# Quick question about uncertainty calculation

1. Sep 29, 2008

### mjolnir80

1. The problem statement, all variables and given/known data
lets say we have A * B
A=12.8 + 0.2
B=3.75 + 0.08
how would we calculate the new uncertainty value
ive seen soo many ways of doing this im a bit confused

2. Relevant equations
any equation used to calculate uncertainty

3. The attempt at a solution
the 2 main ways ive seen is one involving partial dervatives and the other is taking the square root of the answer times the (uncertainties/value)2
im a little confused about which one to use

2. Sep 29, 2008

### rock.freak667

If C=AB, then

$$\frac{\delta C}{C}=\frac{\delta A}{A}+ \frac{\delta B}{B}$$

this is obtained using differential calculus.

3. Sep 29, 2008

### granpa

(A+ε1)*(B+ε2)
AB+Aε2+Bε11ε2

so if we disregard the final term the incertainty would be Aε2+Bε1

partial derivative of AB with respect to A is B
partial derivative of AB with respect to B is A

does that help?

4. Sep 29, 2008

### granpa

whats that called? I want to look that up. it looks interesting.

5. Sep 30, 2008

### granpa

nevermind I found it.looks like the derivative rule is the most general.

if the uncertainties are independent you can take the square root of the sum of the squares of the partial derivatives times the uncertainties. that would be probable error not maximum error though.

http://web.mit.edu/fluids-modules/www/exper_techniques/2.Propagation_of_Uncertaint.pdf