Tolerance Stack-Up Calculator — Worst Case & RSS

About Tolerance Stack-Up Calculator — Worst Case & RSS

A housing can be within tolerance, a spacer can be within tolerance, and the assembly can still bind. The missing calculation is the dimension chain: which dimensions create room, which consume it, and how all their allowed variations accumulate. This calculator follows a one-dimensional chain with a sign, nominal size, and symmetric plus/minus tolerance for each component. A positive final value is clearance; a negative one is interference.

Worst-case limits assume every contributing dimension simultaneously reaches the endpoint that makes the gap smallest or largest. Subtracting a dimension reverses its nominal contribution but does not cancel its tolerance. A large spacer and a small housing both close a gap. The tool therefore sums tolerance magnitudes and compares the resulting minimum and maximum with your required interval. It reports acceptance from those limits even if a narrower statistical estimate would appear acceptable.

The optional root-sum-square view is a separate model. Enable it only when the input dimensions are independent and centered, and every entered tolerance represents the same multiple of standard deviation. A drawing limit alone does not establish those assumptions. Common tooling, shared datums, batch shifts, and selective assembly can create dependence. The blue bars show each squared tolerance as a share of the squared-tolerance sum; they identify which dimension most affects that model, not which part is most expensive to improve.

How It Works

1. Choose a closing gap or total dimension and write its signed chain. Use one positive dimension for an enclosing space and negative dimensions for the parts occupying it.
2. Enter each nominal size and its symmetric half-width. A drawing marked 20 ±0.05 mm takes 0.05, not the total 0.10 mm range.
3. Set the permitted minimum and maximum final result. These are assembly requirements you supply, not fit-class values inferred by the calculator.
4. Read the worst-case interval and acceptance result. A negative gap means the chosen chain predicts interference, which can be intended or unacceptable depending on your requirements.
5. If justified by process data, enable the independent centered RSS model. Compare contributions before deciding which tolerance to tighten; keep worst-case acceptance separate.

Worked Example

A 50 ±0.10 mm housing contains a 20 ±0.05 mm spacer and a 29.8 ±0.05 mm bearing. Nominal clearance is 50 − 20 − 29.8 = 0.20 mm. The worst-case half-width is 0.10 + 0.05 + 0.05 = 0.20 mm, so clearance runs from 0.00 to 0.40 mm. It meets a specified 0.00–0.50 mm interval, with no lower-end clearance margin. Under the optional independence assumption, the RSS half-width is √0.015 = 0.12247 mm. That narrower number does not remove the zero-clearance worst case.

Formulas

Signed nominal chain

G = Σ(sᵢdᵢ)

Worst-case limits

T = Σtᵢ; G_min = G − T; G_max = G + T

Optional independent RSS half-width

T_RSS = √Σ(tᵢ²)

Contribution to squared-tolerance sum

cᵢ = 100tᵢ² / Σ(tⱼ²)

Standards & References

• Signed interval arithmetic for a linear chain with coefficients +1 or −1; symmetric limits only.
• NIST Technical Note 1297, section 5 and Appendix A: propagation of standard uncertainty; independent components combine by root sum square. A dimensional tolerance is not automatically a standard uncertainty — https://www.nist.gov/pml/nist-technical-note-1297/nist-tn-1297-5-combined-standard-uncertainty
• NIST SI Units — Length: exact inch-to-mm definition — https://www.nist.gov/pml/owm/si-units-length

Frequently Asked Questions