Planet Equilibrium Temperature Calculator
Calculate a planet’s or exoplanet’s equilibrium (blackbody) temperature from its star’s luminosity, orbital distance and Bond albedo — in kelvin, °C and °F — plus the stellar flux it receives.
How it works
S = 1361 W/m² × L ÷ a² · T_eq = [S (1 − A) ÷ (f σ)]^(1/4) · f = 4 for even heating, 2 for dayside only · σ = 5.670374 × 10⁻⁸ W m⁻² K⁻⁴ · peak wavelength λ = 2898 µm·K ÷ T (Wien)
A planet absorbs the starlight it does not reflect and re-radiates it as infrared. Setting the absorbed power, S(1 − A)πR², equal to the emitted power, σT⁴ × 4πR² (or × 2πR² if only the dayside radiates), gives the equilibrium temperature, which ignores any greenhouse effect. It is the standard first estimate for exoplanets. For Earth it is about 255 K (−18 °C): the real average surface temperature, about 288 K (15 °C), is 33 °C warmer because of the greenhouse effect. Venus has an equilibrium temperature near 230 K but a surface of 737 K.
Worked example
For Earth — a Sun-like star (1 L☉) at 1 AU with a Bond albedo of 0.30 and even heating: S = 1361 W/m², and T = [1361 × 0.70 ÷ (4 × 5.670 × 10⁻⁸)]^(1/4) = 254.6 K, which is −18.6 °C. Its thermal glow peaks at 11.38 µm in the infrared.
Sources: Wikipedia — Planetary equilibrium temperature · NASA — Earth fact sheet (blackbody temperature 254 K)
Frequently asked questions
What is a planet’s equilibrium temperature?
The temperature at which a planet, treated as a blackbody without an atmosphere, emits exactly as much energy as it absorbs from its star.
Why is Earth’s equilibrium temperature −18 °C?
That is the temperature Earth would have without greenhouse gases. Water vapour, CO₂ and other gases trap outgoing infrared and raise the average surface temperature to about 15 °C.
What albedo should I use for an exoplanet?
Often 0.3 as a neutral guess, or 0 to get the maximum temperature. Hot Jupiters typically have very low albedos (below 0.1); icy or cloudy worlds can exceed 0.6.
When should I use dayside-only heating?
For tidally locked planets with thin or no atmospheres, which keep one face to the star. The dayside is then about 19% hotter (2^(1/4)) than with even heating.
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This calculator is for educational purposes. Double-check important results before acting on them.