Tolerance Stack-Up Calculator
Add your dimensions and see the assembly stack both ways — worst-case (nothing ever fails) and RSS (statistically realistic) — compared side by side. Then work backwards: tell it the assembly tolerance you need and it shows what each feature has to hold.
Enter each dimension in the chain. Use a negative nominal for a feature that subtracts (e.g. a gap).
Worst-case vs RSS — and why the difference matters
Worst-case stack-up is the simple one: add every tolerance in the chain. If four features each hold ±0.05 mm, the assembly can theoretically be out by ±0.20 mm. It is arithmetic, it is guaranteed, and if you design to it, the assembly will never fail on tolerance. The problem is that it is pessimistic to the point of being expensive: it assumes every single feature is at its extreme limit, in the same direction, on the same part, at the same time.
RSS — root sum square — takes the statistics seriously: √(t₁² + t₂² + … + tₙ²). Those same four ±0.05 mm features give ±0.10 mm rather than ±0.20 mm, because the probability of all four being at their extreme simultaneously and in the same direction is vanishingly small. The gap widens as the chain lengthens — which is exactly when it matters most.
So which do you use? Worst-case where failure is unacceptable or expensive — safety-critical assemblies, anything where a jam or interference means a recall, and short chains where the penalty for being conservative is small. RSS where you have many contributors, a genuinely controlled process, and can tolerate a small proportion of assemblies needing selection or adjustment. The honest answer is that RSS is a statistical claim: it is only as good as the assumption that your process is centred and in control. A process running at the edge of its tolerance band does not behave the way RSS assumes.
The reverse question is the more useful one in practice, and it is the one that reaches us as a quotation problem. You know the assembly has to hold ±0.2 mm, and you need to know what that demands of each feature. Under worst-case, four features must each hold ±0.05 mm. Under RSS, each can hold ±0.10 mm — twice as loose, for the same assembly result. That is a very large difference in machining cost, and it is decided by which method you trust, not by anything on the shop floor.
Worth saying plainly: a 1D stack is a model. It ignores geometric tolerance, form and orientation error, fixturing, and thermal effects — aluminium moves roughly 23 µm per metre per °C, which will quietly eat a tight stack in a workshop that is not temperature-controlled. If a stack is tight enough that the method changes the answer, that is the moment to talk to us rather than to tighten every tolerance on the drawing.
Tolerance stack-up — FAQ
What is the difference between worst-case and RSS tolerance stack-up?
Worst-case adds all tolerances arithmetically and guarantees the assembly can never exceed the result, but it is pessimistic and expensive. RSS takes the square root of the sum of squares, which is statistically realistic and gives a tighter result, but it assumes each dimension is independent, in control and centred on nominal.
How do you calculate RSS tolerance stack-up?
RSS = square root of (t1 squared + t2 squared + ... + tn squared). For four features each at plus or minus 0.05 mm: sqrt(4 x 0.0025) = 0.10 mm, compared with 0.20 mm worst-case.
When should I use worst-case instead of RSS?
Use worst-case where failure is unacceptable or expensive — safety-critical assemblies, interference that would cause a recall — and on short chains where being conservative costs little. Use RSS where you have many contributors, a genuinely controlled process, and can tolerate occasional selection or adjustment.
How do I work out what tolerance each feature needs?
Divide the assembly requirement across the chain. Worst-case: each feature gets the assembly tolerance divided by the number of features. RSS: each gets the assembly tolerance divided by the square root of the number of features — noticeably looser, and therefore cheaper to machine.
Does a tolerance stack-up account for GD&T?
No. A 1D stack only handles linear dimensions and their tolerances. Geometric tolerances such as flatness, perpendicularity and true position contribute additional variation not captured here, as do fixturing and temperature.
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