Planetary Equilibrium Temperature Calculator
Our planetary & earth system science calculator computes planetary equilibrium temperature accurately. Get results you can export or share.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Teq = ((L(1-A))/(16*pi*sigma*eps*d^2))^0.25
L=stellar luminosity, A=albedo, sigma=Stefan-Boltzmann constant, eps=emissivity, d=distance in meters.
Worked Examples
Example 1: Earth Equilibrium
Problem:L=3.828e26 W, d=1 AU, A=0.30
Solution:Teq = ((3.828e26*0.70)/(16*pi*5.67e-8*(1.496e11)^2))^0.25 = 254.6 K
Result:~255 K (-18 C), 33 K below actual 288 K average
Example 2: Mars Equilibrium
Problem:d=1.524 AU, A=0.25
Solution:Teq = ((3.828e26*0.75)/(16*pi*5.67e-8*(2.28e11)^2))^0.25 = 209.3 K
Result:~209 K (-64 C), matches Mars observed ~210 K
Frequently Asked Questions
What is planetary equilibrium temperature?
Planetary equilibrium temperature is the theoretical temperature a planet reaches as a perfect blackbody with no atmosphere, where incoming solar radiation equals outgoing thermal radiation. Calculated via the Stefan-Boltzmann law, it depends on stellar luminosity, orbital distance, and albedo. For Earth it is approximately 255 K, about 33 degrees below the actual surface temperature. The difference is due to the greenhouse effect trapping heat in the atmosphere.
How does albedo affect equilibrium temperature?
Albedo is the fraction of solar radiation reflected, from 0 to 1. Higher albedo means lower equilibrium temperature since less energy is absorbed. Earth reflects about 30 percent of sunlight with an albedo of 0.30. Ice-covered planets can exceed 0.7, while dark ocean worlds drop below 0.1. Small albedo changes from melting ice can significantly shift the energy balance.
Why is Earth warmer than its equilibrium temperature?
Earth averages 288 K, about 33 K warmer than its 255 K equilibrium temperature. The greenhouse effect causes this, as CO2, water vapor, and methane absorb and re-emit infrared radiation from the surface. This traps heat in the lower atmosphere raising temperatures above pure radiative balance. Without this effect Earth would be frozen with temperatures well below the freezing point of water.
How does orbital distance affect equilibrium temperature?
Temperature decreases with distance following an inverse square root relationship. Doubling distance reduces temperature by a factor of about 1.41 because flux falls as inverse square of distance. A planet at 2 AU receives one quarter the flux of one at 1 AU. Mercury at 0.39 AU reaches about 440 K equilibrium while Mars at 1.52 AU reaches about 210 K.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy