How to calculate the uncertainty when quantities are added or subtracted?

To calculate the uncertainty when quantities are added or subtracted, you need to use the rule of quadrature.

When adding or subtracting quantities with uncertainties, the uncertainty of the result is not simply the sum or difference of the individual uncertainties. Instead, you need to use the rule of quadrature, which involves squaring each uncertainty, adding them together, and then taking the square root of the sum.

For example, if you are adding two quantities A and B with uncertainties of ±0.1 and ±0.2 respectively, the uncertainty of the sum (A + B) would be:

√(0.1² + 0.2²) = √0.05 = ±0.224

Similarly, if you are subtracting two quantities A and B with uncertainties of ±0.1 and ±0.2 respectively, the uncertainty of the difference (A - B) would be:

√(0.1² + 0.2²) = √0.05 = ±0.224

It is important to note that the rule of quadrature only applies when the uncertainties are independent and random. If the uncertainties are systematic or correlated, a different method may be required to calculate the uncertainty of the result.