[fchu]

Am I the only one who thinks the concept of relative error is not meaningful in this context?

It gives a disproportionate meaning to 0 without real physical consideration, eg:

- 0.1⁰C ± 0.1 (wow 100% relative error) - 273.25K ± 0.1 (meh 0.04% relative error)

[_Microft]

The Celsius temperature scale is an interval scale [0] which means that it is possible to calculate differences but not ratios. The Kelvin temperature scale is a ratio scale [0] (it has an "absolute zero") that allows to do that.

Beside that if there are uncertainties involved, one should do proper propagation of uncertainty anyways. [1]

[0] https://en.wikipedia.org/wiki/Level_of_measurement

[1] https://en.wikipedia.org/wiki/Propagation_of_uncertainty

[jcheng]

This is talking about the error in the difference between two values with the same units though. For temperature, it wouldn’t matter if you’re using C, K, or F for your starting values, the % error of the difference would be the same (I think).

[eru]

Yes.

What would make a difference is to change to https://en.wikipedia.org/wiki/Thermodynamic_beta

(Essentially the same difference as miles per gallons vs litres per 100 km.)

[andrepd]

Yes, because there is an arbitrary choice of origin which renders the relative error dependant on units. If you're measuring a length, for instance, or an interval of time, the relative error is independent of which units you choose. If you're measuring e.g. a distance to some point, then again you have an arbitrary choice of origin.

[Archelaos]

I am sometimes joking with friends by suggesting: Let's meet at 12 o'clock ± 5%.