Calculated Results
Results appear above the form after submission, including worst-case, RSS, fit margin, and process capability indicators.
Worst-Case Fail Estimated Yield 100.00% RSS Sigma 0.0226 mm| Nominal Stack | 41.2500 mm |
| Worst-Case Minimum | 41.1100 mm |
| Worst-Case Maximum | 41.4100 mm |
| Worst-Case Spread | 0.3000 mm |
| RSS Sigma | 0.0226 mm |
| 3σ Statistical Minimum | 41.1822 mm |
| 3σ Statistical Maximum | 41.3178 mm |
| Estimated Yield | 100.00% |
| Cp | 2.212 |
| Cpk | 2.212 |
| Worst-Case Pass | No |
| Lower Margin to Target | 0.0100 mm |
| Upper Margin to Target | -0.0100 mm |
Stack Contribution Chart
Dimension Breakdown
| Dimension | Factor | Nominal Contribution (mm) | Minimum Contribution (mm) | Maximum Contribution (mm) | Estimated Sigma (mm) |
|---|---|---|---|---|---|
| Base Plate | 1.00 | 24.0000 | 23.9600 | 24.0500 | 0.0150 |
| Spacer A | 1.00 | 12.5000 | 12.4800 | 12.5300 | 0.0083 |
| Bearing Seat Gap | -1.00 | -8.0000 | -8.0200 | -7.9900 | 0.0050 |
| Housing Width | 1.00 | 15.2500 | 15.2200 | 15.2900 | 0.0117 |
| Shim Pack | -1.00 | -6.0000 | -6.0200 | -5.9800 | 0.0067 |
| Cover Thickness | 1.00 | 3.5000 | 3.4900 | 3.5100 | 0.0033 |
Tolerance Stackup Inputs
Enter each dimension, its bilateral or unilateral tolerances, and a stack factor. Use positive factors for additive dimensions and negative factors for subtractive gaps.
Example Data Table
Use this example to understand how additive and subtractive dimensions influence the final assembly condition.
| Dimension | Nominal | + Tol | - Tol | Factor | Meaning |
|---|---|---|---|---|---|
| Base Plate | 24.00 | 0.05 | 0.04 | +1 | Adds directly to stack height. |
| Spacer A | 12.50 | 0.03 | 0.02 | +1 | Adds to total stack. |
| Bearing Seat Gap | 8.00 | 0.02 | 0.01 | -1 | Subtracts from usable gap. |
| Housing Width | 15.25 | 0.04 | 0.03 | +1 | Adds structural width. |
| Shim Pack | 6.00 | 0.02 | 0.02 | -1 | Consumes available clearance. |
| Cover Thickness | 3.50 | 0.01 | 0.01 | +1 | Adds final closure thickness. |
Formula Used
Total Nominal = Σ(Factor × Nominal Dimension)
For positive factors, minimum uses
Nominal - Minus Tolerance and maximum uses Nominal + Plus Tolerance.For negative factors, the assignment reverses because subtraction flips the limit direction.
Part Sigma = |Factor| × ((Plus Tolerance + Minus Tolerance) / 2) / kTotal Sigma = √(Σ Part Sigma²)Here,
k is the chosen sigma multiplier.
RSS Minimum = Total Nominal - (k × Total Sigma)RSS Maximum = Total Nominal + (k × Total Sigma)
The page assumes independent, centered normal distributions and calculates the probability that the final stack falls between the target minimum and target maximum.
How to Use This Calculator
- Enter a clear label for each dimension in the stack.
- Add nominal values and their plus and minus tolerances.
- Use a positive factor for additive features and a negative factor for subtractive features.
- Set the unit, RSS sigma multiplier, and the acceptable target range.
- Press the calculate button to view summary results above the form.
- Review worst-case pass or fail, statistical spread, yield, and capability indices.
- Export the result summary as CSV or PDF for design reviews or supplier discussions.
FAQs
1. What is a tolerance stackup?
A tolerance stackup combines dimensional variations from multiple features to predict the final assembly size, fit, clearance, or interference. It helps engineers verify whether parts will still function when manufacturing variation is present.
2. Why does the calculator use positive and negative factors?
Some dimensions add to the final stack, while others reduce a gap or clearance. Positive and negative factors let the same model handle both directions without changing the core equations.
3. What is the difference between worst-case and RSS?
Worst-case assumes every dimension reaches its most extreme limit simultaneously. RSS assumes independent variation and combines standard deviations statistically. Worst-case is conservative, while RSS is often more realistic for stable processes.
4. When should I trust the RSS result?
RSS is most useful when dimensions are produced by controlled processes, variation is approximately normal, and contributors are reasonably independent. It is less suitable when dimensions are correlated or intentionally biased.
5. What does the sigma multiplier control?
The multiplier defines how wide the statistical range becomes. A value of 3 creates a ±3σ window around the nominal stack, while larger values create more conservative statistical limits.
6. What do Cp and Cpk mean here?
Cp compares the available specification width to total process spread. Cpk also checks centering by comparing the nominal stack location against both target limits. Higher values indicate stronger capability.
7. Can I use this for gap and interference studies?
Yes. Use negative factors for features that consume gap and positive factors for features that create it. Then set the target range to your acceptable clearance or interference window.
8. Why might worst-case fail while yield still looks strong?
Worst-case assumes every dimension shifts to an extreme at once, which is rare in stable production. Yield estimates the probability of staying within limits under statistical variation, so it can remain high even when worst-case fails.