I am working with two constants, one has units of W/m^2-C and the other is W/m^2-K^4. This bugs me because K=C+273 as opposed to most other conversions…

Is there a way to find how to adjust W/m^2-C to W/m^2-K?
It’s probably staring me in the face, but something about it bugs me…

Ok, I’m chatting with myself here, but to correct myself, the above is simply wrong. However, to answer myself, ultimately I am plugging into a formula that uses dT, not just T, so dT in Celcius = dT in Kelvin, hence it won’t matter.

It really depends on the formula. If the formula contains the difference in two temperatures then C and K are the same. Like say a heat flow formula. If it is instead a like PV=nRT then C and K are not the same.