How to use this tool
- Enter one dimension per line: nominal, symmetric ± tolerance, and optional direction +1 or −1.
- Calculate nominal stack and worst-case min/max assembly extremes.
- Compare RSS cautiously where dimensions are independent and centered.
- Apply engineering acceptance conditions using the worst-case bounds or a separately validated statistical model.
Calculation method and formula
Nominal stack = Σ(signed nominal dimensions). Worst-case ± = Σ(|individual tolerance|). RSS ± = √Σ(individual tolerance²).
WORKED EXAMPLE
For +10 ±0.10 mm, +20 ±0.20 mm and −5 ±0.05 mm, nominal = 25 mm, worst case = ±0.35 mm and RSS ≈ ±0.22913 mm.
What the calculation does not cover
- RSS does not guarantee every assembly fits.
- Real distributions can be off-center, correlated, non-Gaussian or truncated by inspection.
- This tool assumes symmetric tolerance values, not unilateral position tolerances.
Common questions
Why is RSS smaller than the worst-case sum?
Worst case assumes every feature lands at a limiting extreme together; RSS models statistically independent variation.
Can I use RSS for a safety-critical assembly?
Not without independently validated distribution/correlation assumptions and engineering review.
Engineering use: This calculator is a transparent estimate for its defined model; confirm units, applicability, standards and engineering decisions independently.