# Error Calculation

by Shyan
Tags: calculation, error
 P: 734 Consider a physical quantity e.g. w,related to some other quantities by $w=f(x,y,z)$. Imagine an experiment is done for finding the value of w and the measurement errors for x,y and z are known. I wanna know what is the standard method for calculating the error in w resulting from the errors in x,y and z? I can think of several ways but don't know which is better! 1-$\Delta w=\frac{\partial f}{\partial x}\Delta x+\frac{\partial f}{\partial y}\Delta y+\frac{\partial f}{\partial z}\Delta z$ 2-$\Delta w^2=(\frac{\partial f}{\partial x})^2 \Delta x^2+(\frac{\partial f}{\partial y})^2 \Delta y^2+(\frac{\partial f}{\partial z})^2 \Delta z^2$ and some others...! Thanks
 Homework Sci Advisor HW Helper Thanks ∞ PF Gold P: 11,009 The "pythagoras" approach is where x,y,z are independent.
 Mentor P: 16,477 2 is the standard for independent errors.
PF Gold
P: 2,197

## Error Calculation

Why not have a look at the GUM?

http://www.bipm.org/en/publications/guides/gum.html

It is surprisingly readable with quite a few examples. It is also (litteraly) the standard which just about everyone ultimately follows (albeit not always directly), i.e. as long as you folllow the GUM you are pretty safe.
 Homework Sci Advisor HW Helper Thanks ∞ PF Gold P: 11,009 Maybe the GUM should be made sticky?
 P: 734 GUM is just too long and detailed that you don't know where is the main point! I couldn't find my answer there!