{
  "id": "power",
  "version": "1b3ddbc70ba2",
  "status": "published",
  "name": "Power Calculator",
  "question": "How do I calculate power?",
  "summary": "Computes power from energy and time, voltage and current, current and resistance, voltage and resistance, or force and speed, or converts a power, in watts, kilowatts, horsepower, metric horsepower and BTU per hour.",
  "category": "physics",
  "subcategory": "energy",
  "url": "https://www.acalculator.org/physics/power-calculator",
  "markdown": "https://www.acalculator.org/physics/power-calculator.md",
  "kind": "function",
  "method": "P = E ÷ t; P = V × I; P = I² × R; P = V² ÷ R; P = F × v. 1 hp = 550 ft·lbf/s; 1 PS = 75 kgf·m/s; 1 BTU/h = 1055.05585262 J ÷ 3,600 s.",
  "assumptions": [
    "Power is the average over the time: the energy or work divided by the time.",
    "The electrical modes are for DC or for AC in phase (a resistor): V and I are steady or RMS values.",
    "Force and speed point the same way."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "mode": {
        "title": "I know",
        "description": "The two values you know, or a power to convert.",
        "type": "string",
        "enum": [
          "energy",
          "vi",
          "ir",
          "vr",
          "fv",
          "convert"
        ]
      },
      "e": {
        "title": "Energy or work",
        "description": "The energy used or the work done.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "energy",
        "minimum": 1e-9,
        "maximum": 1000000000000
      },
      "t": {
        "title": "Time",
        "description": "The time the energy is used or the work is done over.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "time",
        "minimum": 1e-9,
        "maximum": 1000000000000
      },
      "v": {
        "title": "Voltage",
        "description": "The voltage across the load.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "voltage",
        "minimum": 1e-9,
        "maximum": 1000000000000
      },
      "i": {
        "title": "Current",
        "description": "The current through the load.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "current",
        "minimum": 1e-9,
        "maximum": 1000000000000
      },
      "r": {
        "title": "Resistance",
        "description": "The resistance of the load.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "resistance",
        "minimum": 1e-9,
        "maximum": 1000000000000
      },
      "f": {
        "title": "Force",
        "description": "The force pushing or pulling along the motion.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "minimum": 1e-9,
        "maximum": 1000000000000
      },
      "s": {
        "title": "Speed",
        "description": "The speed along the force.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 1e-9,
        "maximum": 1000000000000
      },
      "p": {
        "title": "Power",
        "description": "A power in any unit, to convert.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "power",
        "minimum": 1e-9,
        "maximum": 1000000000000
      }
    }
  },
  "outputs": {
    "watts": {
      "label": "Watts (W)",
      "description": "The power in watts: joules per second.",
      "format": "number"
    },
    "kilowatts": {
      "label": "Kilowatts (kW)",
      "description": "The power in kilowatts (1,000 W).",
      "format": "number"
    },
    "horsepower": {
      "label": "Horsepower (hp)",
      "description": "The power in mechanical horsepower: 550 ft·lbf/s = 745.69987158227022 W.",
      "format": "number"
    },
    "metricHorsepower": {
      "label": "Metric horsepower (PS)",
      "description": "The power in metric horsepower: 75 kgf·m/s = 735.49875 W.",
      "format": "number"
    },
    "btuPerHour": {
      "label": "BTU per hour",
      "description": "The power in International Table BTU per hour: 1 BTU/h = 0.29307107017222 W.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "mode": "energy",
      "e": 1500,
      "t": 30,
      "v": 120,
      "i": 10,
      "r": 12,
      "f": 500,
      "s": 2,
      "p": 745.6998715822702
    },
    "outputs": {
      "watts": 50,
      "kilowatts": 0.05,
      "horsepower": 0.06705110447975139,
      "metricHorsepower": 0.06798108086519522,
      "btuPerHour": 170.6070816563971
    },
    "text": "The power is 50 W, which is 0.067051 hp."
  },
  "examples": [
    {
      "given": {
        "mode": "energy",
        "e": 1500,
        "t": 30
      },
      "expect": {
        "watts": 50,
        "kilowatts": 0.05,
        "horsepower": 0.06705110447975139,
        "metricHorsepower": 0.06798108086519522,
        "btuPerHour": 170.6070816563971
      },
      "source": "NIST SP 811 (2008), B.8: 1 hp = 550 ft·lbf/s = 745.699872 W, 1 PS = 735.49875 W, 1 BTU(IT)/h = 0.2930711 W; hand calculation in content.mdx: 1,500 ÷ 30 = 50 W"
    },
    {
      "given": {
        "mode": "vi",
        "v": 120,
        "i": 10
      },
      "expect": {
        "watts": 1200,
        "kilowatts": 1.2
      },
      "source": "Electric power P = V × I (NIST SP 330, the SI Brochure, 2019: 1 W = 1 V·A); hand calculation in content.mdx"
    },
    {
      "given": {
        "mode": "ir",
        "i": 2,
        "r": 50
      },
      "expect": {
        "watts": 200
      },
      "source": "Joule heating P = I² × R (OpenStax, University Physics Volume 2, §9.5); hand calculation in content.mdx: 2² × 50 = 200 W"
    },
    {
      "given": {
        "mode": "vr",
        "v": 230,
        "r": 52.9
      },
      "expect": {
        "watts": 1000
      },
      "source": "P = V² ÷ R (OpenStax, University Physics Volume 2, §9.5); hand calculation in content.mdx: 52,900 ÷ 52.9 = 1,000 W"
    },
    {
      "given": {
        "mode": "fv",
        "f": 444.82216152604997,
        "s": 1.6764000000000001
      },
      "expect": {
        "horsepower": 1,
        "watts": 745.6998715822702
      },
      "source": "NIST SP 811 (2008), B.8: horsepower (550 ft·lbf/s) = 745.6999 W; hand calculation in content.mdx: 100 × 5.5 = 550 ft·lbf/s"
    },
    {
      "given": {
        "mode": "convert",
        "p": 1000
      },
      "expect": {
        "watts": 1000,
        "horsepower": 1.341022089595028,
        "btuPerHour": 3412.141633127942
      },
      "source": "NIST SP 811 (2008), B.8 (1 hp = 745.69987158227022 W; 1 BTU(IT) = 1055.05585262 J); hand calculation in content.mdx"
    }
  ],
  "sources": [
    "NIST Special Publication 811 (2008), Guide for the Use of the International System of Units, Appendix B.8: horsepower (550 ft·lbf/s) = 745.6999 W, horsepower (metric) = 735.4988 W, British thermal unit (IT) per hour = 0.2930711 W, pound-force = 4.4482216152605 N. https://www.nist.gov/pml/special-publication-811",
    "NIST Special Publication 330 (2019), The International System of Units (SI): the watt is one joule per second and one volt ampere. https://www.nist.gov/pml/special-publication-330",
    "OpenStax, University Physics Volume 1, §7.4 Power (P = W ÷ t, P = F · v). https://openstax.org/books/university-physics-volume-1/pages/7-4-power",
    "OpenStax, University Physics Volume 2, §9.5 Electrical Energy and Power (P = IV = I²R = V²/R). https://openstax.org/books/university-physics-volume-2/pages/9-5-electrical-energy-and-power"
  ],
  "related": [
    "ohms-law",
    "electricity-cost",
    "solar-panel"
  ],
  "changelog": []
}