Net Radiative Cooling to the Sky

Every surface facing the open sky is in a losing exchange. It radiates upward according to the Stefan-Boltzmann law at its own temperature, and it receives back the downward longwave from an atmosphere that behaves like a body considerably colder. The difference of the two fourth powers, scaled by the surface's emissivity, is the net loss. A roof at 5 °C under a sky radiating at −15 °C, with the emissivity of 0.95 that almost every non-metal has in the longwave, sheds 83 W/m². That is the number behind "60 to 100 watts per square metre on a clear night", and it is more than a small room's worth of heat leaving every few square metres of roof, all night, for free.

This is one page removed from Stefan-Boltzmann and one page removed from the net exchange between surfaces: the sky is simply a very large enclosure at T_sky, so the view factor is one and the area cancels out into a flux per square metre. The fourth powers are taken in kelvin, always, whatever unit you type — the engine converts before it computes, which is the whole reason a Celsius entry does not quietly produce a nonsense answer here.

Emissivity is the term people get wrong, and they get it wrong in a specific way: they reach for a shortwave figure. Longwave emissivity and solar absorptance are different properties of the same surface. White paint reflects most of the sun and is nonetheless a near-perfect longwave emitter at about 0.9; polished aluminium is a poor longwave emitter at 0.05 or lower and barely cools radiatively at all, which is why a bare metal roof frosts less readily than the painted one beside it. If your surface is not a metal, 0.90 to 0.95 is nearly always right.

Two things to keep in view. First, this is the NET longwave term only; it is not the whole surface energy balance. Convection, evaporation and conduction into whatever is underneath all run at the same time, and by day the absorbed solar swamps everything here. Use this figure as one term, and balance it against convection if you want the surface temperature that results. Second, the emissivity brain on this page will refuse an answer above 1, because a heat loss larger than a blackbody could manage means something else is cooling that surface — a wet surface evaporating is the usual culprit, and wind is the other.

One last thing this page quietly explains: passive radiative cooling below air temperature is not a trick, it is the default. Any surface with a clear view of a dry night sky does it. The reason it is a research field rather than a household fact is that the useful version has to work in DAYLIGHT, which means a coating that reflects almost all the incoming sun while still emitting hard in the 8-13 micron window where the atmosphere is transparent. The physics on this page is the ceiling those materials are chasing, and the flux you compute here is roughly what they have to work with.