Pulley System Calculator
Calculate the effort force required to lift a load using fixed, movable, or compound pulley systems at a given mechanical efficiency. Ideal for rigging engineers, physics students, and maintenance teams planning lifts.
Last updated: September 2026
Formula below · 2 sources (asme.org, Wikipedia) · Updated Sep 2026
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About this calculator
A pulley system reduces the effort force needed to lift a load by distributing the weight over multiple rope segments. For a fixed pulley, it only redirects force, so effort F = W / η, where W is the load weight and η is efficiency. A single movable pulley doubles the mechanical advantage, giving F = W / (2η). A compound (block-and-tackle) system with n moving pulleys in the moving block has 2n rope segments supporting the load: F = W / (2n × η). Ideal mechanical advantage (IMA) equals 2n for a block and tackle (a cascade of separate single movable pulleys, each with its own rope, reaches 2ⁿ, but that arrangement is uncommon and this calculator uses the more conservative 2n), but real systems lose force to rope friction, sheave bearing friction, and rope stiffness, all captured in the efficiency factor η (expressed here as a percentage and divided by 100). Higher efficiency means more of the theoretical advantage is realised. Understanding these relationships helps select the right hoist for a job and calculate safe working loads.
How to use
You need to lift a 2000 N engine block using a block and tackle with 3 moving pulleys and 85% system efficiency. Step 1: Identify the formula — F = W / (2n × η) = 2000 / (6 × 0.85). Step 2: 2n = 6 supporting rope segments. Step 3: F = 2000 / 5.1 ≈ 392 N. So the operator needs to pull with approximately 392 N of force instead of 2000 N, an actual mechanical advantage of about 5.1:1 rather than the ideal 6:1 due to friction losses.
Frequently asked questions
What is the difference between a fixed pulley, a movable pulley, and a compound pulley system?
A fixed pulley is anchored to a support and only changes the direction of the applied force without providing any mechanical advantage — you still pull with a force equal to the load (minus efficiency losses). A movable pulley is attached to the load itself and travels with it, halving the required effort by spreading the load across two rope segments. A compound (block-and-tackle) system combines multiple fixed and movable pulleys, multiplying the mechanical advantage with each additional moving pulley, allowing very heavy loads to be lifted with relatively small forces.
How does pulley system efficiency affect the effort force required to lift a load?
In a frictionless ideal system, mechanical advantage equals the number of rope segments supporting the load. In reality, every sheave introduces friction and rope bending losses, reducing the usable advantage. A system rated at 80% efficiency means 20% of the input force is wasted overcoming friction. As efficiency drops, the required effort force rises proportionally — a low-efficiency system may even negate the benefit of having more pulleys. Regular lubrication of sheave bearings and using flexible, low-stretch rope keeps efficiency high.
How do I calculate the mechanical advantage of a block-and-tackle pulley system?
In a block and tackle, the ideal mechanical advantage (IMA) equals the number of rope segments supporting the moving block, which is 2n for n moving pulleys: 1 moving pulley gives 2, 2 give 4, 3 give 6. The actual mechanical advantage is IMA × efficiency, and the required effort is the load divided by it. (Only a cascade of separate movable pulleys, each on its own rope, gives 2ⁿ.) Adding pulleys increases the advantage but also the friction, so efficiency falls as sheaves are added.