Enrichment · STEM Explorations · Engineering

Every part is in
tolerance. Does the
assembly still fit?

Walk around the loop of parts that sets a gap and type each size and tolerance. The calculator gives the gap's worst-case and statistical range, checks it against your limits and names the part to tighten.

Stack the tolerancesWhat you get

The tolerance stack-up calculator

The worked example is a made-up pin assembly: a 50 mm bore holding two spacers and a washer, which needs at least 0.25 mm of clearance. Nothing you type leaves this browser.

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What you get

Enrichment · STEM ExplorationsFree

What you finish with
The nominal gap, its worst-case and root-sum-square ranges, each dimension's share of the variation, and a pass or fail against your limits. It prints as a summary and downloads as a spreadsheet.
Who it is for
Engineering and technology students, robotics and maker teams, and career and technical education classes learning fits and tolerances.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Up to 30 dimensions. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The STEM Explorations space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Name the assembly and choose the units.
  2. Add each dimension around the loop with its nominal, ± tolerance and whether it adds or takes away.
  3. Type the smallest and largest gap that work.
  4. Read the worst-case and statistical ranges and the biggest contributor.
  5. Print the summary for a design review.

Stack the tolerances

How the stack is worked out

Worst case and root-sum-square.

The worked example: the pin gapNominal gap0.50 mm50 − 20 − 20 − 9.5Worst case± 0.280.10 + 0.05 + 0.05 + 0.08Root-sum-square± 0.146√(0.10² + 0.05² + 0.05² + 0.08²)Against 0.25 minWC fails0.22 < 0.25 ≤ 0.354The worked example: the pin gapNominal gap0.50 mm50 − 20 − 20 − 9.5Worst case± 0.280.10 + 0.05 + 0.05 + 0.08Root-sum-square± 0.146√(0.10² + 0.05² + 0.05² + 0.08²)Against 0.25 minWC fails0.22 < 0.25 ≤ 0.354
Worst case assumes every part lands at its limit in the bad direction at once. Root-sum-square assumes the errors are random and mostly cancel, which is why it is narrower.

The arithmetic

The nominal gap is the sum of the dimensions that make it bigger minus those that make it smaller. Worst case adds every tolerance: the range if each part sits at the wrong limit at the same time. Root-sum-square takes the square root of the sum of the squared tolerances, the spread you expect when errors are random and independent. A dimension's share of the variation is its tolerance squared over that sum.

Which to trust

Worst case guarantees fit for every assembly and suits a few parts or safety-critical gaps. Root-sum-square suits many parts made by centred, stable processes and lets each tolerance be looser. When the two disagree, as in the example, tighten the biggest contributor first, or change the design so fewer parts sit in the loop.

Sources

  1. American Society of Mechanical Engineers. ASME Y14.5, Dimensioning and Tolerancing (asme.org).
  2. Fortini, E. T. Dimensioning for Interchangeable Manufacture. Industrial Press: worst-case and statistical tolerance stacks.
  3. National Institute of Standards and Technology. NIST/SEMATECH e-Handbook of Statistical Methods: propagation of error and variance of sums (itl.nist.gov/div898/handbook).
  4. Massachusetts Institute of Technology OpenCourseWare. Design and Manufacturing: tolerance analysis (ocw.mit.edu).

The worked example is made up. Asymmetric tolerances, geometric tolerances and 3D stacks need fuller methods. Your figures stay in this browser. Support: team@caveatacademic.com.