Enrichment · STEM Explorations · Physics

Four strands of rope,
a quarter of the pull,
four times the haul.

Type the load and count the strands holding the moving block. The calculator gives the pull you need, the rope you will haul and the work it takes, ideal and with friction.

Work out the pullWhat you get

The pulley calculator

The worked example is made up: hoisting a 120 lb canoe 6 feet with a four-strand block and tackle. Nothing you type leaves this browser.

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What you get

Enrichment · STEM ExplorationsFree

What you finish with
Ideal and actual mechanical advantage, the pull needed, rope to haul, work in and out, and a comparison table for one to six strands. It prints as a summary and downloads as a spreadsheet.
Who it is for
Physics and physical science students, STEM and engineering clubs, and families rigging a hoist at home.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The STEM Explorations space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Choose pounds and feet or newtons and metres.
  2. Type the load.
  3. Count the strands that hold up the moving block.
  4. Set the efficiency and the lift height.
  5. Read the pull and compare strand counts in the table.

Work out the pull

How the advantage works

Force times distance stays the same.

The worked example: a canoe hoist4 strands share30 lb each120 ÷ 4, ideal÷ 85% efficiency35.3 lbyour pullLift 6 ft24 ft of rope4 × 6 ftWork in847 ft·lb720 out, the rest frictionThe worked example: a canoe hoist4 strands share30 lb each120 ÷ 4, ideal÷ 85% efficiency35.3 lbyour pullLift 6 ft24 ft of rope4 × 6 ftWork in847 ft·lb720 out, the rest friction
Pulleys never reduce the work; they spread the load over more rope. Four strands mean a quarter of the force over four times the distance, plus a little more for friction.

Counting strands

The ideal mechanical advantage of a pulley system equals the number of rope segments that hold up the moving load. A single fixed pulley has one: it only changes the direction of the pull. A single movable pulley has two. A block and tackle with two pulleys above and two below has four. Each strand carries an equal share of the load.

No free work

Work is force times distance. With four strands you pull a quarter as hard, but every foot the load rises takes four feet of rope, so the work is the same. Friction in the pulleys means the real advantage is lower: the efficiency figure accounts for it, and the extra work becomes heat.

Sources

  1. OpenStax. College Physics 2e (2022), section 9.5, Simple machines (openstax.org).
  2. OpenStax. Physics (high school, 2020), section 9.3, Simple machines: mechanical advantage and efficiency (openstax.org).
  3. Occupational Safety and Health Administration. Rigging equipment for material handling, 29 CFR 1926.251 (osha.gov).
  4. National Institute of Standards and Technology. Special Publication 811: the newton, the joule and the pound-force (nist.gov).

The worked example is made up. For real lifts, use rated gear and follow its instructions. Your figures stay in this browser. Support: team@caveatacademic.com.