | [22] | > **In Pax Abyssi** > > Whether a star in Pax Abyssi has planets is decided by one probability. A single, solar-metallicity, main-sequence star draws its base value from a curve read off its spectral subtype: 0.89 for a G2 dwarf like the Sun, 0.96 for M dwarfs, falling to 0.64 at F0, 0.57 at A0 and 0.10 at B0. Across G, K and M the curve is the fit > > $$ > P_0(T) = 0.55 + \frac{0.41}{1 + e^{(T - 6250\,\mathrm{K})/300\,\mathrm{K}}}, > $$ > > built to match the measured host fractions above with an allowance for the cold planets that transit surveys cannot see. For O stars, where no planet, survey or model exists, the sim uses 0.03 to 0.06 and labels it an assumption. The base value is then multiplied by factors for a close companion star (0.25 for one between 1 and 10 AU), low metallicity (0.6 below a tenth of the Sun's iron), the old thick disc or halo, an evolved star (0.75 for a giant, 0.35 for a supergiant) and extreme youth. Stars with real, catalogued exoplanets always keep them. > > Measured on 12,000 generated stars, 88 per cent of single G dwarfs came out with planets. The sky you can click on in the game is dominated by bright stars, many of them hot, evolved or double, so there the fraction is lower: 2,188 of the 5,160 stars generated so far have planets, 8,751 planets and 7,495 moons in all, each system identical every time it is generated. What kinds of system those planets form is set by the [archetype](https://paxabyssi.com/wiki/Planetary_system_archetypes.md) a star draws. ## See also - [Planetary system archetypes](https://paxabyssi.com/wiki/Planetary_system_archetypes.md) - [Star system generation](https://paxabyssi.com/wiki/Star_system_generation.md) - [Habitable zone](https://paxabyssi.com/wiki/Habitable_zone.md) - [Radius valley](https://paxabyssi.com/wiki/Radius_valley.md) - [Hot Jupiter](https://paxabyssi.com/wiki/Hot_Jupiter.md) - [Mini-Neptune](https://paxabyssi.com/wiki/Mini-Neptune.md) - [Super-Earth](https://paxabyssi.com/wiki/Super-Earth.md) - [Red dwarf](https://paxabyssi.com/wiki/Red_dwarf.md) - [Orbit](https://paxabyssi.com/wiki/Orbit.md) ## References 1. Mayor, M. and Queloz, D. (1995). A Jupiter-mass companion to a solar-type star. Nature 378, 355-359. 2. NASA Exoplanet Archive. NASA Exoplanet Archive: confirmed planet count. NASA Exoplanet Science Institute, Caltech/IPAC. 3. Zhu, W. et al. (2018). About 30% of Sun-like Stars Have Kepler-like Planetary Systems: A Study of Their Intrinsic Architecture. The Astrophysical Journal 860, 101. 4. Fulton, B. J., Petigura, E. A. and Howard, A. W. (2017). The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets. The Astronomical Journal 154, 109. 5. Wittenmyer, R. A. (2020). Cool Jupiters greatly outnumber their toasty siblings: occurrence rates from the Anglo-Australian Planet Search. Monthly Notices of the Royal Astronomical Society 492, 377-383. 6. Ribas, I. (2023). The CARMENES search for exoplanets around M dwarfs. Guaranteed time observations Data Release 1 (2016-2020). Astronomy & Astrophysics 670, A139. 7. Cassan, A. (2012). One or more bound planets per Milky Way star from microlensing observations. Nature 481, 167-169. 8. Nielsen, E. L. (2019). The Gemini Planet Imager Exoplanet Survey: Giant Planet and Brown Dwarf Demographics from 10 to 100 au. The Astronomical Journal 158, 13. 9. He, M. Y., Ford, E. B. and Ragozzine, D. (2021). Architectures of Exoplanetary Systems. II. An Increase in Inner Planetary System Occurrence toward Later Spectral Types for Kepler's FGK Dwarfs. The Astronomical Journal 161, 16. 10. Dressing, C. D. and Charbonneau, D. (2015). The Occurrence of Potentially Habitable Planets Orbiting M Dwarfs Estimated from the Full Kepler Dataset and an Empirical Measurement of the Detection Sensitivity. The Astrophysical Journal 807, 45. 11. Giacalone, S. and Dressing, C. D. (2025). Small and Close-in Planets are Uncommon Around A-type Stars. The Astronomical Journal 169, 45. 12. Fressin, F., Torres, G. and Charbonneau, D. (2013). The False Positive Rate of Kepler and the Occurrence of Planets. The Astrophysical Journal 766, 81. 13. Wright, J. T. et al. (2012). The Frequency of Hot Jupiters Orbiting Nearby Solar-type Stars. The Astrophysical Journal 753, 160. 14. Zhou, G. (2019). Two New HATNet Hot Jupiters around A Stars and the First Glimpse at the Occurrence Rate of Hot Jupiters from TESS. The Astronomical Journal 158, 141. 15. Gan, T. (2023). Occurrence Rate of Hot Jupiters Around Early-type M Dwarfs Based on Transiting Exoplanet Survey Satellite Data. The Astronomical Journal 165, 17. 