Tolerance Stack-Up: Worst-Case and RSS
Worst-case tolerance = sum of the half-widths; statistical RSS = sqrt(sum of squares), always tighter.
Example
You enter
- Nominal (mean) gap (in) 0.02
- Tolerance half-widths (in, comma or space separated) 0.005, 0.005, 0.005
You get
- Tol wc 0.015
- Tol rss 0.00866
Checked against published worked examples from: University of Washington (Fritz Scholz).
Details, formula, and sources
ScopeThree dims at +/-0.005 -> +/-0.015 worst-case, +/-0.00866 RSS; a 0.020 gap fits 0.005-0.035 (WC) or 0.0113-0.0287 (RSS). The RSS benefit widens as the chain grows. A design aid; the drawing tolerances govern.
Formula or tabletol_wc = sum(|tol_i|); tol_rss = sqrt(sum(tol_i^2)); gap = nominal +/- tol.
Source and editionWorst-case and RSS (root-sum-square) tolerance stack-up, standard mechanical-design / GD&T practice, by name.
Free accessThe worst-case sum and the RSS square-root-of-sum-of-squares are public tolerance-analysis results.
What governsEstimate. AHJ and licensed professional govern.
API field namesnominal_gap_in, tolerances, tol_wc, tol_rss
- Worst-case tol_wc = sum of the half-widthstolerance analysis
- RSS tol_rss = sqrt(sum of squares)statistical tolerance analysis
- RSS assumptions centered, independent, normally distributed dimensionsscope of this tile