8.01 Determining the precision of the results of calculations

When calculations are made using measurement values the uncertainties in the individual values will combine to determine the uncertainty interval (and therefore the precision) of the result.

Imagine you have measured the length of a rectangle as 10.0 +/-1mm and the width as 5.0 +/-1mm.
The area of the rectangle is determined by multiplying length by width.
The area may be any value between 9mm x 4mm = 36mm2 and 11mm x 6 mm = 66mm2
so the area is between 36 and 66 mm i.e. 51 +/- 15mm2

Rather than having to carry out more lengthy calculations as above there are some simple rules for determining the precision of the result of a calculation.