Tolerance Stack-Up Calculator
Add up the tolerances on a chain of dimensions and you get the worst-case or statistical spread at the gap. This calculator sums ± tolerances by worst-case (straight add) and RSS (square-root-of-sum-of-squares) so you can see whether your stack closes before you machine the first part. Basis: ASME Y14.5 / ISO 1101.
Your Assembly Doesn't Fit — Yet Every Part Measured In Tolerance
You inspected all three plates, every dimension sat inside its ± band, and still the stack won't close by half a millimetre. That's a tolerance stack-up, and it's the most common "mystery" in machined assemblies. Each part is individually good; the tolerances just add along the chain. The fix isn't tighter machining on part two — it's understanding the total spread before you cut anything, then breaking the chain where it matters.
Worst-Case vs RSS — What Each Tells You
They answer different questions. Pick the one that matches how many parts you're making and what's at stake.
| Method | Formula | What it assumes | Use it when |
|---|---|---|---|
| Worst-case (WC) | ±(t₁ + t₂ + … + tₙ) | All dims drift the wrong way at once | Safety-critical, low-volume, or coupled features |
| RSS (statistical) | ±√(t₁² + t₂² + … + tₙ²) | Independent, normal, centered tolerances | High-volume runs where averages cancel |
RSS is always smaller than WC because it assumes the deviations partly cancel — which is only true across a population, not on a single part. The two numbers together bracket the real risk. This is the same math behind GD&T stack-up studies referenced in ASME Y14.5 and ISO 1101.
Run Your Own Stack-Up
Enter each link in the chain as its ± tolerance in millimetres. Add or remove rows as needed — the totals update instantly.
When to Use Which — and How to Break the Chain
You don't shrink a stack by tightening every tolerance; you shrink it by structuring the chain so fewer links add up. Reference dependent features to a single hard datum instead of stacking them end to end, relax the tolerances on surfaces that don't function, and move critical fits to GD&T so the MMC bonus tolerance works in your favor. For one-off or safety parts, plan to worst-case and accept the wider window. For a run of thousands, RSS is the honest expected spread. Either way, doing this on paper — or in the tool above — before the first cut is what stops the "it measured fine but won't fit" call.
Tolerance Stack-Up — Common Questions
What's the difference between worst-case and RSS stack-up?
When should I use worst-case instead of RSS?
Does this calculator handle GD&T position tolerances?
What assumptions does RSS make?
How do I reduce a tolerance stack on my part?
Where This Comes From
- ASME Y14.5 — dimensioning and tolerancing; the reference for stack-up and GD&T methods.
- ISO 1101 — geometrical product specifications (GPS); GD&T symbols and rules.
- Worst-case and RSS are the two standard linear stack-up methods taught in GD&T and tolerance-analysis practice.
The arithmetic here is a linear ± adder. It is not a substitute for a full GD&T stack-up on position, profile or runout callouts, and RSS results are only valid for independent, normally distributed, centered tolerances.
Not sure your stack closes?
Send us the assembly drawing with the chain of dimensions called out. We'll run the stack-up, flag the link that blows the fit, and return DFM feedback and a per-drawing quote within 24 hours — before any metal is cut.
Embed or Cite This Calculator
Link to it, cite it in a report, or embed the tool on your own engineering blog. It's free and runs entirely in the browser.
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