{
  "id": "energy",
  "version": "6f0ceb582d65",
  "status": "published",
  "name": "Energy Calculator",
  "question": "How much energy is it?",
  "summary": "Computes energy from power and time (E = P × t), from force and distance (W = F × d), or the mechanical energy of a moving, raised mass (½mv² + mgh), in joules, kWh, kcal, BTU and ft·lbf.",
  "category": "physics",
  "subcategory": "energy",
  "url": "https://www.acalculator.org/physics/energy-calculator",
  "markdown": "https://www.acalculator.org/physics/energy-calculator.md",
  "kind": "function",
  "method": "E = P × t; W = F × d; E = ½ m v² + m g h.",
  "assumptions": [
    "Power × time: the power is steady over the whole time. Force × distance: a steady force that points along the motion.",
    "Motion and height: kinetic energy ½ m v² (classical, well below light speed) plus gravitational potential energy m g h near a planet’s surface.",
    "Exact unit sizes: 1 hp = 550 ft·lbf/s; 1 BTU = 1,055.05585262 J; 1 kcal = 4,184 J; 1 kWh = 3,600,000 J; 1 lbf = 4.4482216152605 N; 1 ft = 0.3048 m; 1 mph = 0.44704 m/s."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "Energy from",
        "description": "Work out the energy from power and time, from force and distance, or from mass, speed and height.",
        "type": "string",
        "enum": [
          "power",
          "work",
          "motion"
        ]
      },
      "P": {
        "title": "Power",
        "description": "The steady power used or delivered.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "power",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "t": {
        "title": "Time",
        "description": "How long the power runs.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "time",
        "exclusiveMinimum": 0,
        "maximum": 10000000000
      },
      "F": {
        "title": "Force",
        "description": "The steady force, pushing along the direction of motion.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "d": {
        "title": "Distance",
        "description": "How far the force moves the object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "m": {
        "title": "Mass",
        "description": "The mass of the object.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "v": {
        "title": "Speed",
        "description": "How fast the object moves.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0,
        "maximum": 1000000
      },
      "h": {
        "title": "Height",
        "description": "How high the object is above the level you measure from.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0,
        "maximum": 10000000
      },
      "g": {
        "title": "Gravity (m/s²)",
        "description": "The acceleration of gravity in m/s²: 9.80665 on Earth.",
        "type": "number",
        "minimum": 0.001,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "joules": {
      "label": "Energy (J)",
      "description": "The energy in joules.",
      "format": "number"
    },
    "kwh": {
      "label": "Energy (kWh)",
      "description": "The same energy in kilowatt-hours (1 kWh = 3,600,000 J).",
      "format": "number"
    },
    "kcal": {
      "label": "Energy (kcal)",
      "description": "The same energy in kilocalories, or food Calories (1 kcal = 4,184 J).",
      "format": "number"
    },
    "btu": {
      "label": "Energy (BTU)",
      "description": "The same energy in British thermal units (1 BTU = 1,055.05585262 J).",
      "format": "number"
    },
    "ftlbf": {
      "label": "Energy (ft·lbf)",
      "description": "The same energy in foot-pounds (1 ft·lbf = 1.3558179483314004 J).",
      "format": "number"
    },
    "kinetic": {
      "label": "Kinetic energy (J)",
      "description": "In the motion mode: ½ m v².",
      "format": "number"
    },
    "potential": {
      "label": "Potential energy (J)",
      "description": "In the motion mode: m g h.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "power",
      "P": "1500 W",
      "t": "2 h",
      "F": "100 N",
      "d": "10 m",
      "m": "1000 kg",
      "v": "20 m/s",
      "h": "10 m",
      "g": 9.80665
    },
    "outputs": {
      "joules": 10800000,
      "kwh": 3,
      "kcal": 2581.261950286807,
      "btu": 10236.424899383826,
      "ftlbf": 7965671.212194466
    },
    "text": "That is 10,800,000 J of energy, or 3 kWh."
  },
  "examples": [
    {
      "given": {
        "from": "power",
        "P": 1500,
        "t": 7200
      },
      "expect": {
        "joules": 10800000,
        "kwh": 3
      },
      "source": "OpenStax, University Physics Volume 1, §7.4 Power (P = W ÷ t), https://openstax.org/books/university-physics-volume-1/pages/7-4-power; hand calculation in content.mdx: E = 1,500 W × 7,200 s = 10,800,000 J = 3 kWh"
    },
    {
      "given": {
        "from": "work",
        "F": 100,
        "d": 10
      },
      "expect": {
        "joules": 1000,
        "kcal": 0.2390057361376673
      },
      "source": "OpenStax, University Physics Volume 1, §7.1 Work (W = F d for a constant force along the motion), https://openstax.org/books/university-physics-volume-1/pages/7-1-work; hand calculation in content.mdx: W = 100 × 10 = 1,000 J = 0.239006 kcal"
    },
    {
      "given": {
        "from": "motion",
        "m": 1000,
        "v": 20,
        "h": 10,
        "g": 9.80665
      },
      "expect": {
        "joules": 298066.5,
        "kinetic": 200000,
        "potential": 98066.5
      },
      "source": "OpenStax, University Physics Volume 1, §8.3 Conservation of Energy (E = K + U), https://openstax.org/books/university-physics-volume-1/pages/8-3-conservation-of-energy; hand calculation in content.mdx: ½ × 1,000 × 20² + 1,000 × 9.80665 × 10 = 200,000 + 98,066.5 = 298,066.5 J"
    },
    {
      "given": {
        "from": "power",
        "P": 1055.05585262,
        "t": 3600
      },
      "expect": {
        "btu": 3600,
        "kwh": 1.05505585262
      },
      "source": "OpenStax, University Physics Volume 1, §7.4 Power (P = W ÷ t), https://openstax.org/books/university-physics-volume-1/pages/7-4-power; NIST SP 811 (1 BTU = 1,055.05585262 J), https://www.nist.gov/pml/special-publication-811; hand calculation in content.mdx"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §7.4 Power (P = W ÷ t, so W = P t for a steady power). https://openstax.org/books/university-physics-volume-1/pages/7-4-power (retrieved 2026-10-03)",
    "OpenStax, University Physics Volume 1, §7.1 Work (W = F d for a constant force along the displacement). https://openstax.org/books/university-physics-volume-1/pages/7-1-work (retrieved 2026-10-03)",
    "OpenStax, University Physics Volume 1, §8.3 Conservation of Energy (mechanical energy E = K + U). https://openstax.org/books/university-physics-volume-1/pages/8-3-conservation-of-energy (retrieved 2026-10-03)",
    "NIST SP 811, Appendix B.8 Factors for Units Listed Alphabetically (British thermal unit (IT), calorie (thermochemical), kilowatt hour, horsepower, foot-pound-force). 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": [
    "power",
    "kinetic-energy",
    "potential-energy"
  ],
  "changelog": []
}