Tolerance stack-up calculator

What a stack-up answers

A tolerance stack-up predicts the range of an assembly result, such as a gap, end play or clearance, from the tolerances of the parts in the chain. Start at one side of the gap and walk through each dimension to the other side. Dimensions that make the gap larger carry a plus sign; dimensions that make it smaller carry a minus sign. The nominal gap is the signed sum of the nominal dimensions.

Worst case

The worst-case (arithmetic) method assumes every part can be at its limit in the direction that hurts. The gap tolerance is the plain sum of the individual tolerances: T = ΣTᵢ. If the worst case meets the requirement, every assembly built from in-tolerance parts works. It is the conservative answer and needs no assumptions about the processes.

Root sum of squares (RSS)

The statistical method assumes the dimensions are independent, roughly normal, centered on their nominal and each toleranced at about ± 3 standard deviations. Then the variances add, and the gap tolerance is T = √(ΣTᵢ²), smaller than the worst case. With four tolerances of 0.005, 0.002, 0.003 and 0.002, the worst case is ± 0.012 and the RSS is ± 0.0065.

RSS is a prediction about a population, not a guarantee for each assembly. If a supplier runs near one limit, or the dimensions are correlated, the RSS answer is optimistic.

Unequal tolerances

A dimension such as 1.000 +0.002 / −0.004 is converted to its mean, 0.999, with an equal tolerance of ± 0.003 before stacking. The mean gap can then differ from the nominal gap, which is why the tool shows both.

Using the result

• If worst case meets the requirement, the design is safe.
• If worst case fails but RSS meets it, the design depends on capable, centered processes; confirm with process data.
• If both fail, change the design or tighten tolerances. The share-of-variance chart shows where tightening does the most good, because RSS squares each tolerance.

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