EngCalc › Tolerance stack-up calculator
Free tool · runs in your browserTolerance stack-up calculator: worst case and RSS
Add each dimension in the loop, pick its direction, and enter its tolerances. You get the worst-case and RSS gap, each dimension's contribution, and every intermediate step. No signup, nothing leaves your browser, and the link shares the exact stack.
2. Results
3. Every step
How the calculator works
- Centre each dimension. For nominal N with upper deviation U and lower deviation L: mean m = N + (U + L)/2 and equal-bilateral tolerance t = (U − L)/2.
- Mean gap = Σ dᵢ·mᵢ, where dᵢ is +1 or −1. The nominal gap Σ dᵢ·Nᵢ is shown too; they differ only when tolerances are asymmetric.
- Worst case: TWC = Σ tᵢ. Gap range = mean ± TWC. The tool also checks this against every min/max corner combination.
- RSS: TRSS = √(Σ tᵢ²). Gap range = mean ± TRSS. This assumes independent, roughly normal dimensions centred in their tolerance bands, each tolerance at the same ±kσ level.
- Contribution: worst-case share = tᵢ / Σ t; RSS share = tᵢ² / Σ t² (share of the variance). Tighten the biggest RSS contributor first.
- Out-of-spec estimate (RSS): σgap = TRSS / k; P(out) = Φ((LSL − mean)/σ) + 1 − Φ((USL − mean)/σ).
Limits: this is a 1-D linear stack (all dimensions along one direction, sensitivity ±1). It doesn't handle angles, GD&T position/flatness conversions, non-normal distributions, or process mean shifts. Use worst-case for safety-critical fits and small builds.
Questions
What is the difference between worst-case and RSS stack-up?
Worst-case adds every tolerance at its limit, so the result always holds but is pessimistic. RSS (root sum of squares) assumes each dimension varies independently and is roughly normally distributed, so it predicts the spread you will actually see in most builds. RSS is narrower than worst-case whenever there are two or more contributors.
How are asymmetric tolerances like +0.20 / −0.00 handled?
Each dimension is converted to its mean and an equal ± tolerance first: mean = nominal + (upper + lower) / 2 and ± = (upper − lower) / 2. For 25.00 +0.20/−0.00 that is 25.10 ± 0.10. The stack is then computed from the means, so the gap mean shifts away from the nominal gap, and the tool shows that shift.
What does the sigma setting do?
It only affects the out-of-spec estimate. The default of 3 treats each tolerance as ±3 standard deviations of that dimension. The RSS gap tolerance is then also ±3σ of the gap, and the estimate uses a normal distribution around the gap mean.
Is my data sent anywhere?
No. All calculation happens in your browser. The share link stores the inputs in the part of the URL after #, which browsers do not send to the server.
Can I use this for certified work?
Treat it as a check, not a sign-off. Verify safety-critical results against your company's standards and approved methods. The formulas used are written out below every result so you can check them.
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