Your Tolerance Stack-Up Calculator
Calculate a 1D tolerance stack-up: worst-case and RSS results, Monte-Carlo simulation, percentage out of spec, Cpk and a contribution chart.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Tolerance Stack-Up Calculator with sample data entered and the result showing.
What is the Tolerance Stack-Up Calculator?
Tolerance stack-ups answer a simple but important question: given the tolerances on every part in an assembly, how big or small can the gap, clearance or overall length become? Enter each dimension in the chain with its nominal value, plus and minus tolerances, whether it adds to or subtracts from the gap, and the process capability, and the calculator returns the mean gap, the worst-case range (every part at its limit in the unfavourable direction) and the statistical RSS range (mean ± 3σ), together with a contribution table showing which dimension drives the variation.
If you also enter lower and upper specification limits for the gap it predicts the fraction out of spec and the Cpk, tells you whether worst case always passes, and optionally runs a Monte-Carlo simulation of 20,000 to 100,000 assemblies with a histogram on the chart. Asymmetric (unilateral) tolerances shift the mean automatically. For the three-part example 25 ± 0.1, 10 ± 0.05 minus 34.5 ± 0.1 the mean gap is 0.5 mm, the worst case is 0.25 to 0.75 mm and RSS is 0.35 to 0.65 mm.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
Both methods side by side, with mean and σ.
Histogram of simulated assemblies and out-of-spec percentage.
Which dimension drives the variation — by variance and by worst case.
Predicted ppm out of spec and Cpk for the gap.
AZRS tools are free to open and use.
It opens in your browser, so there is nothing to download.
Used for
Pick one to see how it fits.
How it compares
A plain look at this tool next to the usual alternative.
| This engineering calculator | Desktop software | |
|---|---|---|
| Install | Nothing to install | Usually an app or program to install |
| Account | No signup | Depends on the product |
| Cost | Free to use | Free or paid, depends on the product |
| Where it runs | In your browser tab | On your computer |
Questions people ask
What is the difference between worst case and RSS?
Worst case adds all tolerances; RSS combines them statistically as √Σσ².
What is Cp?
Process capability: tolerance width divided by six standard deviations.
Does it handle 2D/3D stacks?
No — one-dimensional chains only.
Is it free?
Yes.
How do I use the Tolerance Stack-Up Calculator?
1. Enter each dimension, tolerances, direction and Cp. 2. Enter the lower and upper limits for the gap. 3. Read worst-case, RSS and Monte-Carlo results. 4. Tighten the biggest contributor and recalculate.
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Try the Tolerance Stack-Up Calculator now
1D tolerance stack-up with worst-case, RSS, Monte-Carlo simulation, contributors and. Free to use.
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