acalculator

What does my pulley system give?

Pick a block and tackle to get the force needed to lift a load and how much rope you pull, or a belt drive to get the driven pulley’s rpm, the speed ratio and the belt speed. The pulley calculator assumes ideal, frictionless pulleys.

Your numbers

Units
Pulley system
Answer
Pull 50 lbf (222.411 N)

Pull 50 lbf (222.411 N).

Pulling force (lbf)
50
Pulling force (N)
222.411
Rope to pull
40 ft
Mechanical advantage
4

Answer: Pull 50 lbf (222.411 N). Pull 50 lbf (222.411 N).

How to calculate

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.

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).

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

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Pulley system Block and tackle, Load 200 lb, Supporting rope segments 4, Lift height 10 ft gives Pulling force (lbf) 50, Pulling force (N) 222.411081, Rope to pull 40 ft, Answer 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. Pulley system Block and tackle, Load 220.5 lb, Supporting rope segments 2, Lift height 3.281 ft gives Pulling force (N) 490.3325, Rope to pull 6.56168 ft, Mechanical 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. Pulley system Belt drive, Driver pulley diameter 4 in, Driver speed (rpm) 1,750, Driven pulley diameter 8 in gives Driven speed (rpm) 875, Speed ratio 2, Belt speed (ft/min) 1,832.595715, Answer 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

How it works

Block and tackle. A load of mass m hangs from a moving block held up by n rope segments. With ideal pulleys, each segment carries the same tension, so:

  • Pulling force: F = m × g ÷ n, with g = 9.80665 m/s². In pounds-force, F = load in lb ÷ n.
  • Rope to pull: n × lift height.
  • Mechanical advantage: n.

Belt drive. A belt runs around a driver pulley (diameter D₁, speed N₁ rpm) and a driven pulley (diameter D₂). The belt moves both rims at the same speed, so D₁ × N₁ = D₂ × N₂:

  • Driven speed: N₂ = N₁ × D₁ ÷ D₂ rpm.
  • Speed ratio: D₂ ÷ D₁.
  • Belt speed: π × D₁ × N₁ per minute, in ft/min (÷ 0.3048) and m/s (÷ 60).

Units: 1 lb = 0.45359237 kg; 1 t = 1,000 kg; 1 short ton = 907.18474 kg; 1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m; 1 in = 0.0254 m; 1 cm = 0.01 m; 1 mm = 0.001 m.

Exact arithmetic. Each value is read as the exact decimal you typed, in its unit, and every unit size is exact, so the force, the rope length, the rpm and the ratio are exact fractions until they are rounded for display. The belt speed uses π, a 64-bit float.

Output format. The answer line shows 6 significant figures with no thousands separators: Pull 50 lbf (222.411 N) or Driven pulley: 875 rpm. Every value row shows 6 significant figures; the rope length shows in feet (meters in Metric).

Assumptions

  • Ideal pulleys and rope: no friction, no rope weight, no belt slip or stretch; diameters are where the belt rides.
  • Load more than 0 and at most 10⁹ kg; 1 to 20 rope segments; lift height and diameters 0.0001 to 10,000 m; driver speed 0.001 to 1,000,000 rpm.

Worked examples by hand

200 lb on 4 rope segments, lifted 10 ft. F = 200 ÷ 4 = 50 lbf = 200 × 0.45359237 × 9.80665 ÷ 4 = 222.411 N. Rope: 4 × 10 ft = 40 ft (12.192 m).

100 kg on one movable pulley (2 segments), lifted 1 m. F = 100 × 9.80665 ÷ 2 = 490.3325 N; rope 2 × 1 = 2 m.

A 4 in pulley at 1,750 rpm driving an 8 in pulley. N₂ = 1,750 × 4 ÷ 8 = 875 rpm; ratio 8 ÷ 4 = 2; belt speed π × 4 × 1,750 ÷ 12 = 1,832.60 ft/min.

Other questions people ask

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.