CALCULATORS / PNEUMATICS, HYDRAULICS AND VACUUM

Cylinder extend and retract force calculator

Single-acting ideal cylinder, excluding seal friction

pneumatics-cylinder-force.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	areamm^2	forceN
	1256.64	628.319
	1963.5	981.748

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.

thrust required628.32 N✓ passes

BASELINE INPUTS

pressure500 kPa200800bore40 mm2080

CALCULATED

area1256.6 mm^2

force628.32 N

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Single-acting ideal cylinder, excluding seal friction
pressure = 500 kPa in 200..800
bore = 40 mm in 20..80
area := pi * bore^2 / 4 [mm^2]
force := pressure * area [N]
check thrust required: force >= 500 N
scenario larger bore: bore = 50 mm

Calculated from your source · not saved

Baseline · Baseline

thrust required628.32 N ✓ passes

larger bore · larger bore

thrust required981.75 N ✓ 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 = pi * bore^2 / 4 [mm^2]
force: force = pressure * area [N]

Original worked example

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

Given

pressure: 500 kPa
bore: 40 mm

Calculated

area: 1256.64 mm^2
force: 628.319 N

Assumptions and limits

Single-acting ideal cylinder, excluding seal friction

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: Cylinder extend and retract force. Inputs: bore; rod; chamber pressures; efficiency. Outputs: extend/retract force; pressure demand. Model scope: Pressure, flow and actuator geometry with compressibility 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: bore, rod, chamber pressures, efficiency
Outputs: extend/retract force, pressure demand
Modes: calculate, compare, sweep
Drawing: Actuator and circuit diagram

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