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Tolerance Stack-Up Basics: Worst Case vs RSS

Guide · Updated October 28, 2026

When parts are assembled, their tolerances add up. A stack-up predicts the range of a gap, a clearance or an overall length from the individual part tolerances. It tells you whether parts made inside their own tolerances will always assemble, and which dimension to tighten if they will not.

Check the gap with blocks

Measure the assembled gap with a gage block stack or feeler gages. The free Gage Block Calculator builds the gage block stack for any size you need to set.

Step by step

Pick the result dimension: Choose the gap or length you care about, such as the end clearance of a shaft in a housing.
Draw the loop: Trace a path of dimensions from one side of the gap around the parts to the other side. Mark each as positive or negative.
Add the nominals: Gap nominal = sum of positive dimensions − sum of negative dimensions.
Worst case: Add all the tolerances: worst-case variation = sum of each ± tolerance.
RSS: Root sum square: variation = √(t1² + t2² + …). It assumes sizes vary randomly and are centered.
Compare with the need: If the worst-case range allows interference or too much play, tighten the largest tolerances first; they dominate RSS.
Check real parts: Measure the first assemblies to confirm the prediction.

Worked example: four parts in a housing

A housing pocket is 2.000 ± 0.002 in deep. Four parts stack inside it: 0.500 ± 0.002, 0.750 ± 0.003, 0.250 ± 0.001 and 0.490 ± 0.002 in. The parts total 1.990 in, so the nominal gap is 2.000 − 1.990 = 0.010 in. Worst case: 0.002 + 0.002 + 0.003 + 0.001 + 0.002 = ±0.010 in, so the gap ranges from 0.000 to 0.020 in. RSS: √(0.002² + 0.002² + 0.003² + 0.001² + 0.002²) = √(0.000022) = ±0.0047 in, so the gap is likely between about 0.0053 and 0.0147 in.

Which method to use

Worst case guarantees every assembly works if every part is in tolerance, and it is the safe choice for small quantities, safety-critical fits and when parts may all run to one side, such as from one worn tool. RSS predicts the range that nearly all assemblies fall within when sizes vary randomly around the middle, and suits high-volume production with process control. In a one-off or prototype shop, use worst case unless the designer has said otherwise.

Finding the biggest contributor

Square each tolerance to see its share of the RSS result. In the example the 0.003 in tolerance contributes 9 of 22 parts, about 41%. Tightening only that dimension to ±0.001 in drops the RSS to √0.000014 = ±0.0037 in and the worst case to ±0.008 in. Tightening the 0.001 in part further would barely change anything.

Common mistakes

Leaving a dimension out of the loop, using diameters where radii belong (a diameter tolerance contributes half to a radial stack), mixing inch and metric, and forgetting geometric tolerances such as perpendicularity of a shoulder, which can add to the stack. Always sketch the loop and check signs before adding numbers.

Tips

Prints: blueprint reading.
GD&T: GD&T basics.
Gaps: measure a recess with gage blocks.

FAQ

What is a tolerance stack-up?

A calculation of how individual part tolerances combine in an assembly.

What is worst case?

Adding all tolerances directly; it guarantees fit if all parts are in tolerance.

What is RSS?

Root sum square: the square root of the sum of squared tolerances, a statistical estimate.

Which is larger?

Worst case is always equal to or larger than RSS.

How do I reduce stack-up?

Tighten the largest tolerances or reduce the number of parts in the loop.

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