CALCULATORS / UNITS AND DIMENSIONAL REASONING

Volume estimate and uncertainty bounds calculator

Endpoint bounds on a positive rectangular volume estimate.

units-order-of-magnitude.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	estimatem^3	lowerm^3	upperm^3
	1	0.729	1.331
	0.8	0.5832	1.0648

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.

storage budget1.33 m^3✓ passes

BASELINE INPUTS

length2 mwidth1 mdepth0.5 mrelativeBound0.1

CALCULATED

estimate1 m^3

lower0.729 m^3

upper1.331 m^3

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Order-of-magnitude estimate
# Scope: Endpoint bounds on a positive rectangular volume estimate.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

length = 2 m
width = 1 m
depth = 0.5 m
relativeBound = 0.1

estimate := length*width*depth [m^3]
lower := estimate*(1-relativeBound)^3 [m^3]
upper := estimate*(1+relativeBound)^3 [m^3]

check storage budget: upper <= 2 m^3

scenario alternative: length = 1.6 m

Calculated from your source · not saved

Baseline · 2 m reach · 0.5 m depth

storage budget1.33 m^3 ✓ passes

alternative · 1.6 m reach · 0.5 m depth

storage budget1.06 m^3 ✓ 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.

estimate: estimate = length*width*depth [m^3]
lower: lower = estimate*(1-relativeBound)^3 [m^3]
upper: upper = estimate*(1+relativeBound)^3 [m^3]

Original worked example

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

Given

length: 2 m
width: 1 m
depth: 0.5 m
relative bound: 0.1

Calculated

estimate: 1 m^3
lower: 0.729 m^3
upper: 1.331 m^3

Assumptions and limits

Endpoint bounds on a positive rectangular volume estimate.

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: Order-of-magnitude estimate. Inputs: bounded quantities; arithmetic expression. Outputs: estimate; range; dominant factors. Model scope: Dimensional analysis and explicit reference conventions. 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: bounded quantities, arithmetic expression
Outputs: estimate, range, dominant factors
Modes: convert, solve-for
Drawing: Quantity diagram

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