Every mechanical assembly is a stack of tolerances. Part A has some slop, part B has some slop, and by the time you bolt them together, you’re hoping the total slop doesn’t exceed what the system can handle.
That hope is fine for napkin sketches. For actual production, you need math.
The basic idea
A tolerance stack-up adds up all the tolerances in a chain and tells you the total variation at some point you care about. Usually that’s a gap, an interference, or a clearance hole.
Say you’re designing a bracket that mounts to a frame. The bracket has a hole. The frame has a threaded stud. You need the hole to line up with the stud so you can actually attach the thing.
Each dimension in the chain—bracket hole location, frame stud location, flatness of the mating surfaces—contributes some amount of variation. Add them all up, and you get the worst-case scenario. If the worst case still works, you’re good. If it doesn’t, you need to tighten something.
Three ways to run a stack-up
Most engineers use one of three methods:
Worst-case (arithmetic) adds all the tolerances directly. If you have three parts with ±0.1mm each, your total is ±0.3mm. This is conservative. It assumes every part will be at its worst extreme, all in the same direction, at the same time. In practice, that almost never happens. But if you can’t afford any failures, worst-case is the safe choice.
RSS (root sum squared) assumes tolerances are statistically independent and normally distributed. Instead of adding tolerances, you square them, add the squares, and take the square root. For the same three ±0.1mm parts, RSS gives you ±0.17mm—quite a bit tighter than worst-case. This is more realistic for high-volume production where parts come from controlled processes.
Six Sigma (statistical) is like RSS but adjusted for your process capability. If your suppliers are running Cpk 1.33, you factor that in. If they’re running Cpk 2.0, your stack-up gets even tighter. This is useful when you have real SPC data from your manufacturing process.
When to run one
Not every assembly needs a formal stack-up. If you’ve got plenty of clearance and the parts aren’t particularly expensive, you might get away with intuition.
But stack-ups are worth the effort when:
- The gap is tight. If your clearance is only a couple tenths more than your tolerance budget, you need to verify it mathematically.
- The cost of failure is high. Medical devices, aerospace components, anything where a non-fit means scrap or rework—run the stack-up.
- You’re arguing about tolerances. If manufacturing says your tolerances are too tight and you say they’re fine, the stack-up is the evidence. It ends the argument.
- You’re new to the assembly. First time designing something similar? Run the stack-up to build your intuition. After a few of these, you’ll start to recognize which dimensions are sensitive.
Common mistakes
The most common mistake is forgetting contributors. People stack up the obvious dimensions and miss the stuff like flatness, perpendicularity, or mounting hole position. Each one adds variation. If you leave them out, your analysis is optimistic.
Another mistake is using worst-case when RSS would be appropriate (or vice versa). Worst-case is overkill for most production scenarios. But RSS assumes normal distributions, which doesn’t hold if your process is biased or you’re cherry-picking parts.
Finally, people forget to update the stack-up when the design changes. That initial analysis from three months ago? Probably doesn’t reflect the current state of the drawing.
We built this into DatumPilot
Stack-up analysis is one of the features in DatumPilot. You define your chain, input your tolerances, and it calculates worst-case, RSS, and six sigma results. It also shows you which tolerances are eating up the most budget—useful when you need to decide what to tighten.
The free tier includes five stack-ups. Enough to try it out on a real problem.