Tolerance Stack-up Calculator

What it is for

A nominal clearance can look generous until the opening is at its smallest and the parts inside it are at their largest. This calculator combines a one-dimensional chain of sizes and their tolerances so you can see the smallest and largest resulting gap — both in the absolute worst case and as a statistical estimate.

Enter one comma-separated row for each dimension: name, nominal size, lower deviation, upper deviation and direction. Use direction 1 for a dimension added to the chain and -1 for one subtracted from it. Choose one unit, such as millimetres, and use it consistently; the calculator does not convert units.

It does not account for geometric tolerances, deformation, temperature, assembly methods or measurement uncertainty.

Worked example

For an opening containing two parts, enter:

Opening,100,-0.2,0.2,1
Part A,40,-0.1,0.1,-1
Part B,59,-0.1,0.1,-1

The tool answers: Nominal 1.000; worst case 0.600 to 1.400; statistical (RSS) 0.755 to 1.245. For the worst-case minimum, the opening is 99.8 while the two parts are 40.1 and 59.1. For the maximum, the opening is 100.2 and the parts 39.9 and 58.9.

The RSS range is narrower because all three parts rarely sit at their limits at the same time. It combines the half bands as √(0.2² + 0.1² + 0.1²) ≈ 0.245 around the centred value.

Deviations can both be negative or both positive, as in ISO fits. A 20 mm H7 hole (0 / +0.021) with a g6 shaft (−0.020 / −0.007) gives a worst-case clearance of 0.007 to 0.041 — exactly the values in the ISO 286 fit tables.

How to read the result

• Worst-case dimension: Nominal, Minimum and Maximum, plus the Worst-case spread. Use these when every assembly must fit, for example for a single prototype or a safety-relevant fit.
• Statistical (RSS) estimate: the Centred value (every part in the middle of its band), and RSS minimum and maximum. This assumes independent, normally distributed sizes whose tolerance band is ±3σ, so roughly 99.7 % of assemblies fall inside.
• Contributors: each row with its smallest and largest size. Check the signs here before trusting the totals.

A negative minimum means overlap in that chain; the tool then adds a warning. Decide whether that is an intended interference fit or a problem.

Tips and common mistakes

• Enter deviations relative to nominal, not the absolute smallest and largest sizes.
• The lower deviation must not be larger than the upper one.
• Subtracted parts use their upper limits when calculating the minimum clearance.
• Use RSS only for many parts from stable, independent processes; with two or three parts, or one supplier batch, design to the worst case.
• Include every dimension in the chain and check the signs against your drawing.

FAQ

Does this calculate production yield?

Not directly. The RSS range is a ±3σ estimate under independence and normality; it is not a yield prediction for a real process.

Can I use asymmetric tolerances?

Yes. Lower and upper deviations can have different sizes and signs, such as −0.020 / −0.007 for a g6 shaft.

What does a negative result mean?

For a clearance chain it means the parts can overlap at their limits. Whether that is acceptable depends on the intended fit.

Does it check alignment or flatness?

No. The calculation is one-dimensional and excludes geometric tolerances and deformation.