# Error Propagation Formulas

1. Jan 26, 2010

### ~Sam~

1. The problem statement, all variables and given/known data
What are the uncertainty propagation formulas for:
Area of a rectangle
Density of a sphere
Height of an opposite side wall calculated by tan(θ)=o/a
Resistance

2. Relevant equations

Area of rectangle= side A *side B
Density of a sphere= mass/(4/3piR^3)
Resistance= R=V/I

3. The attempt at a solution

Rectangle I have: A=LW
dA=dlW+dwL
dl and dw are the relative uncertainty of L and W by instrument.

Sphere: I have dp=(3 dm/4piR^3)+(3m/12piR^2dr)
dm and dr are uncertaintities of mass and radius

For heigh: do= tan(θ)da+sec2(θ)a*dtan(θ)
da and dtan(θ) are the relative uncertainties

For resistance: dR= 1dV/I+ VdI/1

If these are correct would I use a sum formula like u(c)= sum of all squares? or would I separate the partial derivatives from the uncertainties and then square and sum like (dl2)W2+(dw2)L2? I'm kinda confused which formula is the general formula for uncertainty propagation.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Jan 26, 2010