CALCULATORS / GEOMETRY AND MASS PROPERTIES

Section modulus and radius of gyration calculator

Concentric circular tube; bending and torsion properties.

geometry-section-properties.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	areamm^2	inertiamm^4	polarmm^4
	215.984	20586	41172
	-38.4845	-2888.74	-5777.49

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.

positive wall30.00 mm✓ passes

BASELINE INPUTS

outer30 mminner25 mm

CALCULATED

area215.98 mm^2

inertia20586 mm^4

polar41172 mm^4

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Section modulus and radius of gyration
# Scope: Concentric circular tube; bending and torsion properties.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

outer = 30 mm
inner = 25 mm

area := pi*(outer^2-inner^2)/4 [mm^2]
inertia := pi*(outer^4-inner^4)/64 [mm^4]
polar := 2*inertia [mm^4]

check positive wall: outer > inner

scenario alternative: outer = 24 mm

Calculated from your source · not saved

Baseline · Baseline

positive wall30.00 mm ✓ passes

alternative · alternative

positive wall24.00 mm × 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.

area: area = pi*(outer^2-inner^2)/4 [mm^2]
inertia: inertia = pi*(outer^4-inner^4)/64 [mm^4]
polar: polar = 2*inertia [mm^4]

Original worked example

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

Given

outer: 30 mm
inner: 25 mm

Calculated

area: 215.984 mm^2
inertia: 20586 mm^4
polar: 41172 mm^4

Assumptions and limits

Concentric circular tube; bending and torsion properties.

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: Section modulus and radius of gyration. Inputs: cross section; dimensions. Outputs: area, section modulus, radius of gyration. 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: cross section, dimensions
Outputs: area, section modulus, radius of gyration
Modes: calculate, compare, sweep
Drawing: Parametric solid

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