Tool
Tolerance stack-up
Every dimension in a chain contributes. Enter each nominal and its tolerance, and see the worst-case range and the statistical (RSS) range at the end of the chain.
| # | Feature | Nominal (mm) | ± tolerance (mm) |
|---|
Nominal total
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Worst case
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RSS (statistical)
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How the two methods differ
Worst case adds every tolerance at full value: 4 × ±0.1 mm gives ±0.4 mm. It assumes every part in the chain lands at the same extreme, which is unlikely but possible — so it is the guaranteed limit.
RSS takes the square root of the sum of squares: √(0.1² + 0.1² + 0.1² + 0.1²) = 0.2 mm. It assumes the errors are random and independent, which is reasonable for separately machined parts in volume, and gives a result that is typically 40–60% of the worst case.
The practical rule: use worst case for safety-critical assemblies, small quantities, or when one supplier makes the whole chain. Use RSS for long chains in production — but never for a feature that must not fail.
What the answer is used for
Compare the range with the clearance the design provides. If the stack-up is ±0.4 mm and the fit allows 0.2 mm, the assembly will jam on some percentage of units — and the fix is cheaper on the drawing than on the line: remove a part from the chain, move the tolerance to one slotted hole, or make one part the locating feature and open the rest.
Questions
What is tolerance stack-up?
Adding the tolerances of every dimension in a chain to see what the assembly can actually measure. Four parts at ±0.1 mm can produce a 0.8 mm range at the end of the chain — enough to jam a fit that looked fine on each drawing.
What is the difference between worst case and RSS?
Worst case adds every tolerance at full value and assumes all parts land at the same extreme — it is the guaranteed limit. RSS (root-sum-square) assumes errors are random and independent, giving a statistically likely range that is much narrower but not guaranteed.
When should I use RSS instead of worst case?
RSS is reasonable for long chains of independently machined parts in volume production. Worst case is the right choice for safety-critical assemblies, small quantities, or when the same supplier makes every part in the chain.
How much clearance should I design in?
At minimum, the worst-case stack-up plus a margin — typically 0.2–0.3 mm for a locating fit. If that is impossible, reduce the number of parts in the chain or move the tolerance to a single slotted hole.
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