Propagating Errors in Calculations

An observational uncertainty needs to be propgated through any calculation. If the uncertainties are independent of each other, then the uncertainty of y(x,z)  is given by 

where sigma_y is the uncertainty in y, sigma_x is the uncertainty in x, sigma_z is the uncertainty in z, and there are two partial derivatives of y. As long as the uncertainties are independent of each other, then more terms can be added in quadrature. See the Propagation of Errors page.