Albedo and Planetary Energy Balance Calculator

Planetary albedo is the fraction of incoming solar radiation a planet reflects back to space, on a scale from 0 (a perfectly absorbing black surface) to 1 (a perfectly reflecting white surface). Earth's average albedo is about 0.30, mostly from clouds, ice, and snow.

It first finds the absorbed solar flux as S(1-A)/4, where S is the solar constant and A is albedo, dividing by 4 for the ratio of a sphere's surface area to its sunlit cross-section. It then applies the Stefan-Boltzmann law, Te = (absorbed flux / sigma)^0.25, where sigma is 5.67x10^-8 W/m^2K^4, to find the equilibrium temperature in kelvin.

A planet intercepts sunlight only across its cross-sectional disk, area pi*r squared, but radiates heat away from its entire spherical surface, area 4*pi*r squared. Spreading the intercepted flux over the full sphere (a factor of 4 larger area) approximates the average flux per unit surface area, accounting for day/night rotation and the sphere's curvature.

The equilibrium temperature calculated here, about -18 degrees Celsius for Earth, only accounts for solar input and blackbody radiation loss. It excludes the greenhouse effect, the trapping of outgoing longwave radiation by water vapor, CO2, and other gases, which adds roughly 33 degrees Celsius of extra warming, bringing Earth's actual average surface temperature to about 15 degrees Celsius.

Ice-albedo feedback is a self-reinforcing climate loop: cooling allows more ice and snow to form, ice and snow have high albedo and reflect more sunlight, which absorbs less solar energy and cools the surface further, allowing yet more ice to form. This calculator lets you see the effect directly by raising albedo and watching equilibrium temperature drop.

Published snowball Earth estimates typically place global albedo between 0.55 and 0.65 for an ice-covered planet, compared to about 0.30 for today's Earth. Entering 0.60 with Earth's solar constant of 1361 W/m squared gives an equilibrium temperature of roughly 221 kelvin (about -52 degrees Celsius), illustrating why a fully ice-covered Earth would be extremely difficult to escape once established.

Change the solar constant S to that planet's value at its orbital distance (S scales as 1/distance squared from the Sun), and set the albedo A to that planet's known or estimated reflectivity. For example, Mars has S around 590 W/m squared and an albedo around 0.25, while Venus has S around 2601 W/m squared and a very high albedo around 0.75 from its thick cloud cover.

The Stefan-Boltzmann constant, sigma = 5.67x10^-8 W/m^2K^4, relates the power radiated by a blackbody per unit area to the fourth power of its absolute temperature (P = sigma*T^4). Solving that relationship for T gives the equilibrium temperature formula used by this calculator, treating the planet as an idealized blackbody radiator in balance with the sunlight it absorbs.

Only indirectly, through the single albedo value you enter. Clouds and ice are the largest real-world contributors to Earth's albedo, so a higher albedo input implicitly represents more cloud or ice cover. The calculator does not separately model the atmosphere's greenhouse trapping of outgoing radiation. See the companion Radiative Forcing Calculator (CO2) for that effect.

Use 1361 W/m squared, the commonly cited total solar irradiance at Earth's mean distance from the Sun (1 astronomical unit), measured at the top of the atmosphere. This is the calculator's default value.