Combining Uncertainties
The mathematical rules used to propagate individual measurement uncertainties into calculated final results.
Governing formula
Addition: ΔZ = √(ΔX² + ΔY²); Product: ΔZ/Z = √((ΔX/X)² + (ΔY/Y)²)
SI unit
Various
In depth
Error propagation rules dictate how errors accumulate: absolute uncertainties add in quadrature for sums/differences, while fractional/percentage uncertainties add in quadrature for products/quotients.
Examples in the real world
Calculating density ρ = m/V: the percentage uncertainty in density is the quadrature sum of percentage uncertainties in mass and volume.