CALCULATORS / TOLERANCES, FITS AND METROLOGY

Linear sensor calibration calculator

Two-point linear calibration mapping sensor reading to length.

tolerances-calibration.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	positionmm
	37.5
	27.5

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.

reading within calibration2.00 V✓ passes

reading upper bound2.00 V✓ passes

BASELINE INPUTS

reading2 VzeroReading0.5 VspanReading4.5 Vspan100 mm

CALCULATED

position37.5 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Linear sensor calibration
# Scope: Two-point linear calibration mapping sensor reading to length.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

reading = 2 V
zeroReading = 0.5 V
spanReading = 4.5 V
span = 100 mm

position := (reading-zeroReading)*span/(spanReading-zeroReading) [mm]

check reading within calibration: reading >= zeroReading
check reading upper bound: reading <= spanReading

scenario alternative: reading = 1.6 V

Calculated from your source · not saved

Baseline · Baseline

reading within calibration2.00 V ✓ passes

reading upper bound2.00 V ✓ passes

alternative · alternative

reading within calibration1.60 V ✓ passes

reading upper bound1.60 V ✓ 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.

position: position = (reading-zeroReading)*span/(spanReading-zeroReading) [mm]

Original worked example

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

Given

reading: 2 V
zero reading: 0.5 V
span reading: 4.5 V
span: 100 mm

Calculated

position: 37.5 mm

Assumptions and limits

Two-point linear calibration mapping sensor reading to length.

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: Linear sensor calibration. Inputs: reference points; observed outputs; uncertainty. Outputs: gain; offset; residuals. 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: reference points, observed outputs, uncertainty
Outputs: gain, offset, residuals
Modes: calculate, compare, sweep
Drawing: Tolerance interval diagram

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