16. Fernandes, R. B. et al. (2019). Hints for a Turnover at the Snow Line in the Giant Planet Occurrence Rate. The Astrophysical Journal 874, 81. 17. Fischer, D. A. and Valenti, J. (2005). The Planet-Metallicity Correlation. The Astrophysical Journal 622, 1102-1117. 18. Buchhave, L. A. (2012). An abundance of small exoplanets around stars with a wide range of metallicities. Nature 486, 375-377. 19. Zhu, W. and Wu, Y. (2018). The Super Earth-Cold Jupiter Relations. The Astronomical Journal 156, 92. 20. Knutson, H. A. (2014). Friends of Hot Jupiters. I. A Radial Velocity Search for Massive, Long-period Companions to Close-in Gas Giant Planets. The Astrophysical Journal 785, 126. 21. Mulders, G. D. et al. (2018). The Exoplanet Population Observation Simulator. I. The Inner Edges of Planetary Systems. The Astronomical Journal 156, 24. 22. Bryson, S. (2021). The Occurrence of Rocky Habitable-zone Planets around Solar-like Stars from Kepler Data. The Astronomical Journal 161, 36. 23. Petigura, E. A., Howard, A. W. and Marcy, G. W. (2013). Prevalence of Earth-size planets orbiting Sun-like stars. Proceedings of the National Academy of Sciences 110, 19273-19278. ## Infobox (physics concept) | Field | Value | | --- | --- | | Name | Planet occurrence rate | | Sim use | Pax Abyssi decides whether a star has planets with one probability, P(planets), read off a curve along the main sequence and multiplied by factors for companions, metallicity, population, evolutionary state and age (utils/archetype_generators/no_planets_share.py; config/architecture_probabilities.json). | | Validity | Every rate applies only inside the size and period window it was measured in. Adding windows together needs care, because planets cluster in systems rather than falling on stars independently. | | Definition | The average number of planets per star, or the fraction of stars with at least one planet, inside a stated range of planet size or mass and orbital period, after correcting for the planets a survey could not have detected. | | Misconceptions | Kepler's early finding that roughly half of Sun-like stars have planets refers to one window of size and period. Stars that looked empty to Kepler can still hold cold giants, small planets or distant ones., A planets-per-star figure and a fraction-of-stars figure are different numbers. Thirty per cent of Sun-like stars host Kepler-like systems averaging three planets each, so the planets-per-star rate in that window is about 0.9. | | Worked example | An observer far away sees Earth transit the Sun from only about 0.47% of random directions (R_sun / 1 AU = 696,000 km / 149.6 million km). Earth pulls the Sun back and forth at 9 cm/s; Jupiter at 12.5 m/s. | ## Related pages - [Habitable zone](https://paxabyssi.com/wiki/Habitable_zone.md): The band of distances from a star where an Earth-like planet could keep liquid water on its surface, bounded by the runaway greenhouse on the inside and the maximum greenhouse on the outside. - [Super-Earth](https://paxabyssi.com/wiki/Super-Earth.md): A planet more massive than Earth but lighter than Neptune, usually rocky, with no counterpart in the Solar System. Super-Earths are among the most common planets found around other stars. - [Mini-Neptune](https://paxabyssi.com/wiki/Mini-Neptune.md): A planet between about 1.7 and 4 times Earth's radius with a rocky or icy core wrapped in a thin envelope of hydrogen and helium. The most common kind of planet Kepler found, and one the Solar System lacks. - [Radius valley](https://paxabyssi.com/wiki/Radius_valley.md): A shortage of planets between about 1.5 and 2 Earth radii that splits small close-in planets into rocky super-Earths and gas-wrapped sub-Neptunes. - [Star system generation](https://paxabyssi.com/wiki/Star_system_generation.md): How Pax Abyssi builds the planets, moons, rings and belts of every star system except our own, from a star's catalogue row, published occurrence rates and planetary physics, the same way every time. - [Orbit](https://paxabyssi.com/wiki/Orbit.md): The path one body follows around another under gravity. For two bodies alone it is an ellipse, fixed by Kepler's three laws and described by six orbital elements. Categories: [Planetary systems](https://paxabyssi.com/wiki/Category:Planetary_systems.md), [Exoplanets](https://paxabyssi.com/wiki/Category:Exoplanets.md), [Occurrence rates](https://paxabyssi.com/wiki/Category:Occurrence_rates.md)