CALCULATORS / GEOMETRY AND MASS PROPERTIES

Rectangular grid packing calculator

Axis-aligned rectangular grid packing; no rotation.

geometry-packing.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	columns	rows	count
	6	5	30
	5	5	25

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.

packing target30.00 ✓ passes

BASELINE INPUTS

trayLength300 mmtrayWidth200 mmitemLength40 mmitemWidth30 mmgap5 mm

CALCULATED

columns6

rows5

count30

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Circle and rectangle packing
# Scope: Axis-aligned rectangular grid packing; no rotation.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

trayLength = 300 mm
trayWidth = 200 mm
itemLength = 40 mm
itemWidth = 30 mm
gap = 5 mm

columns := floor((trayLength+gap)/(itemLength+gap))
rows := floor((trayWidth+gap)/(itemWidth+gap))
count := columns*rows

check packing target: count >= 20

scenario alternative: trayLength = 240 mm

Calculated from your source · not saved

Baseline · Baseline

packing target30.00 ✓ passes

alternative · alternative

packing target25.00 ✓ 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.

columns: columns = floor((trayLength+gap)/(itemLength+gap))
rows: rows = floor((trayWidth+gap)/(itemWidth+gap))
count: count = columns*rows

Original worked example

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

Given

tray length: 300 mm
tray width: 200 mm
item length: 40 mm
item width: 30 mm
gap: 5 mm

Calculated

columns: 6
rows: 5
count: 30

Assumptions and limits

Axis-aligned rectangular grid packing; no rotation.

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: Circle and rectangle packing. Inputs: container; item sizes; clearance. Outputs: feasible count; unused space. 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: container, item sizes, clearance
Outputs: feasible count, unused space
Modes: calculate, compare, sweep
Drawing: Parametric solid

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