Pulley ratio and belt speed calculator

No-slip belt drive, neglect belt stretch

belts-pulley-ratio.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	ratio	drivenSpeedrpm
	2	600
	3	400

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.

driven speed600.00 rpm✓ passes

BASELINE INPUTS

driverDiameter50 mm20100drivenDiameter100 mm40200driverSpeed1200 rpm2003000.0000000000005

CALCULATED

ratio2

drivenSpeed600 rpm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# No-slip belt drive, neglect belt stretch
driverDiameter = 50 mm in 20..100
drivenDiameter = 100 mm in 40..200
driverSpeed = 1200 rpm in 200..3000
ratio := drivenDiameter / driverDiameter
drivenSpeed := driverSpeed / ratio [rpm]
check driven speed: drivenSpeed <= 1000 rpm
scenario large pulley: drivenDiameter = 150 mm

Calculated from your source · not saved

Baseline · Baseline

driven speed600.00 rpm ✓ passes

large pulley · large pulley

driven speed400.00 rpm ✓ 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.

ratio: ratio = drivenDiameter / driverDiameter
driven speed: drivenSpeed = driverSpeed / ratio [rpm]

Original worked example

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

Given

driver diameter: 50 mm
driven diameter: 100 mm
driver speed: 1200 rpm

Calculated

ratio: 2
driven speed: 600 rpm

Assumptions and limits

No-slip belt drive, neglect belt stretch

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: Pulley ratio and belt speed. Inputs: pitch diameters; driver RPM. Outputs: speed ratio; belt speed. Model scope: No-slip kinematics with explicit tension and efficiency assumptions. 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: pitch diameters, driver RPM
Outputs: speed ratio, belt speed
Modes: calculate, compare, sweep
Drawing: Animated belt or chain

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