Tolerance stack-up calculator
Worst-case adds every tolerance; RSS adds them in quadrature: √(t₁² + t₂² + …). Three ±0.1 contributors stack to ±0.3 worst-case but only ±0.173 RSS. Enter each dimension in the chain with its tolerance and direction; the calculator returns both totals so you can see what the assembly guarantees versus what it will statistically do.
Worst-case is the contractual answer — every part at its limit simultaneously. RSS assumes independent, centered processes and is how a stack that "never fails in practice" earns that reputation. Which one your customer accepts is a drawing/flow-down question, not a math one.
Contributions
- Nominal sum
- Worst-case min
- Worst-case max
- Worst-case plus
- Worst-case minus
- RSS plus/minus
- RSS min
- RSS max
How it’s calculated
Worst-case sums signed min/max intervals; RSS = sqrt(sum(h_i^2)) where h_i = (+tol + −tol)/2, the tolerances entered as magnitudes (a band wholly on one side of its nominal, such as 25 −0.02/−0.05, is entered as 24.98 +0/−0.03).
RSS assumes independent, normally distributed dimensions, each centred mid-tolerance with its tolerance at ±3σ, so the band holds about 99.73 % of assemblies. It is optimistic with two or three links; use worst case for safety-critical or short stacks.
| Label | Dir | Signed nominal | + tol | − tol | RSS share |
|---|---|---|---|---|---|
| Part A | + | 10.000 mm | 0.100 mm | 0.100 mm | 80.0% |
| Part B | - | -5.000 mm | 0.050 mm | 0.050 mm | 20.0% |
Worst-case or RSS — which stack-up do you use?
A tolerance stack-up adds the tolerances along a chain of dimensions to see how much the final gap or interface can vary. Worst-case sums every tolerance directly — it assumes each part sits at its extreme at once, the guarantee a contract holds you to. RSS adds them in quadrature,√(t₁² + t₂² + …), reflecting what centred, independent processes actually produce.
Enter each contributor with its tolerance and direction, and the calculator returns both totals plus each contributor’s share of the stack, so you can see which dimensions dominate. Which total your customer accepts is a drawing and flow-down decision; the calculator gives you both to argue from.