This article is part of the CNC Tolerances & Quality Control Guide: GD&T, CMM, Cpk, PPAP on CNX Precision.
Tolerance stack-up is the analysis of how individual tolerances add up across a part or an assembly. When three parts each carry a small tolerance, the combined error can be surprisingly large. This guide explains the two main tolerance stack-up methods, walks through a real calculation, and shows how to fix common problems.
Every machined part has variation. No cutter is perfect, and no machine is absolute. Tolerance stack-up is the tool engineers use to decide whether the variation is acceptable before the parts go into production. A few minutes of calculation now can prevent days of rework later.
What Is Tolerance Stack-Up?
A tolerance stack-up predicts the worst case of a dimension after several tolerances combine. Consider a stack of three plates. Each plate has a thickness tolerance. The total height is the sum of the nominal heights, and the total error is the combination of all the tolerances.
Stack-up analysis answers two questions. First, will the parts always fit together? Second, will the critical gap stay within its limit? Without this analysis, engineers discover the problem at assembly, not at design.
Therefore, tolerance stack-up is a standard step in DFM and quality planning for machined parts.
Worst-Case Stack-Up Method
In a tolerance stack-up, the worst-case method adds every tolerance in the chain with the same sign. It assumes all parts are at their extreme size at the same time. This is the simplest and the most conservative approach.
The formula is straightforward: add all tolerances to find the maximum deviation, and subtract all tolerances to find the minimum. For example, three parts with tolerances of plus-or-minus 0.1 mm, 0.2 mm, and 0.05 mm give a worst-case stack of plus-or-minus 0.35 mm.
Worst-case analysis is ideal when a failure is unacceptable, such as a seal gap or a safety clearance. It guarantees that the assembly works even at the extremes. The cost is a tight total tolerance, which may raise machining effort.
A simple spreadsheet makes the calculation repeatable. List each dimension, its tolerance, and the direction of the stack. Then the total appears in seconds, and you can test what-if changes.
Most drawings today show a general profile tolerance plus a few critical callouts. The stack-up method you choose depends on how the parts are produced and how they fail in service.
RSS and Statistical Stack-Up
In a tolerance stack-up, the RSS method, or root sum of squares, uses statistics instead of extremes. It assumes the variations are random and independent, so they rarely align in the worst direction. The formula squares each tolerance, sums the squares, and takes the square root.
For the same three parts, RSS gives the square root of 0.1 squared plus 0.2 squared plus 0.05 squared. That equals the square root of 0.0525, or about 0.23 mm. This is much smaller than the worst-case result of 0.35 mm.
RSS suits high-volume production where each part is made independently. The savings come from looser total tolerances, which lower machining cost. However, RSS needs stable processes; it fails when a supplier has drift or bias. Many quality teams set a process capability target, such as Cpk 1.33, before choosing the RSS model.
The RSS result is also easier to verify. A CMM report on a sample of parts gives the actual distribution, and the quality team can compare it with the prediction.
A Worked Stack-Up Example
Here is how a tolerance stack-up calculation works for a simple assembly of three parts:
| Part | Nominal Dimension | Tolerance |
|---|---|---|
| Base plate | 10.0 mm | plus-or-minus 0.10 mm |
| Spacer | 20.0 mm | plus-or-minus 0.20 mm |
| Cover | 5.0 mm | plus-or-minus 0.05 mm |
The nominal total height is 35.0 mm. Worst case adds all tolerances, which gives plus-or-minus 0.35 mm. The RSS result is the square root of 0.01 plus 0.04 plus 0.0025, which is about plus-or-minus 0.23 mm.
Therefore, the worst-case total is 35.0 mm plus or minus 0.35 mm, while the statistical total is 35.0 mm plus or minus 0.23 mm. The difference of 0.12 mm is free tolerance that improves the chance of first-pass assembly.
Try the same math on the mounting holes. If the hole spacing stacks badly, the cover will not align with the base. A simple chain of three tolerances can decide whether the assembly fits. In practice, most engineers use worst case for safety-critical stacks and RSS for cosmetic or clearance stacks.
How to Reduce Tolerance Stack-Up
A good tolerance stack-up review starts with the assembly, not the single part. You cannot always tighten every tolerance, but you can change the design. Here are the most effective fixes:
- Shorten the stack by reducing the number of parts in the chain.
- Loosen tolerances on parts that do not affect the critical dimension.
- Use one surface as the master datum for all features.
- Add a shim or adjustable element where the stack is hard to control.
- Choose machined and ground parts when the stack must be tight.
For example, a stacked assembly of four plates can become two plates with a machined spacer. This removes two tolerance contributions and cuts the stack nearly in half. The same idea applies to brackets, spacers, and cover plates.
Alignment features also help. A dowel pin or a machined boss forces the parts into the same position every time. The stack then depends on one feature instead of several, which makes the result predictable. Remember that tolerances cost money, so only tighten what the function needs.
Do not forget environmental effects. Thermal expansion changes dimensions with temperature. A stack that works at 20 degrees Celsius may fail at 60 degrees, so include the operating temperature in critical analyses.
Frequently Asked Questions
What is the difference between worst-case and RSS stack-up?
Worst-case assumes all tolerances hit their limits at once, so the result is the maximum possible error. RSS assumes random variation, so the result is a realistic, smaller error. Use worst case for safety and RSS for volume production.
When should I run a tolerance stack-up analysis?
Run a stack-up whenever two or more parts share a critical dimension. Typical cases are bearing fits, seal gaps, and assembly heights. Do the analysis at the design stage, not after the first batch fails.
Can CNC machining hold a tight tolerance stack-up?
Yes. Modern CNC centers hold plus-or-minus 0.005 mm on ground features and plus-or-minus 0.05 mm on standard machined surfaces. CNX Precision uses in-process measurement to keep the stack under control, and we review the stack-up with you before production.
Tolerance stack-up is a small analysis with a large impact on assembly quality. It tells you which tolerances matter and which ones you can loosen. Send your assembly model to CNX Precision, and our engineers will run the tolerance stack-up, suggest design fixes, and quote the parts with realistic tolerances.
For related information, see our guide to cnc machining service and 5-axis cnc machining and cnc milling vs turning and cnc machining tolerances.