Tolerance Stack-Up Calculator
Analyze the cumulative effect of up to 8 component tolerances on an assembly dimension using both worst-case (WC) and root-sum-square (RSS) methods. Enter the nominal gap and the bilateral tolerance (plus or minus value) for each contributing component. The calculator outputs the gap minimum and maximum under both methods.
Tolerance stack-up formulas
Worst case: T(WC) = t1 + t2 + ... + tn
Gap min (WC) = Nominal - T(WC)
Gap max (WC) = Nominal + T(WC)
RSS: T(RSS) = sqrt(t1^2 + t2^2 + ... + tn^2)
Gap min (RSS) = Nominal - T(RSS)
Gap max (RSS) = Nominal + T(RSS)
Enter bilateral (symmetric plus/minus) tolerances for each contributing dimension. Set tolerance to 0 to exclude a component. RSS analysis assumes normal distribution of tolerances and statistically independent errors.
When to use each method
- Worst-case: mandatory for safety-critical assemblies, medical devices, and aerospace per AS9102 first article inspection. Guarantees 100% conformance at higher manufacturing cost.
- RSS: acceptable for non-safety-critical assemblies where approximately 0.27% (3 sigma) fall-out is tolerable. Allows larger individual tolerances and lower manufacturing cost.
- Modified RSS (MRSS): a middle ground that uses a correction factor. T(MRSS) = 1.5 x T(RSS) provides approximately 99.9% conformance without full worst-case conservatism.
Tolerance stack-up: frequently asked questions
What is tolerance stack-up analysis?
Tolerance stack-up analysis determines the cumulative effect of individual part tolerances on an assembly dimension or gap. It answers the question: given the tolerances on each component, what is the range of possible values for the critical assembly dimension?
What is the difference between worst-case and RSS analysis?
Worst-case (WC) analysis assumes all tolerances simultaneously take their worst-case values: total stack = sum of all individual tolerances. RSS (Root Sum Square) analysis is statistical: total RSS tolerance = sqrt(t1^2 + t2^2 + ... + tn^2). WC is guaranteed but often over-conservative, leading to tighter tolerances and higher cost. RSS is less conservative and reflects actual assembly variation when tolerances are independent and normally distributed.
When should I use worst-case vs RSS analysis?
Use worst-case analysis for safety-critical dimensions where 100% of assemblies must conform regardless of the tolerance distribution. Use RSS analysis for non-safety-critical dimensions where a small percentage of assemblies outside the target range is acceptable (typically 99.73% conformance, 3 sigma). Many aerospace and medical standards require worst-case analysis.
What does the nominal gap or dimension represent?
The nominal gap is the target or design value for the assembly dimension being analyzed. For a gap or clearance, the nominal is the intended clearance at nominal component dimensions. The stack-up analysis determines the maximum and minimum possible values of this gap across all combinations of component tolerances.
What standard governs tolerance analysis in manufacturing?
ASME Y14.5 (Geometric Dimensioning and Tolerancing) is the primary US standard for defining and communicating tolerances on engineering drawings. ASME Y14.5.1 covers mathematical definitions. ISO GPS (Geometrical Product Specifications) is the international equivalent. Tolerance stack-up analysis methods are described in ASME Y14.5 and engineering textbooks such as Fortini's Dimensioning for Interchangeability.
Official sources
- ASME Y14.5: ASME Y14.5 Dimensioning and Tolerancing.
- NIST Engineering Statistics Handbook: NIST/SEMATECH e-Handbook of Statistical Methods.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.