{
  "id": "voltage-drop",
  "version": "12403d362f8b",
  "status": "published",
  "name": "Voltage Drop Calculator",
  "question": "What is the voltage drop?",
  "summary": "Computes the voltage drop, the percent drop and the voltage at the load for a copper or aluminium circuit, from the AWG wire size, the one-way length, the current, the supply voltage and the conductor temperature.",
  "category": "physics",
  "subcategory": "electricity",
  "url": "https://www.acalculator.org/physics/voltage-drop-calculator",
  "markdown": "https://www.acalculator.org/physics/voltage-drop-calculator.md",
  "kind": "function",
  "method": "d = 0.005 in × 92^((36 − n) ÷ 39); R = ρ₂₀ × (1 + α × (T − 20 °C)) ÷ (π d² ÷ 4); drop = k × L × I × R ÷ conductors in parallel, with k = 2 (DC or single-phase) or √3 (three-phase).",
  "assumptions": [
    "Solid round wire at the AWG diameter; stranded wire of the same gauge has a little more resistance.",
    "Copper is annealed copper of 100% IACS, 1/58 Ω·mm²/m at 20 °C with α = 0.00393; aluminium is 61% IACS, 0.028264 Ω·mm²/m with α = 0.00403.",
    "AC circuits count resistance only: no inductive reactance, skin effect or power factor, which add a little drop in large wires.",
    "The load draws the typed current whatever the voltage at its end."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "mat": {
        "title": "Conductor",
        "description": "The metal of the wire: copper or aluminium.",
        "type": "string",
        "enum": [
          "copper",
          "aluminum"
        ]
      },
      "awg": {
        "title": "Wire size (AWG)",
        "description": "The American Wire Gauge size of each conductor.",
        "type": "string",
        "enum": [
          "4-0",
          "3-0",
          "2-0",
          "1-0",
          "1",
          "2",
          "3",
          "4",
          "5",
          "6",
          "7",
          "8",
          "9",
          "10",
          "11",
          "12",
          "13",
          "14",
          "15",
          "16",
          "17",
          "18",
          "19",
          "20"
        ]
      },
      "phase": {
        "title": "Circuit",
        "description": "DC or single-phase AC (the current goes out and back), or three-phase AC.",
        "type": "string",
        "enum": [
          "single",
          "three"
        ]
      },
      "v": {
        "title": "Supply voltage",
        "description": "The voltage at the source: line to line for three-phase.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "voltage",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "i": {
        "title": "Load current",
        "description": "The current the load draws, in amperes.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "current",
        "exclusiveMinimum": 0,
        "maximum": 100000
      },
      "l": {
        "title": "One-way length",
        "description": "The length of the circuit from the source to the load, one way.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 100000
      },
      "sets": {
        "title": "Conductors in parallel",
        "description": "How many conductors of this size share the current in each leg or phase; usually 1.",
        "type": "integer",
        "minimum": 1,
        "maximum": 20
      },
      "t": {
        "title": "Conductor temperature",
        "description": "The temperature of the wire in use; 75 °C is a common rating for building wire.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 223.14999999999998,
        "maximum": 423.15
      }
    }
  },
  "outputs": {
    "drop": {
      "label": "Voltage drop",
      "description": "The voltage lost in the wires between the source and the load.",
      "format": "quantity",
      "unit": "V"
    },
    "percent": {
      "label": "Voltage drop, percent",
      "description": "The voltage drop as a percent of the supply voltage.",
      "format": "percent"
    },
    "atLoad": {
      "label": "Voltage at the load",
      "description": "The supply voltage less the voltage drop.",
      "format": "quantity",
      "unit": "V"
    },
    "ohmsPerKft": {
      "label": "Resistance, Ω per 1,000 ft",
      "description": "The resistance of one conductor per 1,000 feet at the temperature.",
      "format": "number"
    },
    "ohmsPerKm": {
      "label": "Resistance, Ω per km",
      "description": "The resistance of one conductor per kilometre at the temperature.",
      "format": "number"
    },
    "diameterIn": {
      "label": "Diameter, inches",
      "description": "The diameter of the bare wire: 0.005 in × 92^((36 − n) ÷ 39).",
      "format": "number"
    },
    "areaMm2": {
      "label": "Area, mm²",
      "description": "The cross-section of the bare wire in square millimetres: π × d² ÷ 4.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "mat": "copper",
      "awg": "12",
      "phase": "single",
      "v": 120,
      "i": 20,
      "l": 30.48,
      "sets": 1,
      "t": 348.15
    },
    "outputs": {
      "drop": 7.726221376119816,
      "percent": 6.4385178134331795,
      "atLoad": 112.27377862388019,
      "ohmsPerKft": 1.931555344029954,
      "ohmsPerKm": 6.337123832119271,
      "diameterIn": 0.08080808616117906,
      "areaMm2": 3.3087728761114765
    },
    "text": "Over 100 ft of 12 AWG wire at 20 A, the voltage drop is 7.73 V (6.44% of 120 V), leaving 112.27 V at the load."
