Rules of error propagation.
| Operation | Form | Error (standard deviation) |
|---|---|---|
| Addition and subtraction | $z=x\pm y$ | $\delta z = \delta x + \delta y$ |
| Multiplication by a value | $z=kx$ | $\delta z = |k| \delta x$ |
| Multiplication and division | $z=xy$, $z=x/y$ | $\delta z = |z|\left(\frac{\delta x}{|x|}+\frac{\delta |y|}{y}\right) $ |
| Power | $z=x^n$ | $\delta z = |z| \left(|n| \frac{\delta x}{|x|}\right) $ |
For example, $z = xy/t^3$.
$$ \delta z = |z| \left(\frac{\delta x}{|x|}+\frac{\delta y}{|y|}+\frac{3\delta t}{|t|}\right) $$