CALCULATORS / GEOMETRY AND MASS PROPERTIES

Rectangle area with a circular cutout calculator

Rectangle with one circular cutout fully inside it.

geometry-area.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	areamm^2	perimetermm
	18743.4	725.664
	14743.4	645.664

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.

hole fits width40.00 mm✓ passes

BASELINE INPUTS

length200 mmwidth100 mmradius20 mm

CALCULATED

area18743 mm^2

perimeter725.66 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Area of engineering shapes
# Scope: Rectangle with one circular cutout fully inside it.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

length = 200 mm
width = 100 mm
radius = 20 mm

area := length*width-pi*radius^2 [mm^2]
perimeter := 2*(length+width)+2*pi*radius [mm]

check hole fits width: 2*radius <= width

scenario alternative: length = 160 mm

Calculated from your source · not saved

Baseline · Baseline

hole fits width40.00 mm ✓ passes

alternative · alternative

hole fits width40.00 mm ✓ 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.

area: area = length*width-pi*radius^2 [mm^2]
perimeter: perimeter = 2*(length+width)+2*pi*radius [mm]

Original worked example

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

Given

length: 200 mm
width: 100 mm
radius: 20 mm

Calculated

area: 18743.4 mm^2
perimeter: 725.664 mm

Assumptions and limits

Rectangle with one circular cutout fully inside it.

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: Area of engineering shapes. Inputs: shape; dimensions; cutouts. Outputs: area; perimeter. 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: shape, dimensions, cutouts
Outputs: area, perimeter
Modes: calculate, compare, sweep
Drawing: Parametric solid

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