Propagation of Error addition

Description:

Consider two measurement – A with error ΔA and B with error ΔB that are to be added.

Let C be the resulting measurement with error ΔC

C = A + B

ΔC = ±(ΔA + ΔB)

Note − Error are always added, they are never cancelled.

Example 1

Distance between A to B is measured as 112 ± 2 and the distance between B to C is measured as 150 ± 5

Then distance between A and C is given by −

(112 ± 2) + (150 ± 5) = 262 ± 7

Example 2

Distance between A to C is measured as 272 ± 5 and the distance between A to B is measured as 112 ± 2

Then distance between B and C is given by −

(272 ± 5) - (112 ± 2) = 163 ± 7