Tolerance Stack Up Calculator: Worst Case & RSS

Published September 22, 2026 · MfgWorkbench editorial reference

Add a one-dimensional chain of signed dimensions and compare guaranteed arithmetic limits with a conditional statistical estimate. Enter one signed nominal and symmetric tolerance per row.

How to enter a dimension chain

Each row uses the format nominal, tolerance. For a 50 ±0.10 mm opening containing a 30 ±0.05 mm part and a 19.5 ±0.05 mm spacer, enter 50,0.10 on the first row, −30,0.05 on the second and −19.5,0.05 on the third. Use a minus sign for a dimension that closes the gap. Tolerance magnitudes remain positive.

Do not mix inches and millimeters. This model assumes a linear chain with each sensitivity coefficient equal to +1 or −1. Angular effects, position tolerances, datum mobility and nonlinear contact need a more complete analysis.

Worst-case and RSS formulas

Nominal result is the sum of signed nominal dimensions. Worst-case half-width is the sum of all tolerance half-widths. The resulting minimum and maximum cover every combination inside those component limits. For the example, the nominal gap is 0.50 mm and worst-case limits are 0.30 to 0.70 mm.

RSS half-width = √(t₁²+t₂²+…). Here it is 0.122474 mm. Interpreting that as a statistical interval requires independent, centered dimensions whose listed tolerances represent the same multiple of standard deviation. If each input is ±3σ, the output is also approximately ±3σ under a normal linear model. The tool does not infer a probability from drawing limits alone.

When not to rely on RSS

A common setup offset can correlate dimensions, shifting multiple parts together. Process drift can move means off nominal. Either effect undermines a simple centered independent RSS calculation. Do not use RSS to declare a guaranteed minimum clearance or an interference-free assembly.

For asymmetric tolerances, rewrite each interval as its midpoint and half-width before entering it, then maintain the correct sign. For example, 10 +0.20/−0.00 becomes 10.10 ±0.10. Document that conversion alongside the drawing revision.