One-Dimensional Tolerance Stack-Up Calculator
Estimate the nominal result and variation for a signed one-dimensional chain of up to three dimensions. Choose whether each nominal value is added or subtracted, and enter its plus-or-minus tolerance. The calculator reports the arithmetic worst-case range and an RSS estimate separately.
This is a basic size-chain tool. It does not interpret a drawing, datum reference frame, geometric tolerances, fit classes, or a three-dimensional assembly.
Interactive calculator
Enter values and select Calculate.
Worst case and RSS
The nominal result is the signed sum of the dimensions. Worst-case tolerance adds the magnitude of each entered tolerance, regardless of whether its nominal dimension is added or subtracted. The resulting bounds are nominal minus and plus that total.
The root-sum-square estimate is √(t1² + t2² + t3²). It can describe a statistical variation model when the inputs and assumptions support it. RSS does not guarantee that every assembled part will remain inside that range. It assumes more than just independent numbers: the production distributions, centering, process stability, and the meaning of the input tolerances matter.
Worked example
For +100 ±0.2 − 50 ±0.1, the nominal result is 50. The worst-case tolerance is ±0.3, so the arithmetic range is 49.7 to 50.3. RSS is √(0.2² + 0.1²), or about ±0.224. The RSS result is an estimate under statistical assumptions, not a safe substitute for the worst-case condition when every conforming combination must fit.
Know when this model is too simple
A real assembly chain can include correlated features, datums, geometric controls, bonus tolerance, material boundaries, and non-normal or off-center process distributions. Dimensions also need consistent units and a correct functional direction. Use a drawing-based tolerance analysis when assembly acceptance or safety depends on the result.
ASME describes Y14.5 dimensioning and tolerancing as the standard language for stating and interpreting GD&T requirements. This calculator does not implement that standard. For circular-pattern locations, see the bolt circle calculator.
