Physics overview
How a pulley system works
A pulley changes the direction of a pulling force and can reduce the effort needed to lift a load.
In an ideal system, the mechanical advantage is determined by the number of rope segments directly supporting the moving load.
Load force
Calculate the weight of the load
Load forceW = mg
The load force is the weight of the object being lifted. It depends on mass and gravitational acceleration.
Mechanical advantage
Count the supporting rope segments
Ideal mechanical advantageIMA = n
Count only the rope segments that directly support the moving load. A single fixed pulley has an ideal mechanical advantage of 1.
Effort force
Calculate the ideal pulling force
Effort forceFe = W ÷ IMA
Increasing the number of supporting rope segments reduces the ideal effort force required to lift the load.
Distance trade-off
Calculate input rope distance
Input distancede = IMA × dl
The reduction in force comes with a distance trade-off. To lift the load a given distance, more rope must be pulled.
Worked example
Four-segment pulley system
Suppose a 20 kg load is lifted by an ideal pulley with four supporting rope segments using gravity 9.81 m/s².
- Load force: W = 20 × 9.81 = 196.2 N.
- Mechanical advantage: IMA = 4.
- Effort force: Fe = 196.2 ÷ 4 = 49.05 N.
- To lift the load 0.5 m, pull 4 × 0.5 = 2 m of rope.
Correct setup
How to count supporting segments
Identify the pulley or block that moves with the load, then count each tensioned rope segment pulling upward on that moving assembly.
Do not automatically count the total number of pulleys. Mechanical advantage depends on supporting rope segments, not pulley count alone.
Ideal versus real systems
Why real effort force is usually larger
- Axle and bearing friction reduce efficiency.
- Rope bending causes energy loss.
- Real pulleys and ropes have mass.
- Rope stretching can affect movement.
- Misalignment can increase resistance.
Related tools
Continue your mechanics calculations
Use the Weight Calculator to calculate the load force separately.
Use the Force Calculator for force, mass, and acceleration problems.
Use the Work Calculator to compare force and distance in a mechanical system.
Use the Inclined Plane Calculator for another simple-machine force model.
Questions and answers
Pulley calculator FAQ
What does the pulley calculator calculate?
It calculates load force, ideal mechanical advantage, effort force, and input rope distance for an ideal pulley system.
How do you calculate pulley mechanical advantage?
For an ideal pulley system, mechanical advantage equals the number of rope segments directly supporting the moving load.
How do you calculate effort force in a pulley?
Divide the load force by the ideal mechanical advantage using Fe = W ÷ IMA.
Why must more rope be pulled when mechanical advantage increases?
An ideal pulley reduces the required force by increasing the input distance. The rope distance equals mechanical advantage multiplied by load distance.
Does this calculator include pulley friction?
No. It assumes massless rope, massless pulleys, and no friction, so real systems may require more effort force.