# Adding uncertainties when you cannot make any assumptions about the measurements [duplicate]

From what I read, when adding two $x$ and $y$ measurements with uncertainties $\delta x$ and $\delta y$, the resulting uncertainty is determined by doing:

$$\delta z = \sqrt{(\delta x)^2 + (\delta y)^2}$$

I am writing a software library to handle measurements and it includes the concept of precision/uncertainty. However, I have no way of knowing the context of the measurements. Is therefor not more correct for me to "assume the worst" and do:

$$\delta z = \delta x + \delta y$$

I know, from what I read, that this overestimates the uncertainty of $z$, and that it is very unlikely for both uncertainties to be their maximum. But on the other hand, it is theoretically possible and it's not up to me to make assumptions.

At least, that's my thinking process for now, but I'm no physics expert. But I would like my software library to be as correct as possible.

• You can't say that one is more 'correct' than the other. You can be realistic or safe; the only thing that's important is mentioning what calculation technique you've used to the user/reader.
– user191954
Jul 9 '18 at 11:45
• If your $\delta x$ variables are rms errors then their sum is not (generally) a worst-case error. Jul 9 '18 at 14:54

If this were the engineering stack exchange uncertainty could mean 'tolerance', and tolerances do add in a linear way. When an engineer wants to insert a $10 \pm 1$ mm rod into a $12 \pm 1$ mm socket they will expect it to fit every time, not just 'with good probability'.