# Propagating uncertainties of constants in division

I have two constants, $$A$$ and $$B$$, with associated uncertainties $$\sigma_A$$ and $$\sigma_B$$, from observational errors, for example. I need to perform calculations with these constants, by for example making $$f = A/B$$. Therefore, I need to propagate the uncertainties from $$A$$ and $$B$$ to my function $$f$$.

Wikipedia provides the following recipe for a similar case, but when $$A$$ and $$B$$ are variables, not constants, and the errors are assumed to be their standard deviations.

How do I compute the standard deviation $$\sigma_{AB}$$, when $$A$$ and $$B$$ are constants? Should I just make $$\sigma_A$$ times $$\sigma_B$$? Or moreover, how do I propagate the uncertainties of two constants to their ratio?

• Are Ai and Bi dependent or independent ? Jul 10 '20 at 7:09
• Because if non independent, then the ratio of mean might be different than the mean of ratios. Same reasoning for uncertainty. Jul 10 '20 at 7:17
• They are independent, two measured quantities, not variables. Could be for example mass and speed of something. Jul 10 '20 at 10:17

Alright, I learned that, when $$A$$ and $$B$$ are constants with uncertainties $$\sigma_A$$ and $$\sigma_B$$, one just needs to add their relative uncertainties in quadrature, to propagate their uncertainties to a function $$f(A, B)$$, which may as well be $$f(A,B)=\frac{A}{B}$$.
$$\frac{\sigma_f}{f} = \sqrt{\left(\frac{\sigma_A}{A}\right)^2 + \left(\frac{\sigma_B}{B}\right)^2}$$