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

    Ready to run the numbers?

    Open Planet Surface Temperature Calculator