Understanding Tolerance Stack Up
A tolerance stack up study checks how many small part variations combine in an assembly. Each feature may be acceptable alone, yet the final gap, flushness, or interference can fail when all variations move together. This calculator helps engineers compare two common views. Worst case assumes every part reaches the most damaging limit at the same time. RSS assumes independent variation and combines standard deviations by root sum square.
Why It Matters
A clear stack shows whether a design has enough functional margin before tooling, inspection, or supplier work begins. It also shows which dimension drives the most risk. That helps teams spend money where it improves yield. A tight tolerance on a weak contributor may add cost without improving the assembly. A wider tolerance on a strong contributor may create field failures. The stack converts those tradeoffs into numbers.
Using Sensitivity
Sensitivity describes direction and leverage. A value of 1 means the dimension adds directly to the final stack. A value of -1 means it subtracts. Larger values model lever arms, gear ratios, thermal growth, or fixture multipliers. This makes the tool useful for linear assemblies, offsets, gaps, clearances, and simple mechanism paths.
Worst Case Method
Worst case results are conservative. They are useful for safety, hard stops, sealed joints, and low volume builds. The method adds the most harmful upper and lower limits for every component. If the full worst case band fits inside the specification, the design is very robust.
RSS Method
RSS results are better for production risk estimates when parts vary independently. The tool converts each tolerance into an estimated standard deviation. Normal, uniform, and triangular options give different sigma estimates. The component sigmas are squared, summed, and square rooted. The selected coverage factor then creates an expected stack band.
Design Decisions
Use the output to compare nominal position, worst limits, RSS limits, clearance, Cp, Cpk, and estimated defect rate. Review any negative clearance first. Then inspect the contributor list. Improve the largest contributors through datum changes, relaxed geometry, process control, or design centering. Always confirm assumptions with real measurement data. Document each assumption so future reviews can repeat the same logic and challenge weak inputs before release with confidence later.