{
  "id": "power-to-weight-ratio",
  "version": "b9aec05fdd40",
  "status": "published",
  "name": "Power to Weight Ratio Calculator",
  "question": "What is the power to weight ratio?",
  "summary": "Finds the power-to-weight ratio of a car, motorcycle, bike or rider from power and weight, in W/kg, hp per lb, hp per ton and lb per hp, or the power or weight from the ratio.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/power-to-weight-ratio-calculator",
  "markdown": "https://www.acalculator.org/physics/power-to-weight-ratio-calculator.md",
  "kind": "formulas",
  "method": "ratio = power ÷ mass in W/kg; power = ratio × mass; mass = power ÷ ratio. 1 hp = 550 ft·lbf/s = 745.69987 W, 1 lb = 0.45359237 kg, 1 short ton = 2,000 lb.",
  "assumptions": [
    "Weight means mass: the ratio divides power by mass, as is usual for cars, bikes and cyclists.",
    "Horsepower (hp) is mechanical horsepower, 550 ft·lbf/s; metric horsepower (PS) is 75 kgf·m/s = 735.49875 W.",
    "Values run in watts and kilograms, in double precision."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "p": {
        "title": "Power",
        "description": "The engine, motor or rider power output.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "power",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "w": {
        "title": "Weight",
        "description": "The weight (mass) of the vehicle or person, with the driver or rider if you want them counted.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "r": {
        "title": "Power to weight ratio (W/kg)",
        "description": "Power divided by mass, in watts per kilogram.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "p",
      "w",
      "r"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "power": {
      "label": "Power",
      "description": "The engine, motor or rider power output.",
      "format": "quantity"
    },
    "mass": {
      "label": "Weight",
      "description": "The weight (mass) of the vehicle or person, with the driver or rider if you want them counted.",
      "format": "quantity"
    },
    "ratio": {
      "label": "Power to weight ratio (W/kg)",
      "description": "Watts per kilogram.",
      "format": "number"
    },
    "hpPerTon": {
      "label": "hp per ton",
      "description": "Horsepower per US short ton (2,000 lb).",
      "format": "number"
    },
    "hpPerLb": {
      "label": "hp per lb",
      "description": "Horsepower per pound.",
      "format": "number"
    },
    "lbPerHp": {
      "label": "Weight to power (lb per hp)",
      "description": "Pounds per horsepower, the inverse ratio; lower is quicker.",
      "format": "number"
    },
    "kgPerKw": {
      "label": "Weight to power (kg per kW)",
      "description": "Kilograms per kilowatt, the inverse ratio in metric units.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "p": "300 hp",
      "w": "3500 lb"
    },
    "outputs": {
      "ratio": 140.9131548,
      "hpPerTon": 171.4285714285714,
      "hpPerLb": 0.0857142857142857,
      "lbPerHp": 11.666666666666668,
      "kgPerKw": 7.096569524820546
    },
    "text": "The power to weight ratio is 140.91 W/kg, or 11.667 lb per hp."
  },
  "examples": [
    {
      "given": {
        "p": 100000,
        "w": 1000
      },
      "expect": {
        "r": 100,
        "kgPerKw": 10,
        "hpPerLb": 0.0608277387841761,
        "lbPerHp": 16.439868060000002
      },
      "source": "hand calculation in content.mdx: 100,000 W ÷ 1,000 kg = 100 W/kg; OpenStax, University Physics Volume 1, §7.4 Power (power is the rate of doing work, in watts), https://openstax.org/books/university-physics-volume-1/pages/7-4-power (retrieved 2026-10-02); NIST Special Publication 811, Appendix B (1 hp = 550 ft·lbf/s = 745.699 872 W; 1 lb = 0.453 592 37 kg), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02); Python 3: 100*0.45359237/(550*0.3048*9.80665*0.45359237)"
    },
    {
      "given": {
        "p": 223709.9614746811,
        "w": 1587.5732950000001
      },
      "expect": {
        "lbPerHp": 11.666666666666668,
        "hpPerTon": 171.42857142857142,
        "r": 140.9131548
      },
      "source": "hand calculation in content.mdx: 3,500 ÷ 300 = 11.67 lb/hp; 300 ÷ 1.75 tons = 171.4 hp per ton; NIST Special Publication 811, Appendix B (1 hp = 550 ft·lbf/s = 745.699 872 W; 1 lb = 0.453 592 37 kg), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)"
    },
    {
      "given": {
        "r": 4,
        "w": 70
      },
      "expect": {
        "p": 280
      },
      "source": "hand calculation in content.mdx: power = 4 W/kg × 70 kg = 280 W; OpenStax, University Physics Volume 1, §7.4 Power (power is the rate of doing work, in watts), https://openstax.org/books/university-physics-volume-1/pages/7-4-power (retrieved 2026-10-02)"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §7.4 Power (power is the rate of doing work, P = dW/dt, in watts; 1 hp = 746 W). https://openstax.org/books/university-physics-volume-1/pages/7-4-power (retrieved 2026-10-02)",
    "NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B (horsepower, 550 ft·lbf/s = 745.699 872 W; 1 lb = 0.453 592 37 kg). https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-02)"
  ],
  "related": [
    "horsepower",
    "power",
    "kinetic-energy",
    "acceleration"
  ],
  "changelog": []
}