Formula and example
How it is calculated
u(f)²=(∂f/∂a)²u(a)²+(∂f/∂b)²u(b)². For addition or subtraction: u=√[u(a)²+u(b)²].
Worked example
For a=10 with u(a)=0.2 and b=20 with u(b)=0.3, a+b=30. The combined standard uncertainty is √0.13≈0.3606.
Things to check
- Input quantities are assumed independent. Correlations are not included.
- The linear approximation assumes sufficiently small uncertainties. A factor of 2 alone does not establish a particular coverage probability.
- For addition and subtraction, measured values must use the same unit. Products and quotients produce compound units.
Frequently asked questions
Is standard uncertainty a maximum error bound?
No. It describes a measure of spread. A guaranteed maximum deviation or a specific confidence level needs more information about the measurement procedure and distribution.