CALCULATORS / GEOMETRY AND MASS PROPERTIES

Mass from material and geometry calculator

Rectangular plate: ideal solid, uniform material

geometry-mass.napkin / editable

XZ / UNDEFORMED GEOMETRYFITTED TO VIEW

Plate selected · related inputs are marked.

mass budget5.40 kg✓ passes

BASELINE INPUTS

density2700 kg/m^3

CALCULATED

volume0.002 m^3

mass5.4 kg

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Rectangular plate: ideal solid, uniform material
length = 500 mm in 100..1000
width = 200 mm in 50..500
thickness = 20 mm in 5..50
density = 2700 kg/m^3 "Illustrative aluminium density"
part plate "Plate": box length, width, thickness
volume := length * width * thickness [m^3]
mass := density * volume [kg]
check mass budget: mass <= 10 kg
scenario wider: width = 300 mm

Calculated from your source · not saved

Baseline · Baseline

mass budget5.40 kg ✓ passes

wider · wider

mass budget8.10 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.

volume: volume = length * width * thickness [m^3]
mass: mass = density * volume [kg]

Original worked example

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

Given

length: 500 mm
width: 200 mm
thickness: 20 mm
density: 2700 kg/m^3

Calculated

volume: 0.002 m^3
mass: 5.4 kg

Assumptions and limits

Rectangular plate: ideal solid, uniform material

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: Mass from material and geometry. Inputs: volume; density; void fraction. Outputs: mass; sensitivity to material. 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: volume, density, void fraction
Outputs: mass, sensitivity to material
Modes: calculate, compare, sweep
Drawing: Parametric solid

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