Pulley and Block and Tackle Calculator

Work out how much pull a pulley arrangement needs to lift a load, and how much rope you have to haul in.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

A fixed pulley only changes the direction of the pull. A movable pulley shares the load between two rope strands, so the pull is halved. In a block and tackle the pull is the load divided by the number of rope strands holding the moving block.

Enter the mass, count the rope strands holding the moving block, and set an efficiency for friction. The calculator gives the weight, the mechanical advantage, the pull with and without friction, the rope you must haul in, and the load on the overhead beam or anchor.

Formulas used

  • T = \dfrac{W}{n\,\eta}
  • L_{rope} = n\,h
  • W_{in} = W_{out}/\eta

Worked example

With the default numbers in the calculator above:

  1. Weight of the load: 2354.4 N
  2. Mechanical advantage (ideal): 4
  3. Pull needed with no friction: 588.6 N (60 kg-force)
  4. Pull needed at this efficiency: 654 N (66.667 kg-force)
  5. Rope you must haul in to lift the load 2 m: 8 m
  6. Work put in compared with work done: 5232 J in, 4708.8 J out
  7. Total load on the overhead beam (vertical pull, rope off a fixed pulley): 3008.4 N

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Which pulley system needs the least pull?

The one with the most strands holding the moving load. A single fixed pulley needs the full weight, one movable pulley half, and a block with four strands a quarter.

Do I count the rope I pull on?

Only if it is attached to the moving block. A rope that leaves a fixed pulley to your hand is not holding the load.

Does a pulley save work?

No. You trade force for distance: the rope you haul grows by the same factor the pull falls. Friction makes the work slightly more.

Can a vehicle pull this?

The vehicle needs to pull with the force shown, using tyre grip or its own weight. Check the anchor, the rope and the beam as well.

Related calculators

Further reading: Standard mechanics texts (simple machines and mechanical advantage). Lifting gear must be selected and used under the lifting rules for your site.

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