Tolerance stack-up calculator: worst case, RSS and Monte Carlo
Check whether an assembly fits before parts are made. Enter the dimensions of a linear chain with their tolerances and the required gap, and the calculator gives the worst case, the statistical root sum of squares (RSS) and a Monte Carlo simulation of 50,000 assemblies with the PPM outside the gap limits.
A contribution chart shows which dimension drives the variation, so you know which tolerance to tighten and which can be opened to save cost.
How the Tolerance Stack-Up works
Each dimension is added or subtracted along the loop, with symmetric or asymmetric tolerances and a normal or uniform distribution. Worst case adds the half tolerances; RSS adds them in quadrature assuming ±3σ; Monte Carlo samples every dimension from its distribution.
Asymmetric tolerances such as +0 / −0.12 are centred automatically, which is where many hand calculations go wrong.
When to use it
Use the stack-up during design, before releasing a drawing, when an assembly problem appears in production, and when a supplier asks to open a tolerance. It is common for gaps, clearances, preloads, bearing end float, connector engagement and housing fits.
When worst case fails but RSS and Monte Carlo pass, the decision depends on the risk: safety-relevant fits usually need worst case, others can rely on statistics with capable processes.
PDF report in one click
Export the stack-up as a PDF with your header (assembly, gap, revision), the verdict, the dimension table with contributions, the Monte Carlo histogram and the results of all three methods, for a design review or a drawing release.
Private: everything runs in your browser
The stack-up and the simulation run entirely in your browser. Drawing dimensions and tolerances are never uploaded.
How to do a tolerance stack-up
- Draw the loop from one side of the gap to the other through all parts.
- Enter each dimension: + if it increases the gap, − if it reduces it, with nominal and tolerances.
- Enter the gap limits (minimum and maximum clearance).
- Compare worst case, RSS and Monte Carlo and tighten the largest contributor if needed.
Asymmetric tolerances (for example +0 / −0.12) are handled by shifting to the centre of the band.
Frequently asked questions
›Worst case or RSS?
Worst case guarantees that every assembly fits, even if all parts are at their limits, but leads to tight and expensive tolerances. RSS assumes independent, centred, normally distributed dimensions and gives realistic, wider tolerances, accepting a very small risk.
›Why add a Monte Carlo simulation?
It needs no formula assumptions: it builds 50,000 virtual assemblies from the tolerance distributions and counts how many are outside the gap limits, also for uniform or asymmetric tolerances.
›What does the contribution show?
The share of the gap variance coming from each dimension. Tightening the largest contributor has the biggest effect; tightening small contributors changes almost nothing.