CALCULATORS / TOLERANCES, FITS AND METROLOGY

Image-to-dimension scale calculator

Planar image scale from a reference on the same plane; no perspective correction.

tolerances-image-scale.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	scalemm	lengthmm
	0.2	40
	0.16	32

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.

measured length budget40.00 mm✓ passes

BASELINE INPUTS

referenceLength100 mmreferencePixels500 measuredPixels200

CALCULATED

scale0.2 mm

length40 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Image-to-dimension scale
# Scope: Planar image scale from a reference on the same plane; no perspective correction.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

referenceLength = 100 mm
referencePixels = 500
measuredPixels = 200

scale := referenceLength/referencePixels [mm]
length := measuredPixels*scale [mm]

check measured length budget: length <= 50 mm

scenario alternative: referenceLength = 80 mm

Calculated from your source · not saved

Baseline · Baseline

measured length budget40.00 mm ✓ passes

alternative · alternative

measured length budget32.00 mm ✓ 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.

scale: scale = referenceLength/referencePixels [mm]
length: length = measuredPixels*scale [mm]

Original worked example

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

Given

reference length: 100 mm
reference pixels: 500
measured pixels: 200

Calculated

scale: 0.2 mm
length: 40 mm

Assumptions and limits

Planar image scale from a reference on the same plane; no perspective correction.

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: Image-to-dimension scale. Inputs: reference length; pixel correspondences; perspective assumptions. Outputs: pixel scale; length estimate; limitations. 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 length, pixel correspondences, perspective assumptions
Outputs: pixel scale, length estimate, limitations
Modes: calculate, compare, sweep
Drawing: Tolerance interval diagram

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