Tolerance Stack-Up Calculator
List the dimensions between two features, mark each one as opening or closing the gap, and enter its tolerances. The calculator gives the nominal gap, the worst-case range, the statistical (RSS) range and the dimension that drives the result, so you know which tolerance to tighten and which you can open up to save cost.
1D tolerance stack
Walk the loop from one side of the gap to the other. Dimensions that open the gap add (+), dimensions that close it subtract (-). Enter each tolerance in in with its sign as it reads on the drawing: +0.005 / -0.005 for a symmetric tolerance, -0.007 / -0.020 for a shaft that sits wholly under nominal.
| Dimension | Direction | Nominal (in) | Upper tol. | Lower tol. | Remove |
|---|---|---|---|---|---|
Largest contributor: Housing depth, 62.1% of the RSS variance and 47.6% of the worst-case band. Tightening it pays off first.
- Housing depth± 0.0050 in, 62.1%
- Bearing width± 0.0025 in, 15.5%
- Spacer± 0.0030 in, 22.4%
The math
- Nominal gap: the sum of the + nominals minus the sum of the - nominals.
- Worst case: largest gap = every + dimension at its maximum and every - dimension at its minimum; smallest gap the reverse. The range is the sum of all the tolerance bands.
- RSS: each dimension is centered in its band, then the gap is the sum of the centers plus or minus the square root of the sum of the squared half-bands.
- Contribution: each dimension's squared half-band as a share of the total. Because the terms are squared, the widest tolerance dominates quickly: halving it often does more than tightening everything else.
Worked example
A pocket 50.00 ± 0.10 mm deep holds two parts, 20.00 ± 0.05 mm and 29.50 ± 0.08 mm. The nominal gap is 0.50 mm. Worst case, it runs from 0.27 mm to 0.73 mm (± 0.23 mm, the sum of the tolerances). RSS gives ± √(0.10² + 0.05² + 0.08²) = ± 0.137 mm, so 0.363 mm to 0.637 mm. The pocket depth carries 53 percent of the variance, so it is the tolerance to look at first.
Once the stack closes, the parts have to hold it. Send the drawings and U.S. shops quote the machining and the inspection, or check a mating diameter with the fit calculator.
Frequently asked questions
- What is a tolerance stack-up?
- It is the sum of the dimensions and tolerances between two features you care about, such as the end play of a shaft or the gap between a cover and a housing. You trace a loop of dimensions from one side of the gap to the other; the gap is what is left, and its range is what the tolerances along the loop allow.
- Worst case or RSS: which should I use?
- Worst case assumes every part lands at the bad end of its tolerance at once, so if the worst-case range works, every assembly works. RSS (root sum square) assumes each dimension varies independently around its center, with the tolerance at about three standard deviations, so extremes rarely line up. RSS gives a tighter, more realistic range for production runs with capable processes. Use worst case for short stacks, low volumes, safety-critical gaps and parts from unknown sources.
- How do I decide the direction of each dimension?
- Start at one face of the gap and walk around the loop to the other face. A dimension that points the same way you are walking opens the gap and adds (+); one that points back closes it and subtracts (-). A quick check: making a + part longer should make the gap bigger.
- What about unequal tolerances like +0.004 / -0.001?
- Enter them as they are. Worst case uses the limits directly. For RSS the calculator first moves the dimension to the middle of its band (nominal + 0.0015 in this case) with an equal +/-0.0025, which is how statistical stacks treat an unequal tolerance. That is why the RSS range can be centered on a slightly different value than the nominal gap.
- Can I trust the RSS result?
- Only as far as its assumptions hold: independent dimensions, processes centered on nominal, and tolerances near three sigma. A shifted process, a bimodal supplier mix or a stack of three or four parts all push reality toward worst case. A common hedge is to inflate the RSS range (1.5x is a popular factor) or to carry the untrusted dimensions at worst case.
- Does it handle GD&T or 2D stacks?
- This is a one-dimensional stack along a single direction. Convert a position or profile tolerance to its +/- equivalent along the stack direction (half the tolerance zone), and use a 2D or 3D analysis tool when angles, rotation or several directions matter.
