Tolerance Stackup
1D linear tolerance stackup with worst-case, RSS, and modified RSS analysis. Sensitivity ranking shows where your tolerance budget is going.
Trace a path from one side of the gap to the other through each part. + dimensions increase the gap, − dimensions decrease it.
Enter at least 2 dimensions to see results
Understanding Tolerance Stackups
Worst-Case
Every dimension at its worst extreme simultaneously. Guarantees 100%
of assemblies fit. Use for safety-critical assemblies, small runs (<50 units),
or when rework cost is high.RSS (Root Sum Square)
Statistical method assuming normal distributions. Covers ~99.7% of
assemblies (3σ). Use for production quantities where occasional
out-of-spec assemblies can be sorted or reworked.Modified RSS (Bender)
RSS with a safety multiplier (k). Accounts for non-ideal distributions,
tool wear drift, and process variation that isn't perfectly normal.
k=1.5 is the standard starting point. Increase k for less-controlled processes.- Identify the gap or clearance you need to control.
- Trace the shortest path through the assembly from one side of the gap to the other.
- Each part or feature boundary you cross is a dimension in the chain.
- Direction is + if the dimension adds to the gap, − if it subtracts.
- The total should equal the gap when all dimensions are at nominal.
- Missing a contributor (thermal expansion, coating thickness, weld distortion).
- Wrong direction sign — flip + and − and your result inverts.
- Using worst-case tolerances on production runs. Over-constrains the design, drives cost up.
- Forgetting that geometric tolerances (position, flatness, etc.) also contribute — use the bonus tolerance calculator to get the effective tolerance, then add it as a row here.
- Confusing size tolerance with geometric tolerance — they stack independently.
Three dimensions: housing bore, spacer, and pin OD.
| Dim | Nominal | Upper | Lower | Dir |
|---|---|---|---|---|
| Housing bore | 1.0000″ | +0.0050 | +0.0000 | +1 |
| Spacer | 0.2500″ | +0.0020 | −0.0020 | +1 |
| Pin OD | 1.2480″ | +0.0000 | −0.0030 | −1 |
Nominal gap:
Worst-case:
RSS (3σ):
The worst-case analysis shows zero clearance is possible — every part could be at the edge of its tolerance. RSS says that's statistically unlikely and predicts a minimum gap of 0.00246″ at 3σ. Which method you trust depends on your production volume, process control, and consequences of interference.
All three methods assume 1D linear chains. For 2D/3D stackups with angular contributors or form tolerances, use Monte Carlo simulation.
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