  },
  "examples": [
    {
      "given": {
        "mat": "copper",
        "awg": "12",
        "phase": "single",
        "v": 120,
        "i": 20,
        "l": 30.48,
        "sets": 1,
        "t": 293.15
      },
      "expect": {
        "ohmsPerKft": 1.588,
        "diameterIn": 0.0808
      },
      "source": "NBS Handbook 100, Copper Wire Tables (1966), Table 1: 12 AWG, 80.8 mils, 1.588 Ω per 1,000 ft at 20 °C",
      "tolerance": 0.0005
    },
    {
      "given": {
        "mat": "copper",
        "awg": "10",
        "phase": "single",
        "v": 120,
        "i": 20,
        "l": 30.48,
        "sets": 1,
        "t": 293.15
      },
      "expect": {
        "ohmsPerKft": 0.9989
      },
      "source": "NBS Handbook 100, Copper Wire Tables (1966), Table 1: 10 AWG, 0.9989 Ω per 1,000 ft at 20 °C (rounded table value)",
      "tolerance": 0.0005
    },
    {
      "given": {
        "mat": "copper",
        "awg": "12",
        "phase": "single",
        "v": 120,
        "i": 20,
        "l": 30.48,
        "sets": 1,
        "t": 348.15
      },
      "expect": {
        "ohmsPerKft": 1.931555344029954,
        "drop": 7.726221376119816,
        "percent": 6.4385178134331795,
        "atLoad": 112.27377862388019
      },
      "source": "ASTM B258 diameter formula; IEC 60028 copper (1/58 Ω·mm²/m, α = 0.00393); hand calculation in content.mdx: 1.5883 × (1 + 0.00393 × 55) = 1.9316 Ω/kft; 2 × 100 × 20 × 1.9316 ÷ 1,000 = 7.73 V"
    },
    {
      "given": {
        "mat": "aluminum",
        "awg": "4-0",
        "phase": "three",
        "v": 480,
        "i": 200,
        "l": 76.2,
        "sets": 1,
        "t": 348.15
      },
      "expect": {
        "diameterIn": 0.46,
        "drop": 8.500667712999359,
        "percent": 1.7709724402081999
      },
      "source": "ASTM B258 (4/0 AWG = 0.4600 in); IEC 60889 aluminium (0.028264 Ω·mm²/m, α = 0.00403); hand calculation in content.mdx: √3 × 250 × 200 × 0.098157 ÷ 1,000 = 8.50 V"
    },
    {
      "given": {
        "mat": "copper",
        "awg": "6",
        "phase": "single",
        "v": 230,
        "i": 32,
        "l": 30,
        "sets": 1,
        "t": 348.15
      },
      "expect": {
        "ohmsPerKm": 1.576339597874924,
        "drop": 3.0265720279198542,
        "percent": 1.3159008817042843
      },
      "source": "ASTM B258; IEC 60028; hand calculation in content.mdx: 6 AWG is 13.30 mm², 1.5763 Ω/km at 75 °C; 2 × 30 × 32 × 1.5763 ÷ 1,000 = 3.03 V"
    }
  ],
  "sources": [
    "ASTM B258-18, Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors (d = 0.005 in × 92^((36 − n)/39)). https://www.astm.org/b0258-18.html",
    "National Bureau of Standards, Copper Wire Tables, Handbook 100 (1966): annealed copper 100% IACS, 12 AWG = 1.588 Ω and 10 AWG = 0.9989 Ω per 1,000 ft at 20 °C. https://nvlpubs.nist.gov/nistpubs/Legacy/hb/nbshandbook100.pdf",
    "IEC 60028:1925, International standard of resistance for copper: 1/58 Ω·mm²/m at 20 °C, temperature coefficient 0.00393 per °C. https://webstore.iec.ch/publication/1",
    "IEC 60889:1987, Hard-drawn aluminium wire for overhead line conductors: resistivity 0.028264 Ω·mm²/m at 20 °C (61% IACS), temperature coefficient 0.00403 per °C. https://webstore.iec.ch/publication/2011",
    "NFPA 70, National Electrical Code (2020), 210.19(A)(1) Informational Note No. 4: branch-circuit voltage drop of not more than 3%, and 5% overall to the farthest outlet. https://www.nfpa.org/codes-and-standards/nfpa-70-standard-development/70"
  ],
  "related": [
    "ohms-law",
    "power"
  ],
  "changelog": []
}