Example Data Table
| Component |
Nominal |
+ Tol |
- Tol |
Direction |
Distribution |
| Base plate thickness |
25.00 |
0.10 |
0.08 |
Add |
Normal |
| Cover pocket depth |
12.00 |
0.06 |
0.06 |
Subtract |
Normal |
| Compressed gasket |
1.50 |
0.05 |
0.04 |
Add |
Triangular |
| Shim pack |
2.00 |
0.02 |
0.02 |
Add |
Uniform |
Formula Used
Nominal stack: total = sum of signed nominal dimensions. Added parts use a positive sign. Subtracted parts use a negative sign.
Worst case minimum: sum of each signed lowest contribution. For added dimensions, use nominal minus lower tolerance. For subtracted dimensions, use negative of nominal plus upper tolerance.
Worst case maximum: sum of each signed highest contribution. For added dimensions, use nominal plus upper tolerance. For subtracted dimensions, use negative of nominal minus lower tolerance.
RSS method: total sigma = square root of the sum of component variances. RSS limit = nominal stack plus or minus selected sigma multiplier times total sigma.
Capability: Cp = specification width divided by six total sigmas. Cpk uses the smaller distance from mean to each specification limit divided by three total sigmas.
How to Use This Calculator
- Enter the unit name, such as mm, inch, degree, or micron.
- Add lower and upper specification limits when the assembly has a required window.
- Enter each component dimension with plus and minus tolerance values.
- Choose add when the dimension increases the final stack.
- Choose subtract when the dimension decreases the final stack.
- Select the distribution model that best matches the process behavior.
- Set the RSS multiplier and sample count.
- Press the calculation button and review the result above the form.
- Download CSV or PDF files for design records.
Understanding Tolerance Stack Up
Tolerance stack up explains how part variations combine in an assembly. Each part has a nominal size and a permitted plus or minus change. When several parts touch the same functional gap, their changes can increase or reduce the final result. This calculator helps you compare risk before parts are built.
Why the Method Matters
A drawing may show acceptable limits for each component. Yet the assembled gap can still fail when every feature moves in the same direction. Worst case analysis protects critical designs because it assumes all limits act together. RSS analysis gives a more realistic process view when variations are independent and centered. Capability checks compare the predicted stack with assembly limits.
Practical Design Use
Use this tool while planning fixtures, spacers, housings, covers, shafts, and clearance paths. Enter each contributing dimension. Select add when the dimension grows the final stack. Select subtract when it reduces the stack. Use normal distribution for controlled machining. Use uniform distribution when any value inside the tolerance is equally likely. Use triangular distribution when values near nominal are more common.
Reading the Results
The nominal stack shows the expected assembly value. Worst case minimum and maximum show the broadest possible range. RSS limits show a statistical range based on the selected sigma level. Monte Carlo results provide a sampled view of expected spread. Spec status helps identify whether the assembly window is safe.
Improving the Design
Large contributors deserve attention first. Tightening every tolerance can increase cost. A better approach is to control the parts that dominate variation. You may also change datum paths, add adjustment, use selective assembly, or shift nominal dimensions. Review the percentage contribution table before changing drawings. This keeps the decision focused and economical.
Good Engineering Practice
Tolerance studies should match real inspection methods. They should also reflect supplier process data when available. Keep assumptions visible in design reviews. Record the distribution choice, sigma level, and specification limits. Update the stack after design changes. A clear stack up study reduces scrap, rework, noise, binding, leakage, and field issues. Keep revision notes with each saved result. This makes later audits easier and helps teams explain why a tolerance choice was accepted during production reviews.
FAQs
What is tolerance stack up?
It is the combined effect of part tolerances in an assembly. It shows how individual variations change a final gap, height, clearance, or position.
What is worst case analysis?
Worst case analysis assumes every component reaches its most damaging limit at the same time. It is conservative and useful for critical safety or fit checks.
What does RSS mean?
RSS means root sum square. It combines independent variations statistically. It is less conservative than worst case and often reflects real manufacturing behavior better.
When should I use normal distribution?
Use normal distribution when the process is centered and controlled. Machined, molded, or measured features often follow this pattern after process stabilization.
Why does direction matter?
Some dimensions increase the final stack. Others reduce it. Direction tells the calculator whether a component should be added or subtracted from the assembly result.
What are Cp and Cpk?
Cp measures potential capability using the specification width. Cpk also checks centering. A low Cpk means the stack is close to one specification limit.
Can I export the result?
Yes. Use the CSV option for spreadsheets. Use the PDF option for review packets, supplier communication, or stored design records.
Does this replace engineering review?
No. It supports engineering review. Always confirm assumptions, datum paths, measurement methods, and process capability with the design and manufacturing team.