A tolerance stack-up is a calculation of how the tolerances of several parts or features add together along one dimension of an assembly, such as a gap or a clearance. A worst-case stack adds every tolerance at its extreme, so the assembly works even if every part is at its limit. A statistical stack, often root sum square, assumes parts vary randomly and rarely all reach their limits together, which gives a smaller, more realistic range. Engineers use stack-ups to set tolerances and to find which ones matter most.
Example: Three spacers, each 10.00 ± 0.10 mm, sit in a slot 30.50 ± 0.10 mm deep. The nominal gap is 30.50 − 30.00 = 0.50 mm. Worst case adds all four tolerances: 0.50 ± 0.40 mm, a gap of 0.10 to 0.90 mm. Root sum square gives ± √(4 × 0.10²) = ± 0.20 mm, a gap of 0.30 to 0.70 mm.
When nobody does a stack-up, assemblies can bind or rattle even though every part is in tolerance, and the shop gets blamed for parts that met the drawing. A stack-up also shows which few tolerances drive the result, so the others can be opened up to save machining cost.
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