# Error Calculation

Gold Member
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 Helper
The "pythagoras" approach is where x,y,z are independent.

Mentor
2021 Award
2 is the standard for independent errors.

Gold Member
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 Helper
Maybe the GUM should be made sticky?

Gold Member
GUM is just too long and detailed that you don't know where is the main point!
I couldn't find my answer there!