Last updated: 2026-07-13

Definition

A block and tackle is an arrangement of pulleys threaded by a single rope between a fixed block and a moving block. By spreading the load across several rope segments, it lets a small pull raise a heavy weight. The mechanical advantage measures how much the system multiplies the input force. For an ideal, frictionless tackle it equals the number of rope segments that support the moving block.

The formula

Each rope segment running to the moving block carries an equal share of the load, so with n supporting segments the ideal mechanical advantage is

The effort you must apply to the free end follows from dividing the load by that advantage and by the efficiency η of the real system:

where F_L is the load and F_E is the effort force. At the same time the rope pays for the reduced force with extra distance: to raise the load by one unit you must pull n units of rope through the system, so the velocity ratio equals the ideal mechanical advantage.

Worked example

A block and tackle with 4 supporting rope segments lifts a 1000 N load. Assume an ideal, frictionless system (η = 100%).

Ideal mechanical advantage: MA = 4

Required effort force: 1000 ÷ (4 × 1.00) = 250 N

Rope pulled per unit lift: 4 — you haul 4 m of rope for every 1 m the load rises.

The tackle cuts the effort to a quarter of the load. If friction drops the efficiency to a more realistic 80%, the effort climbs to 1000 ÷ (4 × 0.80) = 312.5 N, while the ideal advantage and the rope you pull stay the same.

Counting the supporting rope segments

The only quantity that sets the ideal advantage is n, the number of rope segments pulling up on the moving block. Count every strand between the sheaves that runs to the moving block; a segment that leaves the fixed block only changes direction and does not add to the count.

A single fixed pulley gives no force advantage at all — it simply lets you pull down instead of up. Every extra sheave you add to the moving block adds one more supporting segment, and one more unit of ideal advantage.

The distance trade-off

A pulley cannot create energy; it only trades force for distance. Ignoring friction, the work you put in equals the work delivered to the load:

Because the effort is n times smaller than the load, the rope you pull must be n times longer than the load's rise. That is why a high-advantage tackle feels light but takes many long, slow pulls to move the load a short way.

Ideal versus actual mechanical advantage

The value MA = n is the ideal mechanical advantage: it depends only on how the rope is threaded and ignores friction. The actual mechanical advantage is the real load divided by the real effort you must supply, and it always comes out lower because friction at the sheaves and the stiffness of the rope absorb part of the input. The two are linked by the efficiency, AMA = n × η. This calculator reports the ideal advantage and folds the efficiency into the required effort, so the effort figure already reflects the real, slightly larger pull.

Notes

The load and effort come out in the same unit, and the number of supporting segments and the efficiency are both dimensionless, so no unit conversion is needed between them. There must be at least one supporting segment, and the efficiency must be greater than 0% and no more than 100%.