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Tolerance Stack Up Calculator

Work out tolerance stack up instantly with clear inputs, formula shown and shareable results.

About Tolerance Stack Up Calculator

Worst case stack-up adds tolerances arithmetically and guarantees every assembly fits, at the cost of very tight part tolerances. Root sum square assumes the individual variations are independent and normally distributed, which is realistic in volume production and typically yields a stack 30-40 percent smaller.

Formulas

Worst case

Total = t1 + t2 + t3

Statistical

Total = sqrt(t1² + t2² + t3²)

Worked example

With the default values below, Tolerance Stack Up Calculator returns Stack-up by chosen method of 0.1000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First toleranceminimum 0 mm
0.05 mm
Second toleranceminimum 0 mm
0.03 mm
Third toleranceminimum 0 mm
0.02 mm
Stack-up methodone of Worst case (arithmetic sum), Statistical (root sum square)
Worst case (arithmetic sum)

Results

Stack-up by chosen method
0.1000 mm
Worst case stack
0.1000 mm
Root sum square stack
0.0616 mm
Reduction using RSS
38.4% %

Step by step

  1. 1Values used
  2. 2Worst case
  3. 3Statistical
  4. 4Stack-up by chosen method= 0.1000 mm
  5. 5Worst case stack= 0.1000 mm
  6. 6Root sum square stack= 0.0616 mm
  7. 7Reduction using RSS= 38.4 %

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
  • Preliminary estimate only. Tolerance analysis for functional or safety-critical assemblies should be verified by a qualified engineer including process capability data.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Preliminary estimate only. Tolerance analysis for functional or safety-critical assemblies should be verified by a qualified engineer including process capability data.

Frequently Asked Questions

How is the Tolerance Stack Up figure worked out?

Total = t1 + t2 + t3. Worst case stack-up adds tolerances arithmetically and guarantees every assembly fits, at the cost of very tight part tolerances.

When must I use worst case?

For safety-critical interference, single-piece or low-volume builds, or where the processes are not centred and in statistical control. RSS assumes randomness that a biased process does not provide.

What values do I need to enter?

This calculator takes 4 inputs: First tolerance, Second tolerance, Third tolerance, Stack-up method. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.

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