Also, this is aimed at undergraduates, so it ignores covariance.
For instance: In (a+-b) * (c+-d), you're multiplying the intervals (a-b,a+b) and (c-d,c+d). If all those endpoints are positive, then you get the interval ((a-b) * (c-d),(a+b) * (c+d)).
The answer is then: ((a-b) * (c-d)+(a+b) * (c+d))/2 +- ((a+b) * (c+d) - (a-b) * (c-d))/2
If some of those endpoints have different signs, then you need to break it down into cases.
I can see that ((a-b) (c-d)+(a+b) * (c+d))/2 is different to a*b, and that makes sense when you think about it, but the second part is confusing me a bit.
Also, I'm a bit confused by your suggestion to break it down into cases, do you mean if an uncertainty is negative? Because at the moment I'm making all uncertainties positive, but if there are cases where negative ones are correct, I need to fix that up.
(1+-2) / (1+-2) = 1+-2.8
When, of course, the result could be any real number.
For example, when you use covariance properly you could say: x=2+/-2 x-x=0
since covariance = 1
But this calculator assumes that covariance is zero, so it does the calculation (2+/-2) - (2+/-2) = 0+/-sqrt(2^2 + 2^2) = 0+/-2.8
If I'm misunderstanding and this is another problem, please help me, I'm not all that good with uncertainties, but am trying to learn more in this area as it's very useful.
There's lots ways to measure uncertainty, but based on this quote "What this means is that the actual length of the pencil could be anywhere between 15.1+0.05cm (15.15cm) and 15.1-0.05cm (15.05cm)." from your page, I infer you're doing interval arithmetic. However, the calculator isn't calculating any measurement of uncertainty correctly. (The mathematics behind multiplying and dividing normally-distributed variables is nuanced and not close to as easy as the addition and subtraction cases.)
I recommend at least reading the Wikipedia article on interval arithmetic: http://en.wikipedia.org/wiki/Interval_arithmetic
Great idea, but as other comments have noted, completely wrong.
