🎯 Tolerance Stack-Up

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 1 independent reference calculation · how PhDino checks its numbers

Two different ways of combining several individually toleranced dimensions into one overall tolerance.

When a finished assembly's critical dimension depends on several individual parts (or several features on one part) each with their own manufacturing tolerance, those individual tolerances combine into some overall variation in the final dimension. How they combine depends on which of two common assumptions is more realistic for the situation.

Worst-case stack-up simply adds every tolerance together, assuming the unlikely (but not impossible) scenario where every single dimension happens to land at its worst extreme simultaneously, all in the same unfavorable direction. It's guaranteed never to be exceeded, but it's also often needlessly conservative for anything beyond a small handful of dimensions.

Statistical (root-sum-square, RSS) stack-up instead treats each dimension's variation as statistically independent and random, which is a much more realistic model of how real manufactured parts actually vary — most parts land near the middle of their tolerance band, not at the extreme edge, so having every single one hit its worst-case extreme at once is actually quite unlikely.

Key formula

Worst-case stack = t₁ + t₂ + t₃ + t₄
Statistical (RSS) stack = √(t₁² + t₂² + t₃² + t₄²)

Notes & limitations

• RSS gives a smaller number than worst-case for the same set of tolerances (except in the trivial single-dimension case) — the gap between them grows as more dimensions are added to the stack, which is exactly why RSS matters more for stacks with many contributing dimensions.
• RSS is only statistically valid when the individual dimensions really are independent and roughly normally distributed around their nominal value — a process with systematic bias (consistently running to one side of nominal) breaks that assumption and makes the RSS estimate optimistic.