# What does my pulley system give?

Works out a block and tackle’s pulling force and rope length from the load and the number of supporting rope segments, or a belt drive’s output rpm, speed ratio and belt speed from the pulley diameters.

- Page: https://www.acalculator.org/physics/pulley-calculator
- JSON spec: https://www.acalculator.org/physics/pulley-calculator.json
- Version: 73cb05dd83aa

## Default answer

Example with the default inputs (Pulley system Block and tackle, Load 200 lb, Supporting rope segments 4, Lift height 10 ft): Pull 50 lbf (222.411 N).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| kind | Pulley system | A block and tackle that lifts a load, or a belt drive between two pulleys. |
| w | Load | The mass being lifted, including the moving pulley block. |
| n | Supporting rope segments | How many rope segments hold up the moving block (the ideal mechanical advantage). |
| h | Lift height | How high the load is raised. |
| d1 | Driver pulley diameter | The diameter of the pulley on the motor. |
| n1 | Driver speed (rpm) | How fast the driver pulley turns, in revolutions per minute. |
| d2 | Driven pulley diameter | The diameter of the pulley being turned. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The pulling force for a block and tackle, or the driven pulley’s speed for a belt drive. |
| effortLbf | Pulling force (lbf) | Block and tackle: the load’s weight ÷ the rope segments, in pounds-force. |
| effortN | Pulling force (N) | The same force in newtons. |
| rope | Rope to pull | Block and tackle: rope segments × lift height. |
| advantage | Mechanical advantage | Block and tackle: the number of supporting rope segments. |
| rpm2 | Driven speed (rpm) | Belt drive: driver rpm × driver diameter ÷ driven diameter. |
| ratio | Speed ratio | Belt drive: driven diameter ÷ driver diameter (how many driver turns per driven turn). |
| beltFpm | Belt speed (ft/min) | Belt drive: π × driver diameter × driver rpm, in feet per minute. |
| beltMps | Belt speed (m/s) | The same belt speed in meters per second. |

## Method

Block and tackle: effort = m g ÷ n, rope = n × h. Belt drive: N₂ = N₁ × D₁ ÷ D₂; belt speed = π D₁ N₁.

## Assumptions

- Block and tackle: ideal pulleys and rope, no friction and no rope weight; real systems need 5% to 10% more force per sheave.
- Belt drive: the belt does not slip or stretch, and the diameters are pitch diameters (where the belt rides).
- Exact unit sizes: 1 lb = 0.45359237 kg; g = 9.80665 m/s²; 1 lbf = 4.4482216152605 N; 1 in = 0.0254 m; 1 ft = 0.3048 m.

## Worked examples

1. kind = lift, w = 90.718474, n = 4, h = 3.048 gives effortLbf = 50, effortN = 222.411081, rope = 12.192, result = Pull 50 lbf (222.411 N). Source: OpenStax, College Physics 2e, §9.5 Simple Machines (a pulley system’s mechanical advantage is the number of ropes that support the load), https://openstax.org/books/college-physics-2e/pages/9-5-simple-machines.
2. kind = lift, w = 100, n = 2, h = 1 gives effortN = 490.3325, rope = 2, advantage = 2. Source: OpenStax, College Physics 2e, §9.5 Simple Machines (a pulley system’s mechanical advantage is the number of ropes that support the load), https://openstax.org/books/college-physics-2e/pages/9-5-simple-machines.
3. kind = belt, d1 = 0.1016, n1 = 1,750, d2 = 0.2032 gives rpm2 = 875, ratio = 2, beltFpm = 1,832.595715, result = Driven pulley: 875 rpm. Source: OpenStax, University Physics Volume 1, §10.1 Rotational Variables (v_t = r ω), https://openstax.org/books/university-physics-volume-1/pages/10-1-rotational-variables.

## FAQ

### How do I calculate the force needed with a pulley system?

Divide the load’s weight by the number of rope segments that hold up the moving block. A 200 lb load on 4 segments needs a pull of 200 ÷ 4 = 50 lbf, with ideal pulleys.

### What is the mechanical advantage of a pulley?

For an ideal pulley system it is the number of rope segments that support the load. A single fixed pulley has a mechanical advantage of 1 (it only changes the direction of the pull); a single movable pulley has 2.

### How much rope do I have to pull?

The rope segments × the lift height. To raise a load 10 ft on 4 segments you pull 40 ft of rope. The work (force × distance) stays the same: 50 lbf × 40 ft = 200 lb × 10 ft.

### How do I calculate pulley rpm?

With a belt between them, driver diameter × driver rpm = driven diameter × driven rpm. A 4 in pulley on a 1,750 rpm motor turns an 8 in pulley at 1,750 × 4 ÷ 8 = 875 rpm.

### What is the belt speed?

The belt moves at the rim speed of each pulley: π × diameter × rpm. A 4 in pulley at 1,750 rpm drives the belt at π × 4 × 1,750 ÷ 12 = 1,833 ft/min.

### Why does a real pulley need more force?

Friction in each sheave and the stiffness and weight of the rope add to the pull, often 5% to 10% per sheave. The page gives the ideal force; plan for more.

## Sources

- OpenStax, College Physics 2e, §9.5 Simple Machines (pulleys; the mechanical advantage of a pulley system is the number of ropes that support the load). https://openstax.org/books/college-physics-2e/pages/9-5-simple-machines (retrieved 2026-10-03)
- OpenStax, University Physics Volume 1, §10.1 Rotational Variables (tangential speed v_t = r ω). https://openstax.org/books/university-physics-volume-1/pages/10-1-rotational-variables (retrieved 2026-10-03)
- NIST SP 811, Appendix B.8 (1 lb = 0.45359237 kg; standard gravity 9.80665 m/s²; 1 lbf = 4.4482216152605 N; 1 in = 0.0254 m). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-03)