error propagation dec-02 x, a, b, c = numbers sa, sb, sc = corresponding uncertainties sx = uncertainty we want to calculate 1. x = a+b-c sx = sqrt(pow(sa,2)+pow(sb,2)+pow(sc,2)) 2. x = a*b/c sx = x*sqrt(pow(sa/a,2)+pow(sb/b,2)+pow(sc/c,2)) 3. x = pow(a,b) sx = x*b*(sa/a) [assuming sb=0] 4. x = log10(a) sx = 0.434*(sa/a) 5. x = log(a) sx = sa/a 6. x = pow(e,a) sx = x*sa 7. x = f(a, b, c, ...) sx = sqrt(pow((df/da)*sa,2)+pow((df/db)*sb,2)+pow((df/dc)*sc,2)+...) (d = partial derivative) ref: http://science.widener.edu/svb/stats/error.html http://www.rit.edu/~vwlsps/uncertainties/Uncertaintiespart2.html http://lectureonline.cl.msu.edu/~mmp/labs/error/e2.htm