CALCULATORS / UNITS AND DIMENSIONAL REASONING

Length, area and volume unit calculator

Length, square area and cube volume conversions.

units-length-area-volume.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	millimetresmm	areacm^2	volumeL
	300	900	27
	240	576	13.824

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.

length positive0.30 m✓ passes

BASELINE INPUTS

length0.3 m

CALCULATED

millimetres300 mm

area900 cm^2

volume27 L

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Length, area and volume conversion
# Scope: Length, square area and cube volume conversions.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

length = 0.3 m

millimetres := length [mm]
area := length^2 [cm^2]
volume := length^3 [L]

check length positive: length > 0 m

scenario alternative: length = 0.24 m

Calculated from your source · not saved

Baseline · Baseline

length positive0.30 m ✓ passes

alternative · alternative

length positive0.24 m ✓ 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.

millimetres: millimetres = length [mm]
area: area = length^2 [cm^2]
volume: volume = length^3 [L]

Original worked example

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

Given

length: 0.3 m

Calculated

millimetres: 300 mm
area: 900 cm^2
volume: 27 L

Assumptions and limits

Length, square area and cube volume conversions.

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: Length, area and volume conversion. Inputs: quantity; source and target units. Outputs: converted quantity; dimensional check. Model scope: Dimensional analysis and explicit reference conventions. 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: quantity, source and target units
Outputs: converted quantity, dimensional check
Modes: convert, solve-for
Drawing: Quantity diagram

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