Circumstellar Habitable Zone Calculator

Background.

The circumstellar habitable zone is the range of orbital distances in which a rocky planet with an Earth-like atmosphere could hold liquid water on its surface. Too close and the oceans boil away; too far and even a thick carbon-dioxide greenhouse cannot keep the surface above freezing. This calculator computes all five standard boundary distances from a star's bolometric luminosity and effective temperature, and tells you which band a planet at a given semi-major axis falls into.

The model implemented is Kopparapu et al. (2013), "Habitable Zones Around Main-Sequence Stars: New Estimates", using the **corrected coefficients from that paper's erratum** rather than the values in the paper as first printed. That distinction is not pedantry: the publisher's own erratum notice says "several changes and corrections made at the proof stage were not included in the published version of the paper", and the corrected numbers move the Sun's runaway-greenhouse edge from 0.975 to 0.981 au and its maximum-greenhouse edge from 1.705 to 1.689 au. The widely quoted "0.99 to 1.70 au" conservative zone comes from the paper's abstract, computed with the superseded coefficients; the erratum gives 0.99 to 1.69 au. Both figures are recorded here, and the page uses the erratum.

With the Sun's luminosity and the fit's reference temperature of 5780 K, the five limits come out as 0.750 au (recent Venus), 0.981 au (runaway greenhouse), 0.993 au (water loss — the conservative inner edge), 1.689 au (maximum greenhouse — the conservative outer edge) and 1.766 au (early Mars). Earth at 1.000 au sits inside the conservative zone but not far from its inner edge. Mars at 1.524 au is also inside it, which is a genuine and much-discussed result: Mars is not too far from the Sun for liquid water, it is too small to have kept the atmosphere that would have provided it.

**Two boundary pairs, two kinds of claim.** The water-loss and maximum-greenhouse limits come out of a climate model. The recent-Venus and early-Mars limits are empirical: they say only that Venus has apparently had no surface water for at least about a billion years and that Mars was wet around 3.8 billion years ago, and convert those epochs into flux limits. The optimistic pair is wider and rests on planetary history rather than on radiative transfer, so the two should not be read as equally strong.

**What the model assumes, and where it fails.** It is a one-dimensional, cloud-free radiative–convective calculation for a planet with an N₂–H₂O–CO₂ atmosphere and a water reservoir, on a circular orbit, around a star characterised by a single effective temperature. Clouds are not in it at all, and three-dimensional general-circulation models generally push the inner edge inward. Planet mass is not in the 2013 version either — Kopparapu et al. returned to that in 2014 and found the runaway-greenhouse flux limit changes by roughly −10% for a 0.1-Earth-mass planet and +7% for a 5-Earth-mass one. This page reports all three of those 2014 inner edges beside the 2013 numbers, so the size of that uncertainty is visible rather than implied. For the Sun they span 0.917 to 1.005 au, against the 2013 model's 0.981 au.

**A habitable zone is not habitability.** Being inside these boundaries means only that a particular kind of planet, with a particular kind of atmosphere, could in principle sustain surface liquid water at that flux. It says nothing about whether a real planet at that distance has an atmosphere at all, whether it retained its water, whether it is tidally locked, whether its star's flares have stripped it, or whether anything lives there. Earth, Venus and Mars have all spent time inside the optimistic zone, and only one of them is inhabited.

One hard limit worth knowing before you start. The polynomial fit is defined only for effective temperatures between 2600 K and 7200 K, roughly M through F main-sequence stars. Outside that range a quartic extrapolates into confident nonsense, so this calculator raises an error rather than returning a number. Several well-known targets sit just below the floor — TRAPPIST-1's effective temperature is around 2560 K — and for those a different model is required.

What is habitable zone calculator?

The habitable zone, sometimes called the Goldilocks zone, is defined by flux rather than by distance. What matters to a planet's climate is the stellar energy it receives per unit area, S = L/d², and the boundaries are set by the values of that flux at which a climate model stops being able to sustain surface liquid water.

Kopparapu et al. parametrise each boundary as an effective stellar flux S_eff that depends on the star's effective temperature through a quartic in T* = T_eff − 5780 K, and then convert to a distance with d = √((L/L☉)/S_eff) astronomical units. Temperature enters because the boundary depends on the spectrum as well as the total flux: a cool red star emits mostly in the near-infrared, where water and CO₂ absorb strongly and Rayleigh scattering is weak, so a planet around it is warmed more efficiently per watt received than one around a hot blue star.

