{
  "id": "pulley",
  "version": "73cb05dd83aa",
  "status": "published",
  "name": "Pulley Calculator",
  "question": "What does my pulley system give?",
  "summary": "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.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/pulley-calculator",
  "markdown": "https://www.acalculator.org/physics/pulley-calculator.md",
  "kind": "function",
  "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."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "kind": {
        "title": "Pulley system",
        "description": "A block and tackle that lifts a load, or a belt drive between two pulleys.",
        "type": "string",
        "enum": [
          "lift",
          "belt"
        ]
      },
      "w": {
        "title": "Load",
        "description": "The mass being lifted, including the moving pulley block.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "n": {
        "title": "Supporting rope segments",
        "description": "How many rope segments hold up the moving block (the ideal mechanical advantage).",
        "type": "integer",
        "minimum": 1,
        "maximum": 20
      },
      "h": {
        "title": "Lift height",
        "description": "How high the load is raised.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.0001,
        "maximum": 10000
      },
      "d1": {
        "title": "Driver pulley diameter",
        "description": "The diameter of the pulley on the motor.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.0001,
        "maximum": 10000
      },
      "n1": {
        "title": "Driver speed (rpm)",
        "description": "How fast the driver pulley turns, in revolutions per minute.",
        "type": "number",
        "minimum": 0.001,
        "maximum": 1000000
      },
      "d2": {
        "title": "Driven pulley diameter",
        "description": "The diameter of the pulley being turned.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.0001,
        "maximum": 10000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The pulling force for a block and tackle, or the driven pulley’s speed for a belt drive.",
      "format": "text"
    },
    "effortLbf": {
      "label": "Pulling force (lbf)",
      "description": "Block and tackle: the load’s weight ÷ the rope segments, in pounds-force.",
      "format": "number"
    },
    "effortN": {
      "label": "Pulling force (N)",
      "description": "The same force in newtons.",
      "format": "number"
    },
    "rope": {
      "label": "Rope to pull",
      "description": "Block and tackle: rope segments × lift height.",
      "format": "quantity",
      "unit": "ft"
    },
    "advantage": {
      "label": "Mechanical advantage",
      "description": "Block and tackle: the number of supporting rope segments.",
      "format": "number"
    },
    "rpm2": {
      "label": "Driven speed (rpm)",
      "description": "Belt drive: driver rpm × driver diameter ÷ driven diameter.",
      "format": "number"
    },
    "ratio": {
      "label": "Speed ratio",
      "description": "Belt drive: driven diameter ÷ driver diameter (how many driver turns per driven turn).",
      "format": "number"
    },
    "beltFpm": {
      "label": "Belt speed (ft/min)",
      "description": "Belt drive: π × driver diameter × driver rpm, in feet per minute.",
      "format": "number"
    },
    "beltMps": {
      "label": "Belt speed (m/s)",
      "description": "The same belt speed in meters per second.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "kind": "lift",
      "w": "200 lb",
      "n": 4,
      "h": "10 ft",
      "d1": "4 in",
      "n1": 1750,
      "d2": "8 in"
    },
    "outputs": {
      "result": "Pull 50 lbf (222.411 N)",
      "effortLbf": 50,
      "effortN": 222.411080763025,
      "rope": 12.192,
      "advantage": 4
    },
    "text": "Pull 50 lbf (222.411 N)."
  },
  "examples": [
    {
      "given": {
        "kind": "lift",
        "w": 90.718474,
        "n": 4,
        "h": 3.048
      },
      "expect": {
        "effortLbf": 50,
        "effortN": 222.41108076302498,
        "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; hand calculation in content.mdx: 200 lb ÷ 4 = 50 lbf; rope 4 × 10 ft = 40 ft"
    },
    {
      "given": {
        "kind": "lift",
        "w": 100,
        "n": 2,
        "h": 1
      },
      "expect": {
        "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; hand calculation in content.mdx: 100 × 9.80665 ÷ 2 = 490.3325 N"
    },
    {
      "given": {
        "kind": "belt",
        "d1": 0.1016,
        "n1": 1750,
        "d2": 0.2032
      },
      "expect": {
        "rpm2": 875,
        "ratio": 2,
        "beltFpm": 1832.5957145940458,
        "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; hand calculation in content.mdx: 1,750 × 4 ÷ 8 = 875 rpm; belt π × 4 in × 1,750 ÷ 12 = 1,832.60 ft/min"
    }
  ],
  "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)"
  ],
  "related": [
    "gear-ratio",
    "rpm",
    "torque"
  ],
  "changelog": []
}