Tolerance stack-up calculator
A tolerance stack tells you how much variation five parts add up to. The worst-case method assumes every part sits at its limit at once; the statistical method combines them in quadrature. This calculator shows both, and how much the statistical assumption buys you.
| Part | Nominal | Tolerance | Share of variance |
|---|---|---|---|
| Part 1 | 10.00 mm | ±0.100 | 20.0% |
| Part 2 | 20.00 mm | ±0.100 | 20.0% |
| Part 3 | 30.00 mm | ±0.100 | 20.0% |
| Part 4 | 15.00 mm | ±0.100 | 20.0% |
| Part 5 | 25.00 mm | ±0.100 | 20.0% |
A part with twice the tolerance carries four times the variance.
T_wc = Σ t_i · Assumes every part at its limit simultaneously.
T_rss = √(Σ t_i²) · Valid when the parts are independent and centred.
t_i² / Σ t_j² · Tolerance contributes quadratically.
A clear path from inputs to results.
A tolerance stack tells you how much variation five parts add up to. The worst-case method assumes every part sits at its limit at once; the statistical method combines them in quadrature. This calculator shows both, and how much the statistical assumption buys you.
How to use
- Enter the nominal size and tolerance for each part.
- Read the worst-case stack.
- Compare it with the root-sum-square stack.
- Use the variance shares to see which part dominates.
The formula
Reference: Worst-case (arithmetic) and statistical (root-sum-square) tolerance analysis, standard practice in mechanical design.
Worked example
Five parts, each ±0.1 mm
- Nominals 10, 20, 30, 15, 25 mm.
- Every tolerance ±0.10 mm.
- 1
Nominal stack: 100.00 mm.
- 2
Worst case: ±(0.1 × 5) = ±0.50 mm.
- 3
RSS: √(5 × 0.01) = ±0.2236 mm.
- 4
The statistical stack is 2.24× tighter.
- 5
Each part contributes 20% of the variance.
Nominal 100.00 · worst case ±0.500 · RSS ±0.224 (2.24× tighter).
Interpreting the result
Worst case is free of statistics but expensive: it assumes five independent parts all sit at their extreme simultaneously, which is very unlikely. RSS is the standard compromise, but it assumes the processes are centred and independent. If one part drifts, the statistical answer is optimistic and the worst case is the honest one.
Assumptions & limitations
- Symmetric tolerances about the nominal.
- RSS assumes independent, centred, normally distributed dimensions at ±3σ.
- No allowance for thermal expansion or assembly shift.
Frequently asked questions
When should I use worst case?
For safety-critical assemblies, very low volume, or when the processes are not statistically controlled.
Does RSS guarantee parts fit?
No. It predicts a small fraction outside the limits — typically about 0.3% at ±3σ for the combined distribution.
What does the tightening factor mean?
How much smaller the statistical tolerance is than the arithmetic one. It grows with the square root of the part count.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.