Tolerance Stack-Up Calculator

Enter the dimensions and tolerances of an assembly chain to get the worst-case and statistical (RSS) stack-up. Use it to check whether part tolerances keep an assembly gap within its required range.

How to use

1. In "Dimension chain", use "Add row" and enter a name, direction, nominal size and tolerance for each dimension. Dimensions that open the gap are +, those that close it are −.
2. Enter each tolerance as ± or as upper and lower deviations, and choose the "Distribution" used for RSS.
3. Enter "Required minimum (min gap)" and "Required maximum (max gap)" to see pass or fail for each method and the expected defect rate.
4. Turn on "Monte Carlo simulation (100,000 runs)" if needed, and export with "Copy table" or "Save as CSV".

How it works

• Worst case is the mean stack ± the sum of tolerances. RSS is ± 3 × √(sum of each σ²); when all rows are normal ±3σ, this equals ±√(sum of tolerances²).
• Unequal tolerances are converted to a mean and an equal-bilateral tolerance. Modified RSS multiplies RSS by a factor (commonly 1.5), capped at the worst case.
• Only one-dimensional linear stacks are covered. Angles, geometric tolerances and 2D or 3D relationships must be converted to their component in the stack direction.

Questions and answers

What is the difference between worst case and RSS?

Worst case assumes every part sits at its tolerance limit at the same time, so the tolerances simply add. RSS assumes part sizes vary at random and uses the square root of the sum of squares, which gives a narrower range.

How is a tolerance stack-up calculated?

In the example, 50 ± 0.1 (+), 20 ± 0.05 (−) and 29.8 +0/−0.1 (−) give a mean stack of 0.25. Worst case is ±0.2, so 0.05 to 0.45; RSS is √(0.1² + 0.05² + 0.05²) ≈ ±0.122.

What does it mean if RSS meets the requirement but worst case fails?

Some assemblies may fall outside the required range. "Expected defect rate (normal assumption)" shows that share, and the contribution chart shows which tolerance to tighten first.

Which distribution should I choose?

Stable production parts are usually treated as "Normal ±3σ"; "Uniform" is more conservative when the distribution is unknown. Uniform uses σ = tolerance ÷ √3, triangular tolerance ÷ √6.