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For Students · Tolerance Stack-Up

Tolerance Stack-Up for a bottleneck station

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a bottleneck station live below — adjust the inputs and watch it respond, right in your browser.

Tolerance Stack-UpLive

worst-case vs statistical

Controls

Presets

Number of parts

Tolerance per part (±mm)

When parts stack in an assembly, their tolerances accumulate. Worst-case analysis simply adds them — safe but pessimistic, since all parts rarely hit their extremes together. Statistical (root-sum-square) analysis adds them in quadrature, giving a much tighter, more realistic range. Choosing between them decides how much precision — and cost — each part really needs.

▶ Run in Python

Data Inspector

Worst-case total±0.50 mm

Statistical (RSS)±0.22 mm

RSS savings55% tighter

Governing equation

T_{w c} = \sum ∣ t_{i} ∣ = 5 \times 0.1 = 0.50, T_{r ss} = \sum t_{i}^{2} = 0.1 5 = 0.22 mm

Reading this result: Across 5 parts, RSS (±0.22 mm) is 55% tighter than the worst-case ±0.50 mm — enough headroom to relax individual part tolerances and cut cost.

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Frequently asked questions

Is this good for students?: Yes — this version of "Tolerance Stack-Up for a bottleneck station" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.