# Uncertainty formula if measured “best” value is zero

If the uncertainty of a function $f(x,y)$ is given by:

$$\delta f = |f_{best}|\sqrt{ \left( \frac{\delta x}{x_{best}} \right)^2 + \left( \frac{\delta y}{y_{best}} \right)^2}$$

what do we do if $x_{best}$ or $y_{best}$ are zero? Presumably, $\delta x$ and $\delta y$ need not be zero.

• The formula you're using is not suitable for the kind of case you're applying it to. – Glen_b Apr 9 '14 at 2:44
• @Glen_b Cool. Do you mind elaborating a little? Or providing a link? – confused guy Apr 9 '14 at 3:00
• @Glen_b What is the equation one should use in that case...? – confused guy Apr 9 '14 at 3:01
• Such formulas rely on assumptions; you've violated the assumptions of the one you used, but you don't indicate which assumptions should apply. [Further, with variables that can be non-positive, I'd suggest you probably want to consider absolute error rather than relative error.] – Glen_b Apr 9 '14 at 3:04
• By the way, can you say where your formula came from? Did they explain anything about it? – Glen_b Apr 9 '14 at 3:04

you don't use relative error in this case: $\delta f=\sqrt{(\delta x)^2+(\delta y)^2}$