Tolerance Stack-Up Calculator (Worst Case & RSS)

How it works

Nominal = Σ (±nominal); worst case = Σ tolerances; RSS = √Σ tolerance²; assembly σ = RSS ÷ k (tolerances taken as ±kσ); reject rate = P(result < min) + P(result > max) from the normal distribution

When parts stack up in an assembly, their tolerances stack too. The worst-case method adds every tolerance and guarantees the gap even if each part sits at its limit in the worst direction — safe, but it forces tight, expensive tolerances on long chains. The statistical (root-sum-square) method notes that parts rarely all land at their limits at once; if each dimension is normally distributed and independent, the assembly variation is the square root of the sum of squared tolerances, typically 30–50% less than worst case, letting individual tolerances loosen for the same assembly yield at the cost of a small, calculable reject rate. Which to use is a business decision: worst case for safety-critical or low-volume fits, RSS for mass production with capable processes. Sign each dimension by whether it opens or closes the gap, and check the nominal sits inside the window before worrying about tolerances.

Worked example

Three parts (+50 ±0.10, +25 ±0.05, +12.5 ±0.05) inside a housing (−87 ±0.15) leave a nominal 0.5 mm gap. Worst case is ±0.35 (0.15 to 0.85 — within a 0.1–0.9 requirement); RSS is ±0.194 at 3σ, and the predicted reject rate is about 0.2 ppm, so the tolerances could be relaxed roughly 2× under RSS while still meeting the window statistically.

Frequently asked questions