Error

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, $z = xy/t^3$.

$$ \delta z = |z| \left(\frac{\delta x}{|x|}+\frac{\delta y}{|y|}+\frac{3\delta t}{|t|}\right) $$