Tolerance Stack-up Calculator
Add the dimensions in a stack-up loop and see the assembly dimension by worst case, RSS, modified RSS and Monte Carlo.
Enter each dimension in the loop, with its tolerance, and say whether it adds to the gap (+) or takes away from it (−). The assembly dimension is the sum.
| Name | Nominal | Plus tol (+) | Minus tol (−) | Adds / subtracts |
|---|
The Monte Carlo run uses 50,000 random assemblies, so its figures change a little each time.
Distribution of 50,000 simulated assemblies
How it works
Each row is one dimension in the chain, with a nominal value and a plus and minus tolerance. A positive row adds to the assembly dimension and a negative row subtracts from it. Worst case puts every dimension at its extreme in the worst direction. RSS treats each dimension as a normal curve whose mean is the middle of its range and whose standard deviation is the range ÷ 6, then predicts the assembly within ±3σ, as in the Machinery’s Handbook. Modified RSS multiplies the RSS tolerance by 1.5. Monte Carlo picks 50,000 random sets of dimensions and combines them. The method is explained on the Tolerance Stack-up Analysis page.
Worked example
The simple gap example: a slot 25.00 ± 0.10 holds two parts, 12.00 ± 0.05 and 10.00 ± 0.05. The gap is 25 − 12 − 10 = 3.00. Worst case is 2.80 to 3.20; RSS is 2.878 to 3.122 (σ = 0.0408). If the gap must never be below 2.9, worst case fails and RSS predicts about 99.3% of assemblies pass. Press “Example: Handbook bearing stack” to reproduce the Handbook’s six-dimension example (worst case 0.1454 to 0.1722; RSS 0.1523 to 0.1653).
Things to know
This calculator handles a one-dimensional chain: all dimensions are in the same direction. For angled features, multiply each tolerance by the cosine of its angle to the gap before entering it.
Enter geometric tolerances as dimensions: a position tolerance of ⌀t contributes ± t ÷ 2 (see the stack-up page). Do not forget fits, clearances and bearing play if they are in the loop.
RSS and the simulation assume the dimensions are independent and, for the normal option, centered in their tolerance. If your processes drift or are skewed, use worst case or modified RSS, or measured data.
Tolerances are entered as positive numbers. A dimension given as 25.00 +0.10 −0.00 is entered with plus 0.10 and minus 0 (the calculator uses the actual limits, not the middle).
Common questions
Why do worst case and RSS differ so much?
Worst case assumes every part is at its extreme in the same direction at once. RSS and the simulation recognize that this is very unlikely when there are several dimensions.
What does the histogram show?
The distribution of the assembly dimension over 50,000 random assemblies. The red dashed lines are your limits, if you entered any. The area outside them is the defect rate.
Why does the Monte Carlo result change each time?
It uses random numbers. With 50,000 trials the percentages are stable to about ±0.1%, but the extreme values (the smallest and largest of all trials) vary.
Can I use inches?
Yes. The calculator does not care about units; use the same unit for every dimension.
Sources
- Machinery’s Handbook, 31st edition, Industrial Press: “Tolerance Analysis and Assignment” (worst-case, statistical, RSS and Monte Carlo methods).
- Fischer, B. R., Mechanical Tolerance Stackup and Analysis, CRC Press (modified RSS).
Last reviewed: October 22, 2026