Calculate Planet Temperature

Blackbody Temperature Greenhouse Effect

The blackbody temperature of a planet can be calcualted using this formula

  • T = temperature (kelvin)
  • KS = Solar constant (For Earth, this value is about 1361 watts/m2)
  • σ = Stefan-Boltzmann constant = 5.670373 x 10-8 watts / m2 K4 (m = meters, K = kelvins)
  • Albedo: For the Earth, this value is 0.31.

The formula can also be rewritten as:

$$T = \sqrt[4]{\frac{F}{σ}}$$

$$F = \frac{K_{S}(1-A)}{4}$$
  • F = Absorbed solar radiation flux (watts/m2)

The formula for the blackbody temperature of a planet can be modified by adding the greenhouse effect in watts per square meter.

$$T = \sqrt[4]{\frac{F+G}{σ}} = \sqrt[4]{\frac{K_{S}(1-A)}{4σ} + \frac{G}{σ}}$$

  • T = temperature (kelvin)
  • KS = Solar constant (watts/m2)
  • σ = Stefan-Boltzmann constant = 5.670373 x 10-8 watts / m2 K4 (m = meters, K = kelvins)
  • A = Albedo (0-1)
  • G = Greenhouse Effect (watts/m2)

However, this formula doesn't take greenhouse effect into account. By adding the equivalent watts/m2 produced by a given volume of greenhouse gasses in the planet's atmosphere to this formula, we can calculate the temperature of the planet more accurately.

With this formula, we can get a better idea of the temperature of the planet, as greenhouse effect is taken into account.

$$T = \sqrt[4]{\frac{K_{S}(1-A)}{4σ}}$$

Formula made with MathJax

Variable Meaning Earth
T Temperature (oK) 287.16
K Solar Constant (W/m2) 1361
A Albedo 0.31
G Greenhouse Effect (W/m2) 150

Instructions

  1. Enter 3 of the following values: Solar Constant, Greenhouse Effect, Albedo, Temperature
  2. Press the "Calculate" button to get the 4th value.
Solar Constant (w/m2) Greenhouse Effect (w/m2) Albedo Temperature (K)

Calculating Greenhouse Effect

The greenhouse effect of a planet is represented as watts/m2, as the greenhouse effect traps heat from a star in the planet's atmosphere, effectively increasing the amount of the sun's heat absorbed by the planet, in addition to what the planet itself already absorbs.

Planet Effect (w/m2)
Earth 150
Compound Concentration in atmosphere (ppm) Contribution to Greenhouse Effect (w/m2) Total Greenhouse Effect (w/m2)
Wikipedia - Greenhouse Gasses*
Water Vapor (H2O)

Carbon Dioxide (CO2)

Methane (CH4)

Ozone (O3)**

Dust***

* Based on percentages of their respective contributions to Earth's greenhouse effect, using 150 w/m2 for Earth's Greenhouse effect.

** The range for the ppm of Ozone in the air provided by Wikipedia is 2-8. The average (5) is used in this calculator.

*** Not included in Earth's greenhouse effect. PPM value calculated by dividing the amount of dust in the air (17 million metric tonnes) by the mass of the atmosphere (5.15*1018kg).

Amount of Compound in Atmosphere
PPM Earths Greenhouse Effect
Water
CO2
Methane
Ozone
Dust
Total Greenhouse Effect
Amount of Compound in Atmosphere
% of Atmosphere Atmospheric Pressure (Earths) Amount of Compound (Earths)
Water
CO2
Methane
Ozone
Dust