Build-plate arrangement calculator

Axis-aligned grid packing on build plate; no rotation or toolhead clearance.

3d-printing-build-layout.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	columns	rows	parts
	4	3	12
	3	3	9

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.

batch count target12.00 ✓ passes

BASELINE INPUTS

plateX220 mmplateY220 mmpartX40 mmpartY50 mmgap10 mm

CALCULATED

columns4

rows3

parts12

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Build-plate arrangement
# Scope: Axis-aligned grid packing on build plate; no rotation or toolhead clearance.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

plateX = 220 mm
plateY = 220 mm
partX = 40 mm
partY = 50 mm
gap = 10 mm

columns := floor((plateX+gap)/(partX+gap))
rows := floor((plateY+gap)/(partY+gap))
parts := columns*rows

check batch count target: parts >= 12

scenario alternative: plateX = 176 mm

Calculated from your source · not saved

Baseline · Baseline

batch count target12.00 ✓ passes

alternative · alternative

batch count target9.00 × 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.

columns: columns = floor((plateX+gap)/(partX+gap))
rows: rows = floor((plateY+gap)/(partY+gap))
parts: parts = columns*rows

Original worked example

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

Given

plate x: 220 mm
plate y: 220 mm
part x: 40 mm
part y: 50 mm
gap: 10 mm

Calculated

columns: 4
rows: 3
parts: 12

Assumptions and limits

Axis-aligned grid packing on build plate; no rotation or toolhead clearance.

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: Build-plate arrangement. Inputs: part footprints; keepout; plate size. Outputs: placement count; utilization. Model scope: Geometry plus explicitly calibrated machine and material parameters. 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: part footprints, keepout, plate size
Outputs: placement count, utilization
Modes: calculate, compare, sweep
Drawing: Part, orientation and layer preview

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