Tolerance Stack-Up Calculator
How the tolerances of parts in a chain add up — the worst case, where every part is at its limit, and the statistical root-sum-square that assembly actually sees.
When parts stack, their tolerances stack.
How the tolerance stack-up calculator works
When parts stack, their tolerances stack. Worst case adds them all: five parts at ±0.1 give ±0.5. But the chance of all five being at the same limit is tiny, and the root-sum-square of the tolerances — ±0.22 here — is what a real assembly sees almost all the time.
The difference between the two is the argument for statistical tolerancing, and the reason worst-case designs are either over-toleranced or over-priced.
Formula: worst case = Σ t_i; RSS = √(Σ t_i²)
Worked examples
| Inputs | Worst-case stack (± mm) | Note |
|---|---|---|
| Five parts in a chain | 0.48 | RSS is half the worst case |
| A tight gap | 0.48 | holds statistically, not worst case |
| Two parts | 0.4 | RSS is 0.28 against 0.4 |
FAQFrequently asked questions
What is a tolerance stack-up?
The way the tolerances of parts in a chain combine into the tolerance of the assembly. It decides whether a gap closes, a pin binds or a cover fits.
Worst case or statistical?
Worst case guarantees fit at any combination and over-tolerances the parts. RSS assumes independent, normally distributed parts and matches reality closely. Safety-critical stacks use worst case; most others use RSS.
Why is RSS so much smaller?
Because the chance of every part being at the same extreme is vanishingly small. Random errors partly cancel, and the root-sum-square captures how much.
When is RSS wrong?
When the parts are not independent — the same machine drifting the same way — or when a process is skewed. Then the truth is between RSS and worst case.
How do I tighten a stack?
Shorten the chain first: fewer parts between the two features that matter. Then tighten the biggest tolerance, since it dominates the RSS.
Where these figures come from
- Nakajima (1988) — Introduction to TPM — the origin of Overall Equipment Effectiveness and its six big losses
- Health and Safety Executive — the UK workplace safety regulator
Last checked: September 2026. Definitions follow standard operations-management practice; where plants commonly differ, the page says so.