The inner boundaries are set by water loss. As a planet warms, its stratosphere becomes wet, ultraviolet light splits the water and hydrogen escapes to space, draining the oceans over geological time — the moist-greenhouse limit. Push closer and the oceans evaporate outright: the runaway greenhouse. The outer boundary is the maximum-greenhouse limit, the point at which adding more CO₂ stops helping, because increased Rayleigh scattering and CO₂ condensation cool the surface faster than the extra opacity warms it.

The zone is not fixed in time. Stars brighten as they age, so the habitable zone migrates outward — the continuously habitable zone, the band that stays habitable for a given duration, is narrower than the instantaneous one this page computes.

What the habitable zone is not: it is not a guarantee, it is not a statement about any specific planet's atmosphere or history, it is not defined for planets very different from Earth in mass or composition, and it does not include subsurface oceans, which is why moons like Europa and Enceladus are of astrobiological interest despite lying far outside every boundary here.

How to use this calculator.

1. 01Enter the star's bolometric luminosity in solar luminosities. If you only have a magnitude, the luminosity calculator will convert it.
2. 02Enter the star's effective temperature in kelvin. It must be between 2600 K and 7200 K — outside that range the fit is not defined and this calculator will not extrapolate.
3. 03Enter the planet's orbital semi-major axis in astronomical units. A circular orbit is assumed.
4. 04Read the two conservative boundaries first — water loss and maximum greenhouse. Those are the model's own answer.
5. 05Read the recent-Venus and early-Mars boundaries as an optimistic bracket resting on planetary history rather than on radiative transfer.
6. 06Compare the three 2014 inner edges to see how much the answer moves with planetary mass before you quote any of it.
7. 07Read the verdict for your orbit and then the model note — the note states what the model excludes, and that being inside the zone is not a claim about habitability.

The formula.

Each boundary is defined by a critical effective stellar flux S_eff — the insolation, in units of what Earth receives, at which that climate limit is reached. Because the limit depends on the shape of the stellar spectrum as well as its total power, S_eff is a function of the star's effective temperature, and Kopparapu et al. fit that dependence as a quartic in T* = T_eff − 5780 K. Converting a flux to a distance is then the inverse-square law: the planet receives (L/L☉)/d² Earth-fluxes at d astronomical units, so setting that equal to S_eff gives d = √((L/L☉)/S_eff).

At T_eff = 5780 K exactly, T* = 0 and every polynomial collapses to its leading term, which is why that temperature reproduces the published solar values 1.7763, 1.0385, 1.0146, 0.3507 and 0.3207. The page's test suite asserts this in reverse: it recomputes 1/d² from each returned distance and checks it equals the published S_eff to ten decimal places. **The reference temperature 5780 K is part of the fit and must not be replaced with the IAU nominal solar value of 5772 K** — doing so evaluates the polynomial at the wrong point and shifts every boundary. For comparison, at 5772 K the water-loss edge moves from 0.99278 to 0.99310 au.

Units and dimensions. Luminosity in solar luminosities, temperature in kelvin, distance in astronomical units, S_eff dimensionless (in units of Earth's insolation). The dimensional guard the test suite runs is that at the water-loss distance the returned flux L/d² equals 1.0146 exactly, and that every boundary scales as √L when the luminosity is changed at fixed temperature — a factor of four in luminosity moves every edge by a factor of two.

Rounding stage. No intermediate rounding: forty significant digits through the polynomial and the square root, rounded once to twelve significant digits at the return boundary. One deliberate design choice follows from that: **the zone verdict compares your orbit against the same rounded boundary distances that are displayed**, not against unrounded internal values. A verdict that said "outside the zone" while the printed edge appeared to be further out would be a defect the reader could see, so the comparison uses the printed numbers.

Significant figures. Two, at most. The coefficient sets from 2013 and 2014 disagree by about 3% at the inner edge, clouds are missing entirely, and the planet-mass spread shown on this page is about ±5%. Quoting a habitable-zone edge to three decimal places implies a precision the underlying climate modelling does not have.

