I am trying to back-calculate the greenhouse effect on planetary equilibrium temperature for Earth (in the hope I can then attempt applying it to other calculations.) I know that the actual equilibrium temperature of Earth is 287.89K, +33K above the calculated equilibrium temperature: Teq = (Q x (1- albedo)/ 4 x Stefan-Boltzmann constant)0.25 When Q = 1400 W/m2, (1 - albedo) = 0.7. From here, if I am understanding it aright, the greenhouse effect is (in a simplified form enough for my purposes) basically a multiplier of Q, respresenting the amount of energy reflected back off the atmosphere to the planet. I put the Teq as a spread sheet calculation, with an additional factor (let's call it Z) which multiplies Q that I coud alter manually; experimentally it looks like for Earth it's Z is about 1.6ish. Teq = (Q x Z x (1- albedo)/ 4 x Stefan-Boltzmann constant)0.25 Teq = 254.89K for Earth What I would like to do is see if I can work back, using the known values from Earth, and see if I can determine Z, which would at least give me something more to work with. (At the moment, my estimations for greenhouse effects are "add about 33ºK") I tried rearranging the formula 287.89K = 33K + 254.89K = (Q × Z × (1- albedo)/ 4 × 5.67 × 10-8)0.25 287.894= Q × Z × (1- albedo)/ 4 × 5.67 × 10-8 287.894 × 4 × 5.67 × 10-8 = Q × Z × (1- albedo) 287.894 × 4 × 5.67 × 10-8/ Q × (1- albedo) = Z However, this came out as 3.97, which is clearly wrong. I've obviosuy messed up somewhere, but for the life of me I'm not sure where.