Calculate accumulated manufacturing variation across multiple metal dimensions using worst-case and RSS tolerance stack-up methods.
| Dimension | Direction | Nominal | Tolerance | Contribution |
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Tolerance stack-up is the analysis of how individual manufacturing tolerances accumulate across a series of dimensions. It is commonly used for metal components, fabricated assemblies, machined parts, sheet-metal assemblies and precision mechanical products.
Even when every individual dimension is within its own specification, the combination of several dimensions can create a larger overall variation in the finished assembly.
The tool calculates the nominal dimensional chain first. It then calculates two common estimates of accumulated variation: worst-case tolerance and RSS tolerance.
Worst-case analysis represents a maximum accumulated condition. RSS provides a statistical estimate when the individual variations can reasonably be treated as independent.
Worst-case stack-up assumes the individual dimensions can simultaneously reach their limiting conditions in the direction that produces the largest overall variation.
This method is conservative and is useful when the assembly must function under the full possible dimensional range or when statistical assumptions are not appropriate.
Root-sum-square, commonly abbreviated RSS, combines independent tolerance contributions by squaring each contribution, adding the squares and taking the square root.
RSS can provide a useful statistical estimate when the individual dimensions are sufficiently independent and their variation behavior supports the assumptions being made.
A dimensional chain can contain dimensions that add to the final assembly dimension and dimensions that subtract from it.
The tolerance magnitude is still treated as a positive contribution when calculating worst-case and RSS accumulated variation.
Consider an assembly made from several machined spacers. The final gap or overall length may depend on several individual dimensions.
The nominal stack is 75.00 mm, while the worst-case tolerance is 0.17 mm. The RSS value is smaller because the individual tolerance contributions are combined statistically rather than added directly.
The nominal stack is the theoretical dimension obtained by adding and subtracting the nominal dimensions according to their directions.
Accumulated variation is separate from the nominal dimension. It describes how far the actual assembly could move away from the nominal result because of manufacturing tolerances.
The worst-case total band is the distance between the lower and upper limits of the calculated assembly dimension.
For example, if the nominal assembly dimension is 100 mm and the worst-case accumulated tolerance is ±0.20 mm, the calculated limits are 99.80 mm and 100.20 mm, giving a total band of 0.40 mm.
A simple tolerance stack-up does not automatically account for every geometric characteristic on a drawing. Flatness, straightness, perpendicularity, parallelism, position, runout and other controls can influence functional assembly behavior.
When geometric tolerances contribute to a functional requirement, they should be analyzed using the appropriate engineering method rather than simply added as ordinary linear dimensions.
Worst-case analysis is particularly useful when an assembly must remain functional regardless of how individual dimensions fall within their specified limits.
It is also useful for conservative design checks, clearance requirements and situations where the available production information does not justify a statistical assumption.
RSS can be useful during statistical tolerance analysis when individual manufacturing variations are reasonably independent and the process behavior supports the underlying assumptions.
It should not automatically be interpreted as a guaranteed production limit. Confidence levels, distributions, correlations and process capability can all affect a formal statistical result.
This calculator performs a linear dimensional tolerance stack-up. It does not automatically model datum structures, geometric tolerances, nonlinear relationships, angular dimensions, distributions, correlations, process capability or assembly constraints.
The RSS result is a statistical estimate, while the worst-case result is a conservative arithmetic accumulation of the entered tolerance magnitudes.
What is tolerance stack-up? It is the calculation of how multiple individual dimensional tolerances accumulate into a final assembly variation.
What is worst-case stack-up? It adds the absolute tolerance contributions to estimate the maximum possible accumulated variation.
What is RSS? RSS means root-sum-square. It combines independent tolerance contributions statistically rather than adding them directly.
Why do some dimensions subtract? Some dimensions reduce the final assembly dimension depending on the selected dimensional chain direction.
Can this tool be used for metal assemblies? Yes. It can be used as a preliminary linear tolerance stack-up aid for machined, fabricated and sheet-metal assemblies.
Does RSS give the maximum possible variation? No. RSS is a statistical estimate and should not be treated as a guaranteed worst-case limit.
Does this tool replace a formal GD&T analysis? No. Geometric tolerances and datum relationships may require a separate functional tolerance analysis.