{
  "id": "torque",
  "version": "48ea3703dff7",
  "status": "published",
  "name": "Torque Calculator",
  "question": "What is the torque from this force?",
  "summary": "Computes torque from a force, the lever arm and the angle between them (τ = rF sin θ), or the force or lever arm for a torque, in N·m, lb·ft and lb·in.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/torque-calculator",
  "markdown": "https://www.acalculator.org/physics/torque-calculator.md",
  "kind": "function",
  "method": "τ = r × F × sin θ; F = τ ÷ (r sin θ); r = τ ÷ (F sin θ).",
  "assumptions": [
    "θ is the angle between the lever arm (from the axis to where the force acts) and the force, from 0° to 180°.",
    "The answer is the size of the torque; its direction (clockwise or counterclockwise) is not shown.",
    "1 lb·ft = 1 lbf × 1 ft = 0.3048 × 4.4482216152605 N·m (NIST SP 811)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Which value to work out from the other two.",
        "type": "string",
        "enum": [
          "torque",
          "force",
          "arm"
        ]
      },
      "f": {
        "title": "Force (F)",
        "description": "The push or pull on the lever, such as your hand on a wrench.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "r": {
        "title": "Lever arm (r)",
        "description": "The distance from the axis of turning (the bolt) to where the force pushes.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "t": {
        "title": "Torque (τ)",
        "description": "The torque you need, in the torque unit below.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "u": {
        "title": "Torque unit",
        "description": "Newton-metres, pound-feet or pound-inches.",
        "type": "string",
        "enum": [
          "lbft",
          "nm",
          "lbin"
        ]
      },
      "a": {
        "title": "Angle (θ, degrees)",
        "description": "The angle between the lever arm and the force, in degrees; 90 when you push straight across.",
        "type": "number",
        "minimum": 0,
        "maximum": 180
      }
    }
  },
  "outputs": {
    "answer": {
      "label": "Answer",
      "description": "The value you asked for, in the unit named in the answer.",
      "format": "number"
    },
    "shownUnit": {
      "label": "Answer unit",
      "description": "The unit of the answer.",
      "format": "text"
    },
    "what": {
      "label": "Answer is",
      "description": "What the answer measures: torque, force or lever arm.",
      "format": "text"
    },
    "nm": {
      "label": "Torque (N·m)",
      "description": "The torque in newton-metres.",
      "format": "number"
    },
    "lbft": {
      "label": "Torque (lb·ft)",
      "description": "The torque in pound-feet.",
      "format": "number"
    },
    "lbin": {
      "label": "Torque (lb·in)",
      "description": "The torque in pound-inches.",
      "format": "number"
    },
    "newtons": {
      "label": "Force (N)",
      "description": "The force in newtons.",
      "format": "number"
    },
    "pounds": {
      "label": "Force (lbf)",
      "description": "The force in pounds-force.",
      "format": "number"
    },
    "meters": {
      "label": "Lever arm (m)",
      "description": "The lever arm in metres.",
      "format": "number"
    },
    "feet": {
      "label": "Lever arm (ft)",
      "description": "The lever arm in feet.",
      "format": "number"
    },
    "perpendicular": {
      "label": "Perpendicular lever arm r⊥ (m)",
      "description": "r sin θ: the part of the lever arm square to the force, in metres.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "torque",
      "f": 222.41108076302498,
      "r": 0.30479999999999996,
      "t": 80,
      "u": "lbft",
      "a": 90
    },
    "outputs": {
      "answer": 50,
      "shownUnit": "lb·ft",
      "what": "torque",
      "nm": 67.79089741657002,
      "lbft": 50,
      "lbin": 600,
      "newtons": 222.411080763025,
      "pounds": 50,
      "meters": 0.3048,
      "feet": 1,
      "perpendicular": 0.3048
    },
    "text": "The torque is 50 lb·ft."
  },
  "examples": [
    {
      "given": {
        "find": "torque",
        "f": 40,
        "r": 4,
        "a": 90,
        "u": "nm"
      },
      "expect": {
        "answer": 160,
        "nm": 160
      },
      "source": "OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque, Example 10.14 (40 N at 4 m and 90° gives 160 N·m)"
    },
    {
      "given": {
        "find": "torque",
        "f": 20,
        "r": 0.5,
        "a": 150,
        "u": "nm"
      },
      "expect": {
        "answer": 5,
        "perpendicular": 0.25
      },
      "source": "OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque, Example 10.15 (20 N at r = 0.5 m and 150° gives 5.0 N·m)"
    },
    {
      "given": {
        "find": "torque",
        "f": 44.482216152605,
        "r": 0.6096,
        "a": 90,
        "u": "lbft"
      },
      "expect": {
        "answer": 20,
        "lbft": 20,
        "lbin": 240,
        "nm": 27.11635896662801
      },
      "source": "NIST SP 811 (2008), Appendix B.8 (1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8; hand calculation in content.mdx: 10 × 2 = 20 lb·ft = 240 lb·in = 27.12 N·m"
    },
    {
      "given": {
        "find": "force",
        "t": 80,
        "r": 0.4572,
        "a": 90,
        "u": "lbft"
      },
      "expect": {
        "answer": 53.333333333333336,
        "pounds": 53.333333333333336
      },
      "source": "OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque; hand calculation in content.mdx: F = τ ÷ (r sin θ) = 80 ÷ 1.5 = 53.33 lbf"
    },
    {
      "given": {
        "find": "arm",
        "t": 120,
        "f": 400,
        "a": 30,
        "u": "nm"
      },
      "expect": {
        "answer": 0.6,
        "meters": 0.6
      },
      "source": "OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque; hand calculation in content.mdx: r = τ ÷ (F sin θ) = 120 ÷ (400 × 0.5) = 0.6 m"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §10.6 Torque (|τ| = r⊥F = rF sin θ; Examples 10.14 and 10.15). https://openstax.org/books/university-physics-volume-1/pages/10-6-torque (retrieved 2026-10-02)",
    "NIST SP 811 (2008), Appendix B.8, Factors for Units Listed Alphabetically (1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m; 1 in = 0.0254 m; 1 kgf = 9.80665 N). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-02)"
  ],
  "related": [
    "horsepower",
    "gear-ratio",
    "kinetic-energy"
  ],
  "changelog": []
}