Habitable Zone Calculator (Goldilocks Zone): Inner and Outer Edges for Any Star

How it works

S_eff = S_eff,☉ + a·T* + b·T*² + c·T*³ + d·T*⁴, with T* = Teff − 5780 K (Kopparapu et al. 2014); edge distance d = √(L ÷ S_eff) AU; Sun: recent Venus 1.776, runaway greenhouse 1.107, maximum greenhouse 0.356, early Mars 0.320; planet flux S = L ÷ (a² √(1 − e²)); T_eq = 278.3 K × S^¼ × (1 − A)^¼; L = R² × (Teff ÷ 5772)⁴

A planet’s temperature is set by how much starlight it receives, and that flux falls with the square of distance. The habitable zone is the band of distances where an Earth-like planet with a suitable atmosphere could keep liquid water on its surface. Its edges are set by climate physics, not by one fixed temperature. Too close, water vapour traps heat until the oceans boil away (the runaway greenhouse). Too far, even a thick carbon-dioxide atmosphere cannot keep the surface above freezing (the maximum greenhouse). The optimistic limits come from the evidence that Venus may have had water until about a billion years ago and that early Mars had flowing water. This calculator uses the climate-model fits of Kopparapu et al. (2013, 2014), the same ones behind the NASA and Virtual Planetary Laboratory habitable-zone tools. Each edge is a stellar flux S_eff that depends on the star’s temperature. Cooler, redder stars put more of their light into the infrared, which water and CO₂ absorb well, so their habitable zone sits at a lower flux than the Sun’s. Dividing the star’s luminosity by that flux and taking the square root gives the distance in AU. The fits are valid for stars of 2,600–7,200 K. Larger planets hold their water better, so the inner edge moves about 7% closer for a 5 Earth-mass planet. Equilibrium temperature assumes the planet spreads its heat evenly and has no greenhouse effect. That is why Earth’s value of 255 K sounds frozen: its atmosphere adds about 33 K. Being in the habitable zone does not make a planet habitable, because its size, atmosphere, magnetic field and the star’s flares all matter.

Worked example

For the Sun (L = 1 L☉, Teff = 5,780 K) T* = 0, so the edges are the solar fluxes. Conservative zone: √(1 ÷ 1.107) = 0.950 AU to √(1 ÷ 0.356) = 1.676 AU. Optimistic zone: √(1 ÷ 1.776) = 0.750 AU to √(1 ÷ 0.320) = 1.768 AU. Earth at 1 AU receives 1.000 × Earth’s flux (1,361 W/m²), which puts it in the conservative zone. With albedo 0.30 its equilibrium temperature is 278.3 × 0.70^¼ = 254.6 K, shown as 255 K (−19 °C), and its period is 365.3 days. A planet at the outer edge would take about 792 days per orbit.

Sources: Kopparapu: habitable zone calculator and coefficients (Penn State) · Virtual Planetary Laboratory: calculation of habitable zones · Kopparapu et al. (2014) code with the fit coefficients (hzcalc.py)

Frequently asked questions