The solar flux absorbed by the planet from the star is equal to the flux emitted by the planet:
Assuming a fraction of the incident sunlight is reflected according to the planet's Bond albedo, :
where  represents the area- and time-averaged incident solar flux, and may be expressed as:
The factor of 1/4 in the above formula comes from the fact that only a single hemisphere is lit at any moment in time (creates a factor of 1/2), and from integrating over angles of incident sunlight on the lit hemisphere (creating another factor of 1/2).
Assuming the planet radiates as a blackbody according to the Stefan–Boltzmann law at some equilibrium temperature , a balance of the absorbed and outgoing fluxes produces:
 where  is the Stefan-Boltzmann constant.
Rearranging the above equation to find the equilibrium temperature leads to: