Tolerance Stackup Lab
Explore how component dimensions can combine into an assembly gap or length. Give each part a signed direction, nominal size and separate lower/upper tolerance in millimeters. An exact interval calculation shows the mathematical worst case when every part can vary independently. A second, explicitly assumed model assigns one uniform variation driver to each named group; rows in a group share that driver, and groups are independent. Analytic mean and spread use that model, while seeded samples show an approximate distribution. No manufacturing pass/fail decision is made.
Key features
- Editable signed chain of two to twelve millimeter dimensions with asymmetric bilateral tolerances
- Exact worst-case interval over every component's allowed box, independent of probability assumptions
- Exact support range when same-group parts share one uniform cause and different groups vary independently
- Closed-form model mean and standard deviation with group variance contributions
- Seeded bounded sampling, histogram and interpolated 1/5/50/95/99 percentiles
- Download standalone SVG, histogram/sample CSV and versioned settings JSON
How to use
- Enter each component's nominal millimeters, subtract or add direction, and lower/upper tolerance.
- Assign different group names for independent variation drivers or the same name when rows share one normalized driver; choose a nonzero seed and 1,000–50,000 draws.
- Run the analysis to compare nominal, conservative box worst case and the exact support under the chosen shared-driver assumption.
- Read the analytic model mean and spread, empirical percentiles, part endpoint sensitivity and group variance shares.
- Save the numeric samples and chart for review, then validate real tolerance distributions and physical dependencies before any manufacturing decision.
Use cases
- Explore clearance between a housing span and an insert
- See how a common machining driver may cancel signed dimensions
- Find which component widens the conservative worst-case interval most
- Compare analytic spread with a reproducible finite sample distribution
Frequently asked questions
What does worst case mean here?
The box interval minimizes or maximizes each signed component separately over nominal-minus through nominal-plus tolerance. Its endpoints are exact for that input box even if the assumed shared-group model would not reach all simultaneous extremes.
How are correlated parts modeled?
Each named group draws a common U uniformly from −1 to 1. For U≥0 a part changes by U times its plus tolerance; for U<0 by U times its minus tolerance. All rows in one group share U, while different group U values are independent. This is a chosen common-cause model, not correlation estimated from measurements.
Is the 5th–95th percentile a confidence interval or yield prediction?
No. It is an interpolated percentile of a finite seeded simulation under the chosen uniform group model. It has sampling error and no measurement-based distribution or confidence guarantee. The analytic mean and variance, unlike the percentiles, are exact for that model.
Why can the grouped range be narrower than worst case?
Shared parts cannot choose opposite extreme drivers independently. Their signed deviations can cancel. The grouped support uses the exact extrema of each group's piecewise-linear response, whereas the box interval permits every component to choose its own endpoint.
Does a dimension outside these ranges mean the assembly fails?
No. This tool has no specification limits, measurement uncertainty, process capability or acceptance rule. Check actual drawings, units, distributions, dependencies and manufacturing evidence with qualified engineers.
Are component values uploaded?
No. The chain, analytic calculation, random draws and exports are processed in this browser tab without a tool API submission.
Privacy
Dimensions and generated samples stay in browser memory. Nothing is automatically saved or submitted to a tool API; download occurs only on request.
Comments & questions