Habitable Zone Calculator: Where a Planet Could Have Liquid Water
Inner and outer edges of a star’s habitable zone with the Kopparapu et al. climate limits from luminosity and temperature, radius and temperature, or mass; where a planet at a given distance sits, the stellar flux it receives, its equilibrium temperature, orbital period and a table of every limit.
How it works
S_eff = S☉ + a·T* + b·T*² + c·T*³ + d·T*⁴, with T* = Teff − 5780 K (Kopparapu et al. 2014); distance = √(L / S_eff) AU; conservative zone = runaway greenhouse to maximum greenhouse, optimistic = Recent Venus to Early Mars; T_eq = 278.3 K × (1 − A)^¼ × L^¼ ÷ √a; P = √(a³ / M) years
The habitable zone is the range of distances from a star where a rocky planet with an Earth-like atmosphere could keep liquid water on its surface. Its edges are set by the stellar flux the planet receives. Too close and water vapour triggers a runaway greenhouse that boils the oceans away; too far and even a thick CO₂ atmosphere cannot keep the surface above freezing (the maximum greenhouse limit). These two climate-model limits make the conservative zone. The optimistic zone uses empirical limits from our own Solar System: Venus appears to have had no surface water for the last billion years (Recent Venus), while Mars seems to have had liquid water about 3.8 billion years ago (Early Mars). The flux at each edge depends a little on the star’s temperature, because cooler stars emit more infrared light, which water and CO₂ absorb better and which Rayleigh-scatters less. The calculator uses the polynomial fits of Kopparapu et al. (2014), valid for effective temperatures of 2,600–7,200 K, including the dependence of the inner edge on planet mass (0.1, 1 or 5 Earth masses). Distances then scale with the square root of luminosity: a star four times as bright has a zone twice as far out. Enter the star as luminosity and temperature, radius and temperature (L = R² × (T/5,772 K)⁴), or as a main-sequence mass, which uses rough mass–luminosity and mass–radius relations. The equilibrium temperature ignores greenhouse warming (Earth’s is about 255 K, 33 K below its real average), and the orbital period uses Kepler’s third law with a stellar mass you enter or estimate from luminosity.
Worked example
For a Sun-like star (L = 1 L☉, Teff = 5,780 K) T* = 0, so the edges use the base fluxes: runaway greenhouse 1.107 → √(1 ÷ 1.107) = 0.950 AU, maximum greenhouse 0.356 → 1.68 AU, Recent Venus 1.776 → 0.750 AU and Early Mars 0.320 → 1.77 AU. The conservative zone is 0.950–1.68 AU and the optimistic zone 0.750–1.77 AU. Earth at 1 AU receives 1 × Earth’s flux (1,361 W/m²), sits inside the conservative zone and has T_eq = 278.3 × 0.7^¼ = 254.6 K (−18.6 °C) with albedo 0.3, and an orbital period of 1.00 year.
Sources: Kopparapu et al. (2014), Habitable Zones Around Main-Sequence Stars: Dependence on Planetary Mass, ApJL 787, L29 (arXiv:1404.5292) · Kopparapu et al. (2014), full text with Table 1 coefficients
Frequently asked questions
What is the habitable zone?
The band of orbital distances where a rocky planet with an Earth-like atmosphere could keep liquid water on its surface. It is sometimes called the Goldilocks zone: not too hot and not too cold.
What is the difference between the conservative and optimistic zones?
The conservative zone runs from the runaway-greenhouse limit to the maximum-greenhouse limit, both from climate models. The optimistic zone is wider and uses evidence from Venus (dry for about a billion years) and early Mars (once wet), so it includes planets that may have been habitable only in some conditions.
Where is the Sun’s habitable zone?
With the Kopparapu et al. (2014) limits, the conservative zone is about 0.95–1.68 AU and the optimistic zone about 0.75–1.77 AU. Earth (1 AU) is inside; Venus (0.72 AU) is just outside; Mars (1.52 AU) is inside the conservative zone but too small to keep a thick atmosphere.
Is a planet in the habitable zone habitable?
Not necessarily. It also needs enough mass to hold an atmosphere, water, and protection from stellar flares; planets around red dwarfs are often tidally locked. The zone is a first filter for where to look.
Why does the star’s temperature matter as well as its luminosity?
Cooler stars give out more infrared light, which a planet’s water vapour and CO₂ absorb more easily and its atmosphere scatters less, so the same flux heats the planet more. Habitable-zone edges around red dwarfs therefore sit at slightly lower fluxes than around the Sun.
Why does the old 0.95–1.37 AU zone differ from this one?
Kasting et al. (1993) put the outer edge at 0.53 × Earth’s flux (1.37 AU for the Sun). Updated absorption data led Kopparapu et al. (2013, 2014) to move it to 0.356 × Earth’s flux (1.68 AU); the inner edge stayed near 0.95 AU.
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This calculator is for educational purposes. Double-check important results before acting on them.