CALCULATORS / GEOMETRY AND MASS PROPERTIES

Second moment of area calculator

Solid rectangular section about its centroidal bending axis.

geometry-area-moment.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	inertiamm^4	sectionModulusmm^3
	3600	600
	2880	480

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.

stiffness target3600.00 mm^4✓ passes

BASELINE INPUTS

width25 mmdepth12 mm

CALCULATED

inertia3600 mm^4

sectionModulus600 mm^3

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Second moment of area
# Scope: Solid rectangular section about its centroidal bending axis.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

width = 25 mm
depth = 12 mm

inertia := width*depth^3/12 [mm^4]
sectionModulus := 2*inertia/depth [mm^3]

check stiffness target: inertia >= 3000 mm^4

scenario alternative: width = 20 mm

Calculated from your source · not saved

Baseline · Baseline

stiffness target3600.00 mm^4 ✓ passes

alternative · alternative

stiffness target2880.00 mm^4 × fails

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.

inertia: inertia = width*depth^3/12 [mm^4]
section modulus: sectionModulus = 2*inertia/depth [mm^3]

Original worked example

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

Given

width: 25 mm
depth: 12 mm

Calculated

inertia: 3600 mm^4
section modulus: 600 mm^3

Assumptions and limits

Solid rectangular section about its centroidal bending axis.

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: Second moment of area. Inputs: section geometry; reference axis. Outputs: Ixx, Iyy, product of area. 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: section geometry, reference axis
Outputs: Ixx, Iyy, product of area
Modes: calculate, compare, sweep
Drawing: Parametric solid

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