Tolerance Stack-Up Calculator.
Worst-case and RSS (Root Sum Square) analysis for assembly tolerance stacks. Add up to 20 dimensions with bilateral or unilateral tolerances.
| # | Description | Nominal | + Tol | − Tol | Direction |
|---|
How it works
Worst-Case (WC): Sums all tolerances assuming every dimension is at its limit simultaneously. Most conservative — guarantees fit but may over-tolerance.
Stack = Σ(nominal × dir), Tol = Σ|tol|
RSS (Root Sum Square): Statistical method assuming dimensions are normally distributed. Smaller stack but accepts low (<0.27%) probability of failure.
Tol = √(Σ tol²)
What is Tolerance Stack-Up Analysis?
Tolerance stack-up analysis predicts the cumulative dimensional variation in an assembly built from individually-toleranced parts. It answers the question: "If every part is at the edge of its tolerance, will the assembly still work?"
Two Methods: Worst-Case vs RSS
Worst-Case (WC): ±T_total = Σ(±T_i)
RSS (Root-Sum-Square): ±T_total = √(Σ T_i²)
Worst-Case assumes every dimension simultaneously hits its worst tolerance — extremely conservative but mathematically guaranteed.
RSS assumes dimensions are independent and normally distributed — statistically realistic for batch production. RSS gives smaller stack-up values because all-worst-simultaneously is highly improbable.
Stack-Up Worked Example
A pin must fit through a hole in a 4-plate assembly. Each plate has its hole position toleranced ±0.05 mm.
- Worst-Case: ±(0.05 + 0.05 + 0.05 + 0.05) = ±0.20 mm
- RSS: ±√(0.05² × 4) = ±0.10 mm
For a high-volume product, RSS gives ±0.10 — half the WC envelope. You can spec a smaller pin clearance and still expect >99.7% assembly success. For a one-off custom build, use WC to be safe.
When to Use Each Method
- Worst-Case — Critical safety, low volume, single-piece custom assemblies. Aerospace primary structure.
- RSS — High-volume production, statistical assumptions are valid (normal distribution, independent contributors).
- Modified RSS / Six Sigma stack — RSS with safety factor (1.5×) for medium-volume safety-relevant work.
How to Reduce Stack-Up
If your stack-up is too tight:
- Tighten the largest contributors — Pareto applies. The 1-2 dimensions with the biggest ±tol drive most of the stack.
- Switch from WC to RSS — if production volumes justify the statistical assumption.
- Use selective assembly — sort parts into bins and pair tight with loose. Costly but effective for legacy designs.
- Datum chain redesign — sometimes fewer dimensions in the chain is better than tighter dimensions.
Common Stack-Up Mistakes
- Mixing absolute and signed dimensions — direction (+/-) matters in stack-ups.
- Using mean tolerance instead of full range — for asymmetric tolerances (+0.10/-0.02), use the equivalent symmetric range.
- Stacking GD&T frames as if they were ±tolerances — bonus tolerance and projected tolerance need separate analysis.
- Ignoring temperature effects — steel stacks change with thermal growth; aluminum even more.
Related Tools
For specific position callouts, see Position Tolerance with MMC/LMC. For hole/shaft mating, use ISO 286 Fits. Validate process capability with Cp/Cpk before assuming RSS distribution is valid. For full GD&T reference, visit the GD&T page.