{
  "id": "horsepower",
  "version": "8cecb033f294",
  "status": "published",
  "name": "Horsepower Calculator",
  "question": "How much hp from torque and rpm?",
  "summary": "Computes engine horsepower from torque and rpm with P = τ × ω, or the torque or rpm for a power, in horsepower, kilowatts, and metric horsepower.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/horsepower-calculator",
  "markdown": "https://www.acalculator.org/physics/horsepower-calculator.md",
  "kind": "formulas",
  "method": "P = τ × ω, with ω = 2π × rpm ÷ 60; in US units hp = torque (lb·ft) × rpm ÷ 5,252.11",
  "assumptions": [
    "This is the power at the shaft where the torque is measured: at the crankshaft it is brake horsepower; at the wheels it is lower, after drivetrain losses.",
    "1 hp = 550 ft·lbf/s = 745.69987 W; 1 PS (metric horsepower) = 75 kgf·m/s = 735.49875 W; 1 lb·ft = 1.3558179 N·m, from the exact definitions in NIST SP 811.",
    "5,252.11 is 33,000 ÷ 2π: 33,000 ft·lbf per minute is 1 hp, and one turn is 2π radians."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "tq": {
        "title": "Torque",
        "description": "The twisting force at the crankshaft or shaft, in the torque unit below.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "rpm": {
        "title": "Engine speed (rpm)",
        "description": "How fast the shaft turns, in revolutions per minute.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "p": {
        "title": "Power",
        "description": "The power the shaft delivers at that torque and speed.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "power",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "u": {
        "title": "Torque unit",
        "description": "Pound-feet (lb·ft), as US engine specs give it, or newton-meters (N·m).",
        "type": "string",
        "enum": [
          "lbft",
          "nm"
        ]
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "tq",
      "rpm",
      "p"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "torque": {
      "label": "Torque",
      "description": "The twisting force at the crankshaft or shaft, in the torque unit below.",
      "format": "number"
    },
    "rpm": {
      "label": "Engine speed (rpm)",
      "description": "How fast the shaft turns, in revolutions per minute.",
      "format": "number"
    },
    "power": {
      "label": "Power",
      "description": "The power at that torque and speed.",
      "format": "quantity"
    },
    "hp": {
      "label": "Horsepower (hp)",
      "description": "The power in mechanical horsepower (550 ft·lbf/s).",
      "format": "number"
    },
    "kw": {
      "label": "Kilowatts (kW)",
      "description": "The power in kilowatts.",
      "format": "number"
    },
    "ps": {
      "label": "Metric horsepower (PS)",
      "description": "The power in metric horsepower (75 kgf·m/s).",
      "format": "number"
    },
    "torqueLbft": {
      "label": "Torque (lb·ft)",
      "description": "The torque in pound-feet.",
      "format": "number"
    },
    "torqueNm": {
      "label": "Torque (N·m)",
      "description": "The torque in newton-meters.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "u": "lbft",
      "tq": 300,
      "rpm": 5000
    },
    "outputs": {
      "power": 212971.38530415564,
      "hp": 285.5993321445266,
      "kw": 212.97138530415563,
      "ps": 289.56049932668907,
      "torqueLbft": 300,
      "torqueNm": 406.7453844994201
    },
    "text": "300 lb·ft at 5,000 rpm is 285.599332 hp, or 212.971385 kW."
  },
  "examples": [
    {
      "given": {
        "tq": 300,
        "rpm": 5000,
        "u": "lbft"
      },
      "expect": {
        "hp": 285.5993321445266,
        "kw": 212.97138530415563,
        "torqueNm": 406.7453844994201
      },
      "source": "OpenStax University Physics Volume 1, §10.8, eq. 10.31: P = τω. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion; NIST SP 811 (2008) B.8: 1 hp = 550 ft·lbf/s; hand calculation in content.mdx"
    },
    {
      "given": {
        "tq": 100,
        "rpm": 5252.113122032546,
        "u": "lbft"
      },
      "expect": {
        "hp": 100
      },
      "source": "OpenStax University Physics Volume 1, §10.8, eq. 10.31: P = τω, with 33,000 ÷ 2π = 5,252.11 rpm. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion"
    },
    {
      "given": {
        "tq": 400,
        "rpm": 3000,
        "u": "nm"
      },
      "expect": {
        "kw": 125.66370614359172,
        "p": 125663.70614359173
      },
      "source": "OpenStax University Physics Volume 1, §10.8, eq. 10.31: 400 N·m × 100π rad/s = 40,000π W. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion; hand calculation in content.mdx"
    },
    {
      "given": {
        "p": 223709.96147468107,
        "rpm": 6000,
        "u": "lbft"
      },
      "expect": {
        "tq": 262.6056561016273
      },
      "source": "OpenStax University Physics Volume 1, §10.8, eq. 10.31, solved for τ = P ÷ ω. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion; hand calculation in content.mdx"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §10.8 Work and Power for Rotational Motion, equation 10.31: P = τω (CC BY 4.0), retrieved 2026-10-01. https://openstax.org/books/university-physics-volume-1/pages/10-8-work-and-power-for-rotational-motion",
    "NIST SP 811 (2008), Guide for the Use of the International System of Units, Appendix B.8 (horsepower, 550 ft·lbf/s; foot, pound-force), retrieved 2026-10-01. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "power",
    "gear-ratio",
    "compression-ratio"
  ],
  "changelog": []
}