Circumstellar Habitable Zone Calculator

Background.

On the most widely used climate-model definition, Mars orbits inside the Sun's habitable zone. At 1.524 au it receives 0.4306 times the sunlight Earth gets, more than the 0.3507 below which even a thick carbon-dioxide atmosphere can no longer keep surface water liquid. Mars is frozen because it was too small to keep that atmosphere, not because it is too far out. That is a fair summary of what a habitable zone tells you and what it leaves out: it is a statement about orbits and starlight, not about any particular planet.

The boundaries here come from Kopparapu and colleagues (2013), who ran a one-dimensional, cloud-free climate model for an Earth-mass planet with a nitrogen, water and carbon-dioxide atmosphere and found the stellar flux at which each climate limit is crossed. They fitted those fluxes as a fourth-order polynomial in the star's effective temperature, so for any main-sequence star between 2,600 K and 7,200 K, roughly spectral types M through F, the zone follows from two numbers: luminosity and temperature.

The coefficients used are the corrected ones from the paper's erratum. The publisher's notice says changes made at proof stage were left out of the printed version, which is why the solar zone of 0.99 to 1.70 au quoted in the original abstract differs from the corrected outer edge of 1.69 au.

What is habitable zone calculator?

A circumstellar habitable zone is the range of orbital distances at which a rocky planet with an Earth-like atmosphere could keep liquid water on its surface. It is defined by flux, the starlight received per unit area, which falls with the square of distance. Two limits bound the conservative zone: the moist-greenhouse or water-loss limit inside, where water reaches the upper atmosphere, is split by ultraviolet light and its hydrogen escapes to space, and the maximum-greenhouse limit outside, beyond which adding CO₂ cools the planet because the thicker atmosphere scatters away more sunlight than it traps. A wider, optimistic zone runs from a recent-Venus limit to an early-Mars limit, both set by planetary history rather than by the climate model.

How to use this calculator.

1. 01Enter the star's bolometric luminosity in solar luminosities (1 L☉ = 3.828 × 10²⁶ W). If a catalogue gives only an absolute magnitude, convert it with the luminosity calculator first.
2. 02Enter the effective temperature in kelvin, between 2,600 and 7,200 K. For the Sun, 5,780 K reproduces the published solar boundaries exactly; the IAU nominal 5,772 K gives almost the same answer.
3. 03Enter the planet's semi-major axis in au. A circular orbit is assumed, so for an eccentric orbit see the question on eccentricity below.
4. 04Read the two conservative edges first; treat the optimistic pair and the three 2014 inner edges as the range of reasonable answers.
5. 05Compare the flux at the planet, in Earth units, with each edge's effective flux to see how much margin the verdict has.

The formula.

Each boundary is a critical effective flux, S_eff, in units of the flux Earth receives. Its dependence on the star's spectrum is fitted as S_eff = S_eff,☉ + aT* + bT*² + cT*³ + dT*⁴, with T* = T_eff − 5,780 K and a separate coefficient set for each limit. The distance follows from the inverse-square law: a planet at d au receives (L/L☉)/d² Earth fluxes, so the edge sits at d = √((L/L☉)/S_eff). Because distance goes as √L, a star four times as luminous at the same temperature has every edge twice as far out. Temperature matters because cooler stars put more of their light into the near infrared, where water vapour and CO₂ absorb strongly and less is scattered back to space, so a planet is warmed more per watt; every S_eff falls as the star gets redder. Below about 5,027 K the runaway-greenhouse and water-loss distances cross, and the authors say the two cannot be clearly distinguished below 5,000 K, so a note appears for such stars. Temperatures outside 2,600–7,200 K are refused rather than extrapolated, since a quartic pushed beyond its fitted range can return nonsense.

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.