Error Propagation
The mathematical evaluation of how uncertainties in measured input variables propagate into the final calculated physical quantity.
Governing formula
σ_f² = ∑ (∂f / ∂x_i)² σ_x_i² + 2 ∑ (∂f/∂x_i)(∂f/∂x_j) Cov(x_i, x_j)
SI unit
Uncertainty Units
In depth
Based on first-order Taylor expansion of a multivariable function. For independent variables, individual variance terms combine in quadrature weighted by squared partial derivatives.
Examples in the real world
Calculating the total percentage uncertainty in a density measurement ρ = M / V from measured mass and volume uncertainties.