Dimensional Tolerance Stack Calculator

Method, example, and limits

Formula: Nominal stack = ΣLᵢ; worst-case tolerance = Σtᵢ; RSS = √Σtᵢ².

Inputs and units: Each Lᵢ is a nominal length and each tᵢ is its symmetric ± tolerance, in the same unit. Worst-case limits are nominal sum ± total tolerance.

Worked example: For nominal lengths 50, 30, 20, and 10 mm with tolerances ±0.1, ±0.2, ±0.1, and ±0.2 mm, nominal stack = 110 mm, worst-case ±0.6 mm, and RSS combination ≈ 0.316228 mm.

Assumptions: Worst-case assumes every contributor can simultaneously reach its limiting direction. RSS combines the entered tolerance magnitudes; interpreting it as a statistical one-standard-deviation estimate additionally requires independent, centered contributors and inputs that represent compatible one-sigma uncertainties. It is not a guaranteed bound.

Limits: Does not model geometric dimensioning, correlated processes, asymmetric limits, nonlinear stack geometry, or distributions. RSS must not replace worst-case verification when a hard fit limit is required.