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CALCULATORS / TOLERANCES, FITS AND METROLOGY

Measurement uncertainty propagation calculator

First-order uncertainty in area; independent length uncertainties.

tolerances-uncertainty.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenarioareamm^2sigmaAreamm^2
500020.6155
400016.7631

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

relative uncertainty budget0.00 ✓ passes

BASELINE INPUTS

CALCULATED

area5000 mm^2
sigmaArea20.616 mm^2

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
relative uncertainty budget0.00 ✓ passes
alternative · alternative
relative uncertainty budget0.00 ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

area
area = length*width [mm^2]
sigma area
sigmaArea = sqrt((width*sigmaLength)^2+(length*sigmaWidth)^2) [mm^2]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

length
100 mm
width
50 mm
sigma length
0.1 mm
sigma width
0.2 mm

Calculated

area
5000 mm^2
sigma area
20.6155 mm^2

Assumptions and limits

First-order uncertainty in area; independent length uncertainties.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Measurement uncertainty propagation. Inputs: input uncertainties; sensitivities; covariance. Outputs: combined standard uncertainty. Model scope: Separate manufacturing tolerances, uncertainty and numerical error. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

  • Inputs: input uncertainties, sensitivities, covariance
  • Outputs: combined standard uncertainty
  • Modes: calculate, compare, sweep
  • Drawing: Tolerance interval diagram

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS

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