Calculations

Calculate a one-dimensional tolerance stack

Enter nominal dimensions, signs and symmetric tolerance half-widths in one unit. The default result is the worst-case interval for this linear chain.

Enter values →Sources and scope ↓

Your result

Enter known values and calculate. Source examples are available above.

Formula and worked example

For (10 ± 0.1) − (4 ± 0.2) mm, nominal = 6 mm and worst-case half-width = 0.3 mm: the result is 5.7–6.3 mm. Under a separately justified common-kσ independent model, the RSS half-width would be √(0.1² + 0.2²) ≈ 0.223606798 mm. No yield or ppm is inferred.

Formula

For y = Σ aᵢxᵢ with signs aᵢ = +1 or −1, nominal y₀ = Σ aᵢ nominalᵢ and worst-case half-width T = Σ |aᵢ|tᵢ. A negative direction changes the nominal result, not the sign of a tolerance width.

Optional statistical comparison

Only confirm the RSS option if every entered half-width is a supported common kσ contribution and the contributions are independent. The RSS is then a common kσ half-width, not a guaranteed bound or a prediction of rejected parts.

No hidden distribution assumption

The page does not choose k, impose a normal distribution, infer process centering or calculate ppm. Covariance, mean shifts and unmodelled effects require additional analysis.

Continue your task

Build the dimensional chain before adding tolerances →Plan a Gauge R&R study around the measurement task →Calculate clearance from hole and shaft limits →

All tolerance and surface references →

Sources and review scope

Reviewed 23 October 2026. Arithmetic examples are labelled separately from source-table facts and standard scope.

NIST TN 1297 Appendix A

Equation A-3 includes sensitivity coefficients and covariance. Linear RSS here is a mathematical application, not a manufacturing acceptance rule.

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Your inputs