Tolerance stack root sum square calculator

Calculate combined standard deviation and symmetric assumed interval half-width with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use combined standard deviation and symmetric assumed interval half-width to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Components JSON [sensitivity,standard deviation mm]
[[1,0.2],[2,0.1]]
User interval multiplier k (dimensionless)
3
Combined standard deviation (mm)
0.282843
Symmetric assumed interval half-width (mm)
0.848528

Try another scenario

Components JSON [sensitivity,standard deviation mm]
[[1,0.2],[2,0.1]]
User interval multiplier k (dimensionless)
2
Combined standard deviation (mm)
0.282843
Symmetric assumed interval half-width (mm)
0.565685
Calculation method

Calculation method

Combined standard deviation (mm)

sqrt(sum((coefficient*sigma)^2)).

Symmetric assumed interval half-width (mm)

k*combinedSigma.

Symbols and units
a
Components JSON [sensitivity,standard deviation mm]
b
User interval multiplier k (dimensionless)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Calculation steps and notation

sum(list) adds all entries in the list.

Assumptions & limits

Assumptions & limits

  • Independent input deviations and linear sensitivities. k does not by itself establish a coverage probability; correlation and worst-case bounds excluded. Supported limits: 1..100 rows; sigma>=0; k>=0.
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Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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