# Error Calculation

by Shyan
Tags: calculation, error
 P: 523 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
 HW Helper Sci Advisor Thanks P: 9,029 The "pythagoras" approach is where x,y,z are independent.
 Mentor P: 15,569 2 is the standard for independent errors.
PF Patron
P: 2,140

## 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.
 HW Helper Sci Advisor Thanks P: 9,029 Maybe the GUM should be made sticky?
 P: 523 GUM is just too long and detailed that you don't know where is the main point! I couldn't find my answer there!
PF Patron