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Planet Equilibrium Temperature Calculator

Enter the star luminosity, orbital distance and albedo to find the planet's temperature.

How it is calculated

You give the star's luminosity as a multiple of the Sun's (L), the planet's orbital distance in astronomical units (d), and the Bond albedo (A, between 0 and below 1). First the tool finds the starlight flux at the planet: S = L × 3.828×1026 W ÷ (4π d²), with d converted to metres using 1 AU = 1.496×1011 m. Then it balances absorbed and emitted energy over the whole sphere: T = [S (1 − A) ÷ (4σ)]1/4, where σ = 5.67×10-8 W m-2 K-4. The factor 4 comes from the sphere's surface being four times its sunlit disc. Temperature is reported in kelvin and °C (K − 273.15), and the flux in W/m². It assumes no atmosphere warming and an even temperature all around the planet. Albedo of 1 or above, zero or negative distance, or luminosity of zero or less gives no result.

Worked example

Take a star equal to the Sun (L = 1), a planet at 1 AU, and an albedo of 0.3. Flux: 3.828×1026 ÷ (4π × (1.496×1011)2) = 1,361.17 W/m². Absorbed share: 1,361.17 × (1 − 0.3) = 952.8, divided by 4σ (2.268×10-7) gives about 4.2×109. The fourth root is 254.59 K, which is −18.56 °C. The planet would stay that cold only if it had no greenhouse effect.

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Common mistakes

  • Entering the distance in kilometres or miles. The field is in astronomical units, so Earth's distance is 1, not 150,000,000.
  • Entering the star's luminosity in watts. It is a ratio to the Sun, so the Sun itself is 1, and a star half as bright is 0.5.
  • Using the geometric albedo or a percentage. Bond albedo is a fraction from 0 to under 1, so 30 percent is 0.3, and a value of 1 returns no result.
  • Comparing the result with a measured surface temperature. The figure ignores greenhouse warming, so an actual surface can be much warmer than the equilibrium value.
  • Reading kelvin as degrees Celsius. The tool gives both, and the K value is what the physics formula yields.

About this calculator

A planet's equilibrium temperature is the theoretical temperature at which the energy it absorbs from its star equals the energy it radiates back to space, ignoring greenhouse effects or internal heat. It's calculated from the star's luminosity (L), the planet's orbital distance (d), and its Bond albedo (A) — the fraction of incoming light it reflects — using T_eq = [L(1 − A) ÷ (16πσd²)]^(1/4), where σ is the Stefan-Boltzmann constant.

Astronomers and astrobiologists use this formula as a first-pass estimate when characterizing newly discovered exoplanets, checking whether a planet falls within a star's "habitable zone" before more detailed climate modeling. It's a simplification — Earth's actual surface temperature, for instance, is warmer than its equilibrium temperature because of the greenhouse effect — but it remains the standard starting point in exoplanet research and astronomy education.

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Comments (1)

  • Editorial team

    Equilibrium temperature is a baseline, not a forecast of surface conditions. Feed it a Venus-like case, 0.72 AU and an albedo of 0.77, and it returns 227.16 K (-45.99 °C), colder than Earth's 254.59 K, because a bright cloud deck reflects most light even though Venus sits closer in. Its actual surface is far hotter; the gap is the greenhouse effect this formula leaves out. A Mars-like 1.52 AU at 0.25 gives 210.09 K. Which world are you testing?

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