Relative Error Temperature I have a model to simulate temperatures and I want to compare it to reference values.
I thought that the relative error (or rather percentage error) would be interesting, but I'm rather confused on how to calculate it in the correct way.
Consider the following examples.


*

*My model: 47°C; Reference value: 45°C


Relative error: 2°C/45°C = 4.44%


*My model: 2°C; Reference value: 0°C


Relative error: 2°C/0°C = undefined


*My model: 302°K; Reference value: 300°K


Relative error: 2°K/300°K = 0.66%
Obviously this cannot be the right way to do it. Imagine a piece of iron which is heated up and cooled down. During this simulation an absolute error of 2°C is extremely small compared to the temperature range (from let's say 30°C to 1000°C).
On the other hand, an absolute error of 2°C is huge when examining the fever of a patient as the temperature range is only from about 36°C to 44°C.
My question is, how do I calculate a meaningful error between the values of my model and the reference model with respect to the "context"?
 A: You have to ask yourself what is significant about your "relative error" - and why that number would be useful to have.
Relative error can be helpful to compare different experiments that occur on different scales, and in general to give an idea of the accuracy of an experiment, model etc. dividing by the absolute value may make physical sense (in the case of temperature that must mean using the Kelvin scale) but sometimes you have to ask yourself about the natural scale factor that makes sense. If your simulations allow for temperature to change over a range of 50C, then a scale factor of 50C is a sensible way to get a sense for the "relative error" - it represents how close you get to the true value given the scale of the problem.
Another example: if you try to hit a small target from a long distance (say the laser reflector left on the moon by the Apollo astronauts) you could say that your accuracy of 4 m is "one part in 10^6" since that is the approximate scale of the moon. But if you compared instead to the size of the reflector, 4m would be more than 1000% error (in other words - you miss) while if you were comparing to the distance from Earth to moon, your error is less than of 1 part in 10^8. Any of these would be "acceptable" measures of the relative accuracy of alignment - but they are vastly different numbers and carry different interpretations.
Something to think about.
A: The only relative error that makes a sense here is in K. The reason is that the temperature in K is the only absolute temperature measure. C and F are relative to freezing water. In contrast, Kelvins are in absolute terms, where 0 corresponds to no kinetic motion of molecules whatsoever.
If you were dealing with water, not iron, then maybe relative measure in C would make a sense, after all water is in liquid phase starting at around 0 C. Still, you'd be careful around 0 C, because water freezes at this temperature only at certain pressure, and the freezing temp moves with changing pressure. Basically, if you want to be completely devoid of context, then K is the choice. 
