{
  "id": "power-factor",
  "version": "c91dce11aa51",
  "status": "published",
  "name": "Power Factor Calculator",
  "question": "What is the power factor?",
  "summary": "Works out the power factor from real power and volts and amps (single or three-phase) or kVA, with the phase angle, reactive power, and the capacitor kVAR needed to correct it to a target.",
  "category": "physics",
  "subcategory": "electricity",
  "url": "https://www.acalculator.org/physics/power-factor-calculator",
  "markdown": "https://www.acalculator.org/physics/power-factor-calculator.md",
  "kind": "function",
  "method": "S = V × I ÷ 1,000 kVA (single-phase), √3 × V × I ÷ 1,000 (three-phase), or as typed. pf = P ÷ S; φ = arccos pf; Q = P × √(1 − pf²) ÷ pf. Correction to a target pf₂: Qc = Q − P × √(1 − pf₂²) ÷ pf₂; kVA after = P ÷ pf₂.",
  "assumptions": [
    "RMS values on a sinusoidal supply; three-phase means a balanced load with line-to-line volts and line amps.",
    "The correction assumes a lagging (inductive) load such as a motor, corrected with capacitors. A target at or below the present power factor shows no correction.",
    "Steps are exact on the typed values except √3 and the angle."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "ph": {
        "title": "Supply",
        "description": "Single-phase, or balanced three-phase with the line-to-line voltage. It matters only with volts and amps.",
        "type": "string",
        "enum": [
          "single",
          "three"
        ]
      },
      "from": {
        "title": "I know",
        "description": "The real power with volts and amps, or the real power with the apparent power in kVA.",
        "type": "string",
        "enum": [
          "pvi",
          "ps"
        ]
      },
      "p": {
        "title": "Real power",
        "description": "The real power the load uses, as a wattmeter or nameplate gives it.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "power",
        "minimum": 0.001,
        "maximum": 10000000000
      },
      "v": {
        "title": "Voltage",
        "description": "The RMS voltage; for three-phase, the line-to-line voltage.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "voltage",
        "minimum": 0.001,
        "maximum": 1000000
      },
      "i": {
        "title": "Current",
        "description": "The RMS current in each line.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "current",
        "minimum": 0.000001,
        "maximum": 1000000
      },
      "kva": {
        "title": "Apparent power (kVA)",
        "description": "The apparent power in kilovolt-amperes.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 10000000
      },
      "pf2": {
        "title": "Target power factor",
        "description": "The power factor to correct to with capacitors, from 0.01 to 1. Leave empty to skip.",
        "type": "number",
        "minimum": 0.01,
        "maximum": 1
      }
    }
  },
  "outputs": {
    "pf": {
      "label": "Power factor",
      "description": "Real power ÷ apparent power, from 0 to 1.",
      "format": "number"
    },
    "angle": {
      "label": "Phase angle (°)",
      "description": "The angle φ between voltage and current, where cos φ is the power factor.",
      "format": "number"
    },
    "kva": {
      "label": "Apparent power (kVA)",
      "description": "Volts × amps (× √3 for three-phase) ÷ 1,000.",
      "format": "number"
    },
    "kvar": {
      "label": "Reactive power (kVAR)",
      "description": "√(kVA² − kW²).",
      "format": "number"
    },
    "correction": {
      "label": "Capacitor kVAR to reach the target",
      "description": "kW × (tan φ now − tan φ at the target): the reactive power capacitors must supply.",
      "format": "number"
    },
    "kvaAfter": {
      "label": "kVA after correction",
      "description": "kW ÷ target power factor.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "ph": "single",
      "from": "pvi",
      "p": "9.6 kW",
      "v": "240 V",
      "i": "50 A",
      "kva": 12,
      "pf2": 0.95
    },
    "outputs": {
      "pf": 0.8,
      "angle": 36.86989764584401,
      "kva": 12,
      "kvar": 7.2,
      "correction": 4.044632590282914,
      "kvaAfter": 10.105263157894736
    },
    "text": "The power factor is 0.8 (phase angle 36.87°), with 12 kVA and 7.2 kVAR."
  },
  "examples": [
    {
      "given": {
        "from": "pvi",
        "ph": "single",
        "p": 9600,
        "v": 240,
        "i": 50,
        "pf2": 0.95
      },
      "expect": {
        "pf": 0.8,
        "angle": 36.86989764584402,
        "kva": 12,
        "kvar": 7.2,
        "correction": 4.044632590282914,
        "kvaAfter": 10.105263157894736
      },
      "source": "OpenStax, University Physics Volume 2, §15.4 Power in an AC Circuit (P_ave = I_rms V_rms cos φ; cos φ is the power factor), https://openstax.org/books/university-physics-volume-2/pages/15-4-power-in-an-ac-circuit (retrieved 2026-10-05); Wikipedia, \"Power factor\" (pf = P ÷ S; S² = P² + Q²; correction by capacitors that supply reactive power), https://en.wikipedia.org/wiki/Power_factor (retrieved 2026-10-05); hand calculation in content.mdx: 9.6 ÷ 12 = 0.8; 7.2 − 9.6 × tan(acos 0.95) = 7.2 − 3.1554 = 4.0446 kVAR",
      "tolerance": 1e-12
    },
    {
      "given": {
        "from": "ps",
        "ph": "single",
        "p": 67500,
        "kva": 75
      },
      "expect": {
        "pf": 0.9,
        "kvar": 32.69174207655505
      },
      "source": "Wikipedia, \"Power factor\" (pf = P ÷ S; S² = P² + Q²; correction by capacitors that supply reactive power), https://en.wikipedia.org/wiki/Power_factor (retrieved 2026-10-05); hand calculation in content.mdx: 67.5 ÷ 75 = 0.9; √(75² − 67.5²) = 32.69 kVAR",
      "tolerance": 1e-12
    },
    {
      "given": {
        "from": "pvi",
        "ph": "three",
        "p": 60000,
        "v": 480,
        "i": 90
      },
      "expect": {
        "pf": 0.8018753738744804,
        "kva": 74.82459488697549
      },
      "source": "Wikipedia, \"Three-phase electric power\" (balanced load: S = √3 × line voltage × line current), https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05); hand calculation in content.mdx: √3 × 480 × 90 ÷ 1,000 = 74.8246 kVA; 60 ÷ 74.8246 = 0.8019",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 2, §15.4 Power in an AC Circuit: average power = I_rms V_rms cos φ, and cos φ is the power factor. https://openstax.org/books/university-physics-volume-2/pages/15-4-power-in-an-ac-circuit (retrieved 2026-10-05)",
    "Wikipedia, \"Power factor\": pf = P ÷ S, the power triangle S² = P² + Q², and correction with capacitors. https://en.wikipedia.org/wiki/Power_factor (retrieved 2026-10-05)",
    "Wikipedia, \"Three-phase electric power\": for a balanced load, S = √3 × line voltage × line current. https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05)"
  ],
  "related": [
    "kva",
    "amp",
    "power"
  ],
  "changelog": []
}