 To calculate the average temperature at the top of Earth's atmosphere, we need to look at the balance between the solar radiation energy coming into the Earth's system against the infrared radiation going out of the Earth's system. The solar irradiance is essentially parallel by the time it gets to Earth, so it is intercepted by Earth's cross-section, which is just pi r Earth squared. Since the fraction of the solar radiation is immediately reflected and scattered back out into space, this is what we call the albedo, we have the correct amount of radiation energy that Earth's system absorbs by subtracting off the albedo. On the other hand, Earth radiates all in all directions, so assuming Earth's emissivity is 1, then Earth's irradiance is in watts per meter squared, and if we multiply by Earth's surface area, really the surface area at the top of the atmosphere, then we get the energy leaving the Earth's system every second, that is, in watts. We can use the laws of exponents to rearrange this equation to get an equation for temperature. When we put in typical values for the Earth's system in solar irradiance, we calculate that the radiating temperature at the top of the atmosphere is 255 Kelvin, or minus 18 degrees C, or zero Fahrenheit.