CALCULATORS / GEOMETRY AND MASS PROPERTIES

Surface area and coating area calculator

Closed right circular cylinder; no fillets.

geometry-surface-area.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	areacm^2
	245.044
	186.988

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.

coating budget245.04 cm^2✓ passes

BASELINE INPUTS

radius30 mmheight100 mm

CALCULATED

area245.04 cm^2

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Surface area and coating area
# Scope: Closed right circular cylinder; no fillets.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

radius = 30 mm
height = 100 mm

area := 2*pi*radius*(radius+height) [cm^2]

check coating budget: area <= 300 cm^2

scenario alternative: radius = 24 mm

Calculated from your source · not saved

Baseline · Baseline

coating budget245.04 cm^2 ✓ passes

alternative · alternative

coating budget186.99 cm^2 ✓ 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 = 2*pi*radius*(radius+height) [cm^2]

Original worked example

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

Given

radius: 30 mm
height: 100 mm

Calculated

area: 245.044 cm^2

Assumptions and limits

Closed right circular cylinder; no fillets.

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: Surface area and coating area. Inputs: solid dimensions; exposed faces. Outputs: external area; coating 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: solid dimensions, exposed faces
Outputs: external area, coating area
Modes: calculate, compare, sweep
Drawing: Parametric solid

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