Pulley Calculator

Find the effort force, mechanical advantage, and rope distance needed to lift a load with a pulley system, from the load's mass, the number of supporting rope segments, the lift height, and the system's efficiency.

Quick Facts

Mechanical advantage
MA = N
N is the number of rope segments supporting the moving load in an ideal, frictionless pulley system.
Effort force
F = W / (N x efficiency)
Divide the load's weight by the mechanical advantage and system efficiency to find the required pulling force.
Rope distance
d = h x N
You must pull N times more rope than the load's travel height — the tradeoff for reduced effort force.
Typical efficiency
80% – 95%
Real pulleys lose 5-15% of input work per sheave to axle friction and rope bending; ball-bearing sheaves perform best.

Your Results

Calculated
Effort Force Required
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F = W / (N × efficiency)
Mechanical Advantage
-
Ideal MA = number of supporting rope segments
Rope Pulled Distance
-
Distance of rope you must pull through the system
Work Input Required
-
Energy you must supply, including friction losses

Ready

Enter the load, pulley setup, and lift height, then press Calculate.

How the Pulley Calculator Works

A pulley is a wheel that redirects the tension in a rope, letting you trade pulling force for pulling distance. This calculator uses the load's mass, the number of rope segments that support the moving load (N), the height you need to lift the load, and the system's mechanical efficiency to find the effort force required, the mechanical advantage, how much rope you must pull, and the total work (energy) you must put in.

Deriving the effort force

For an ideal, frictionless pulley the same rope tension runs through every strand supporting the load, so the load's weight W is shared across N segments: the effort force is F = W / N. Real systems lose some input work to axle friction and rope bending, captured by an efficiency η (a decimal between 0 and 1, or a percentage). Because the pulling force must supply the lost work as well as the useful work, the formula becomes F = W / (N × η). A lower efficiency always means a larger effort force for the same load and the same number of supporting ropes.

Ideal mechanical advantage vs. real pulleys

The ideal mechanical advantage of a pulley system, MA = N, depends only on how many rope segments hold up the moving load — it has nothing to do with how many wheels are visible, only how many strands of rope bear the weight. Conservation of energy ties force and distance together: since work in must equal work out (plus losses), pulling the rope a distance d = h × N while the load rises only h keeps the energy balance closed. That is why a system that quarters your effort force also requires four times as much rope pulled through your hands.

Common pulley configurations

  • Single fixed pulley (N = 1): anchored in place; it only changes the direction you pull in, so MA = 1 and effort force equals the load's weight.
  • Single movable pulley (N = 2): the pulley travels with the load and two rope segments support it, halving the ideal effort force.
  • Block and tackle (N = 3, 4, 5…): combining fixed and movable sheaves and running the rope back and forth multiplies N, and therefore the mechanical advantage, further.

Frequently Asked Questions

What is the mechanical advantage of a pulley system?
In an ideal, frictionless pulley system, mechanical advantage equals the number of rope segments (strands) supporting the moving load: MA = N. A single fixed pulley has MA = 1 (it only changes the direction of the force), a single movable pulley supported by two rope segments has MA = 2, and larger block-and-tackle systems increase N further by adding more sheaves and rope wraps.
How do I calculate the effort force needed to lift a load with a pulley?
Divide the load's weight by the mechanical advantage and the system's efficiency: F = W / (N × efficiency). For example, a 490 N load lifted with 4 supporting rope segments at 85% efficiency requires about 490 / (4 × 0.85), or roughly 144 N of pulling force.
Why do I have to pull more rope than the load moves?
Pulleys trade force for distance. Because one continuous rope threads through every supporting segment, pulling 1 meter of rope only raises the load 1/N meters when N segments support it, so lifting a load a height h requires pulling N × h of rope. This follows from conservation of energy: cutting the force by a factor of N means the effort must move N times farther.
What efficiency should I assume for a real pulley system?
Well-maintained ball-bearing pulleys are typically 95-98% efficient per sheave, while simple bushed or plain-bearing pulleys and older rope-and-wood blocks often run 80-90% or lower. Multiply the efficiency of each sheave together for a compound system, or use a single estimated system efficiency (commonly 80-95%) if you do not have per-pulley data.

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