Planet Surface Temperature Calculator Formula

Understand the math behind the planet surface temperature calculator. Each variable explained with a worked example.

Use the Planet Surface Temperature Calculator

Formulas Used

Effective Temperature

surface_temp = pow((luminosity * (1 - albedo)) / (16 * pi * 5.67e-8 * pow(distance, 2)), 0.25)

Temperature (C)

surface_temp_c = pow((luminosity * (1 - albedo)) / (16 * pi * 5.67e-8 * pow(distance, 2)), 0.25) - 273.15

Variables

VariableDescriptionDefault
luminosityStar Luminosity(W)3.828e+26
albedoBond Albedo0.3
distanceOrbital Distance(m)149600000000

How It Works

Estimating a Planet's Surface Temperature

By balancing the incoming stellar radiation with the outgoing thermal emission, we get the equilibrium temperature.

Formula

T = [ L (1 - A) / (16 pi sigma d squared) ]^(1/4)

  • *L* = stellar luminosity
  • *A* = bond albedo (fraction reflected)
  • *sigma* = Stefan-Boltzmann constant 5.67 x 10 to the minus 8
  • *d* = orbital distance

    • This neglects the greenhouse effect, which can raise the actual surface temperature significantly.

    Worked Example

    Earth-like planet: L = 3.828e26 W, A = 0.3, d = 1.496e11 m.

    luminosity = 3.828e+26albedo = 0.3distance = 149600000000
    1. 01T = [L(1-A) / (16 pi sigma d squared)]^0.25
    2. 02Numerator = 3.828e26 * 0.7 = 2.680e26
    3. 03Denominator = 16 * pi * 5.67e-8 * (1.496e11)^2 = 6.39e16
    4. 04Ratio = 4.194e9
    5. 05T = (4.194e9)^0.25 = 254.5 K = -18.6 C

    Frequently Asked Questions

    Why is the result for Earth below freezing?

    This is the equilibrium temperature without the greenhouse effect. Earth's atmosphere traps heat, raising the actual average surface temperature to about 288 K (15 C).

    What is the bond albedo?

    The fraction of total incoming radiation that a planet reflects back into space across all wavelengths. Earth's is about 0.30.

    Can this formula be used for exoplanets?

    Yes, provided you know the host star's luminosity and the planet's orbital distance. The albedo is usually estimated or assumed.

    Ready to run the numbers?

    Open Planet Surface Temperature Calculator