Invalid-domain behaviour. An effective temperature outside 2600–7200 K raises a field error rather than returning a number, because that is the stated validity range of the fit and a quartic extrapolates catastrophically. Zero or negative luminosity raises an error — a star with no luminosity has no habitable zone. Zero or negative orbital distance raises an error, since the received flux L/d² is singular at the origin. One condition attaches a note rather than an error: below 5000 K, Kopparapu et al. state that "there is no clear distinction between runaway greenhouse and water loss limits", and in fact the two boundary distances cross over around 5030 K in these coefficients, so the note tells you to treat them as a single edge.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Kopparapu, R. K., et al. (2013), "Habitable Zones Around Main-Sequence Stars: New Estimates", Astrophysical Journal 765, 131; arXiv:1301.6674, full text retrieved 2026-07-29. Gives the parametrisation S_eff = S_eff☉ + aT* + bT*² + cT*³ + dT*⁴ with T* = T_eff − 5780 K and d = √((L/L☉)/S_eff) au, the 2600–7200 K validity range, and the statement that near the inner edge "there is no clear distinction between runaway greenhouse and water loss limits for stars with T_eff ~< 5000 K". Its abstract quotes the water-loss and maximum-greenhouse limits for the Solar System as 0.99 au and 1.70 au. Peer-reviewed; open-access preprint. NOTE: the coefficients in this version are SUPERSEDED — see the erratum below.
2. [2]Kopparapu, R. K., et al. (2013), "Erratum: Habitable Zones Around Main-Sequence Stars: New Estimates (2013, ApJ, 765, 131)", Astrophysical Journal 770, 82; retrieved 2026-07-29. States that "due to an error at the publisher, several changes and corrections made at the proof stage were not included in the published version of the paper", and supplies the corrected Table 3 used by this calculator: S_eff☉ = 1.7763 / 1.0385 / 1.0146 / 0.3507 / 0.3207 for recent Venus / runaway greenhouse / moist greenhouse / maximum greenhouse / early Mars, with the corresponding a, b, c and d coefficients. Peer-reviewed; freely readable at IOP.
3. [3]Kopparapu, R. K., et al. (2014), "Habitable Zones Around Main-Sequence Stars: Dependence on Planetary Mass", Astrophysical Journal Letters 787, L29; arXiv:1404.5292, full text retrieved 2026-07-29. Uses the same parametrisation and the same 2600–7200 K range, and gives runaway-greenhouse coefficients for 0.1, 1 and 5 Earth-mass planets (S_eff☉ = 0.99, 1.107 and 1.188). States that "the change in the stellar flux at the inner edge of the HZ, compared to Earth, is ∼10% for 0.1 M⊕ and ∼7% for 5 M⊕". This is the second, independent authority for this page: it is a later model that DISAGREES with the 2013 inner edge by about 3%, and all three of its inner edges are reported here rather than silently replacing the 2013 value. Peer-reviewed; open-access preprint.
4. [4]Kasting, J. F., Whitmire, D. P. and Reynolds, R. T. (1993), "Habitable Zones around Main Sequence Stars", Icarus 101, 108–128, doi:10.1006/icar.1993.1010. The original 1-D climate-model habitable zone, superseded by Kopparapu et al. (2013) after the H₂O and CO₂ absorption coefficients were updated from the HITRAN 2008 and HITEMP 2010 databases. Cited as the lineage of the model. Peer-reviewed; PAYWALLED at Elsevier and not independently re-fetched — no number from it is used or quoted on this page.
5. [5]Prša, A., et al. (2016), "Nominal Values for Selected Solar and Planetary Quantities: IAU 2015 Resolution B3", Astronomical Journal 152, 41; arXiv:1510.07674, retrieved 2026-07-29. Source of the nominal solar luminosity 3.828 × 10²⁶ W used to define the luminosity unit, and of the nominal solar effective temperature 5772 K — which this page deliberately does NOT substitute for the fit's 5780 K reference. Peer-reviewed; open-access preprint.
6. [6]NASA Science, "Mars Facts", retrieved 2026-07-29. Gives Mars's average distance from the Sun as 228 million kilometres, which divided by the IAU 2012 astronomical unit of 149 597 870.7 km gives the 1.524 au used in the worked example. Government science resource; open access.