Planetary Equilibrium Temperature Calculator
The equilibrium temperature of a planet — what it would be with no greenhouse effect — from its star’s luminosity, its orbital distance and how much light it reflects, with the difference the greenhouse effect makes on Earth.
A planet absorbs the starlight it does not reflect and radiates as a black body until the two balance: T = [L (1 − a) ÷ (16 π σ d²)]^¼.
How the planetary equilibrium temperature calculator works
A planet absorbs the starlight it does not reflect and radiates as a black body until the two balance: T = [L (1 − a) ÷ (16 π σ d²)]^¼. For Earth that gives 255 K, −18 °C; the atmosphere’s greenhouse effect adds 33 K to reach the real 288 K. Venus would be cooler than Earth on this basis because of its bright clouds, and is hotter because of its atmosphere.
Formula: T_eq = [L (1 − A) ÷ (16 π σ d²)]^¼
Worked examples
| Inputs | Equilibrium temperature | Note |
|---|---|---|
| Earth: 1 L☉, 1 AU, albedo 0.31 | 253.7 K | 254 K, −19 °C |
| Mars: 1.52 AU, albedo 0.25 | 209.8 K | 210 K |
| A hot Jupiter at 0.05 AU of a Sun-like star | 1,212.4 K | 1,200 K |
FAQFrequently asked questions
Why is Earth warmer than this?
The greenhouse effect: water vapour, carbon dioxide and methane absorb outgoing infrared and re-radiate part of it downward, raising the surface about 33 K above the equilibrium figure. Venus’s atmosphere adds over 500 K.
What albedo should I use?
The Bond albedo — the fraction of all incoming light reflected across all wavelengths and angles. Earth’s is about 0.31, mostly clouds; ice worlds reach 0.6–0.8, dark rocky bodies 0.1.
Does the planet rotate fast?
The formula assumes heat spreads evenly over the whole sphere, which fits a rotating planet with an atmosphere. A slowly rotating airless body is hotter on the day side by a factor of 2^¼ and much colder at night.
How is this used for exoplanets?
Luminosity and distance are usually known from the star and the orbit; the temperature then says whether the planet could be habitable, with the caveat that atmospheres — unknown for most — move the surface value a great deal.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- CSIRO Space and Astronomy — Australia's national science agency
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).