Five parts arrive. Every one measures inside its tolerance. Bolt them together and the assembly is 4 mm out and will not close. Nobody made a bad part, and yet you have a bad product — that is tolerance stack-up explained in one paragraph, and it is the reason "we checked every component" is not the same as "it will fit".
Tolerance stack-up is the accumulated deviation of an assembly caused by the individual tolerances of its parts and the gaps between them. A single-part tolerance is a promise about one dimension. A stack-up is a prediction about the dimension nobody drew.
Tolerance, Fit and Stack-Up Are Three Different Things
| Term | What it constrains | Who owns it | Typical mistake |
|---|---|---|---|
| Tolerance | One dimension on one part | The part drawing | Assuming a tight tolerance on each part guarantees a tight assembly |
| Fit | The relationship between two mating features | The pair, not the part | Quoting a clearance without saying at which material condition |
| Stack-up | The sum of variation along a chain of parts and gaps | The assembly drawing — which often does not exist | Nobody owns it, so nobody checks it |
| General tolerance | Every dimension with no individual tolerance shown | The title block | Treating the general tolerance as "small enough to ignore" |
That last row is where most export disputes start. The general tolerance in the title block silently applies to dozens of dimensions, and in a chain of dozens it is not small at all.
Worst Case vs RSS: Two Answers to the Same Question
There are two standard ways to add tolerances up, and they give very different numbers.
Worst case assumes every part lands at its worst limit simultaneously. You add the tolerances arithmetically.
RSS (root sum square) assumes the parts vary independently around the middle of their tolerance, so extremes rarely coincide. You take the square root of the sum of the squares.
| Chain | Worst case | RSS | Ratio |
|---|---|---|---|
| 5 parts at ±0.1 mm | ±0.5 mm | ±0.224 mm | 2.2× |
| 5 parts at ±0.5 mm | ±2.5 mm | ±1.118 mm | 2.2× |
| 4 cabinets at ±2 mm | ±8 mm | ±4 mm | 2× |
| 10 parts at ±0.2 mm | ±2.0 mm | ±0.632 mm | 3.2× |
The gap widens as the chain gets longer, which is why long assemblies are exactly where people are tempted to switch methods — and exactly where switching is most dangerous.
When each one is right
Use worst case when the chain is short, the consequence of a misfit is a rejected container, the parts come from more than one supplier, or you have no process data. Worst case is what you quote to a buyer, because it is a guarantee rather than a probability.
Use RSS when you own the process, you have measured distributions showing parts really do centre in the tolerance, and you accept a small failure rate. RSS is a production planning tool, not a promise.
The failure mode with RSS is specific and worth naming: it assumes centred, independent, normally distributed variation. A supplier whose tooling has worn will run consistently to one side of the tolerance band, a habit that turns the statistical assumption into fiction. RSS applied to a supplier you have not measured is not a calculation, it is an optimism.
The ISO 2768 Trap: Half of It No Longer Exists
Plenty of drawings still carry "ISO 2768-mK" in the title block. Two things about that are worth knowing.
ISO 2768-1 (general tolerances for linear and angular dimensions, classes f / m / c / v) is still current. It was last reviewed and confirmed in 2022, and a consolidated revision is expected.
ISO 2768-2 (general geometrical tolerances — the "K" in mK) was cancelled and replaced by ISO 22081:2021. And ISO 22081 changed the model: it gives the rules for stating a general geometrical specification but does not supply a table of values. You have to state a general geometrical tolerance yourself, plus a datum system.
The practical consequence: a drawing that says "ISO 2768-mK" is citing a withdrawn part for its geometry, and a drawing that just says "ISO 22081" without stating a value has specified nothing at all. Both pass a casual review; neither survives a real dispute.
Where Stack-Up Bites Suppliers, Not Machinists
Stack-up is taught as a machining topic, which is why furniture, building-products and packaging suppliers get caught by it.
Cabinet and wardrobe runs. Four 600 mm units at ±2 mm each is ±8 mm worst case against a wall opening that also has a tolerance. This is the single most common "everything was in spec" installation failure.
Doors and frames. Leaf tolerance plus frame tolerance plus hinge position tolerance plus the seal's compression range. Each is trivial; the sum decides whether the door binds in summer.
Flat-pack hole patterns. A 32 mm system hole pitch tolerance repeated over 10 holes is a 10-link chain. The tenth hole is where the panel refuses to line up.
Packaging and containers. Product, foam, inner carton, master carton, pallet overhang. Each tolerance is generous, the chain is long, and the failure appears only when the last row does not fit the container. This is also where a "small" 3 mm per carton becomes a lost pallet position.
The measurement discipline that prevents all four is the same one that makes a spec image trustworthy: publish the dimension that governs, its tolerance, and the reference it is measured from. If the base numbers are shaky, everything downstream inherits it — nominal vs actual dimensions covers the first place that goes wrong, and installation clearance dimensions covers the gap you must leave once you know your stack.
Next Steps
- Draw the chain before you calculate it. List every part and gap between the two surfaces you care about, with a direction sign. Most stack-up errors are chain-definition errors, not arithmetic errors.
- Quote worst case to the buyer, plan with RSS internally. Never the reverse.
- Fix the title block. Replace "ISO 2768-mK" with ISO 2768-1 class plus an explicit ISO 22081 general geometrical specification and datum system.
- Put the governing dimension and its tolerance on the image, not only in the table. An industrial spec diagram that shows which face the dimension is taken from removes the ambiguity that makes stack-up unresolvable in an email argument. That only works if the callouts carry the measured value locked to the real edge — a number typed next to a rendered or AI-generated image proves nothing about the part in the container.
- Ask new suppliers for measured data, not a capability claim. Twenty parts and a caliper is enough to see whether they centre in the band or hug one limit.
FAQ
What is tolerance stack-up?
It is the accumulated variation across a chain of parts and gaps in an assembly. Each part can be within its own tolerance while the assembly is out of tolerance, because the deviations add up along the chain.
How do I calculate tolerance stack-up?
Define the chain of dimensions between the two surfaces you care about, then either add the tolerances arithmetically (worst case) or take the square root of the sum of their squares (RSS). Five parts at ±0.1 mm give ±0.5 mm worst case and ±0.224 mm RSS.
Which is better, worst case or RSS?
Neither is better; they answer different questions. Worst case is a guarantee and belongs in what you promise a buyer. RSS is a probability and belongs in internal production planning, and only when you have measured distributions to justify it.
Is ISO 2768 still valid?
ISO 2768-1, covering general tolerances for linear and angular dimensions, remains current and was reconfirmed in 2022. ISO 2768-2, covering general geometrical tolerances, was replaced by ISO 22081:2021, which provides rules rather than a table of values — so "ISO 2768-mK" on a modern drawing is half obsolete.
Why do all my parts pass inspection but the assembly fails?
Because inspection checks parts against part tolerances and nobody checked the chain. Add the tolerances along the path between the two surfaces that must fit; if the worst-case sum exceeds the available gap, the assembly was designed to fail some percentage of the time.