CALCULATORS / GEOMETRY AND MASS PROPERTIES

Scale-model dimensions calculator

Geometrically similar solid at unchanged density.

geometry-scale-model.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	scaledLengthmm	scaledMasskg
	500	1
	400	0.512

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.

mass budget1.00 kg✓ passes

BASELINE INPUTS

scale0.5 length1 mmass8 kg

CALCULATED

scaledLength500 mm

scaledMass1 kg

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Scale-model dimensions
# Scope: Geometrically similar solid at unchanged density.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

scale = 0.5
length = 1 m
mass = 8 kg

scaledLength := scale*length [mm]
scaledMass := scale^3*mass [kg]

check mass budget: scaledMass <= 2 kg

scenario alternative: scale = 0.4

Calculated from your source · not saved

Baseline · Baseline

mass budget1.00 kg ✓ passes

alternative · alternative

mass budget0.51 kg ✓ 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.

scaled length: scaledLength = scale*length [mm]
scaled mass: scaledMass = scale^3*mass [kg]

Original worked example

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

Given

scale: 0.5
length: 1 m
mass: 8 kg

Calculated

scaled length: 500 mm
scaled mass: 1 kg

Assumptions and limits

Geometrically similar solid at unchanged density.

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: Scale-model dimensions. Inputs: prototype dimensions; scale denominator. Outputs: model dimensions; reverse scaling. Model scope: Ideal solids and explicitly described coordinate frames. 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: prototype dimensions, scale denominator
Outputs: model dimensions, reverse scaling
Modes: calculate, compare, sweep
Drawing: Parametric solid

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