{
  "id": "voltage-divider",
  "version": "9ecd4061d2a1",
  "status": "published",
  "name": "Voltage Divider Calculator",
  "question": "What is the voltage divider output?",
  "summary": "Finds the output voltage of a two-resistor voltage divider, Vout = Vin × R2 ÷ (R1 + R2), or the input voltage or either resistor from the other three, with the current and power.",
  "category": "physics",
  "subcategory": "electricity",
  "url": "https://www.acalculator.org/physics/voltage-divider-calculator",
  "markdown": "https://www.acalculator.org/physics/voltage-divider-calculator.md",
  "kind": "formulas",
  "method": "Vout = Vin × R2 ÷ (R1 + R2), because the same current I = Vin ÷ (R1 + R2) flows through both resistors and Vout = I × R2.",
  "assumptions": [
    "Nothing is connected across the output (no load), so all the current flows through both resistors.",
    "Ideal resistors and a steady (DC) voltage, or RMS values in a purely resistive AC circuit.",
    "All values are more than 0; Vout must be less than Vin."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "vin": {
        "title": "Input voltage Vin",
        "description": "The voltage across both resistors, from the source.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "voltage",
        "exclusiveMinimum": 0
      },
      "r1": {
        "title": "R1 (top)",
        "description": "The resistor between the input and the output.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "resistance",
        "exclusiveMinimum": 0
      },
      "r2": {
        "title": "R2 (bottom)",
        "description": "The resistor between the output and ground; Vout is the voltage across it.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "resistance",
        "exclusiveMinimum": 0
      },
      "vout": {
        "title": "Output voltage Vout",
        "description": "The voltage across R2, less than Vin.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "voltage",
        "exclusiveMinimum": 0
      }
    }
  },
  "solve": {
    "fillAny": 3,
    "variables": [
      "vin",
      "r1",
      "r2",
      "vout"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "vin": {
      "label": "Input voltage Vin",
      "description": "The voltage across both resistors, from the source.",
      "format": "quantity"
    },
    "r1": {
      "label": "R1 (top)",
      "description": "The resistor between the input and the output.",
      "format": "quantity"
    },
    "r2": {
      "label": "R2 (bottom)",
      "description": "The resistor between the output and ground; Vout is the voltage across it.",
      "format": "quantity"
    },
    "vout": {
      "label": "Output voltage Vout",
      "description": "The voltage across R2.",
      "format": "quantity"
    },
    "current": {
      "label": "Current",
      "description": "The current through both resistors: Vin ÷ (R1 + R2).",
      "format": "quantity"
    },
    "ratio": {
      "label": "Vout ÷ Vin",
      "description": "The divider ratio R2 ÷ (R1 + R2).",
      "format": "number"
    },
    "power": {
      "label": "Power used",
      "description": "The power both resistors turn into heat: Vin × current.",
      "format": "quantity"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "vin": 9,
      "r1": 80,
      "r2": 10
    },
    "outputs": {
      "vout": 1,
      "current": 0.1,
      "ratio": 0.1111111111111111,
      "power": 0.9
    },
    "text": "With 9 V across 80 Ω and 10 Ω, the output is 1 V."
  },
  "examples": [
    {
      "given": {
        "vin": 9,
        "r1": 80,
        "r2": 10
      },
      "expect": {
        "vout": 1,
        "current": 0.1,
        "ratio": 0.1111111111111111,
        "power": 0.9
      },
      "source": "OpenStax, University Physics Volume 2, §10.2 Resistors in Series and Parallel (series resistance R_S = R₁ + R₂ + …, the same current I = V ÷ R_S through each, and the drop across each V_i = I R_i; Example 10.2: 9 V across 90 Ω gives 0.1 A, 2 V across each 20 Ω and 1 V across the 10 Ω), https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel (retrieved 2026-10-02); hand calculation in content.mdx: 9 × 10 ÷ 90 = 1 V"
    },
    {
      "given": {
        "vin": 5,
        "r1": 10000,
        "r2": 10000
      },
      "expect": {
        "vout": 2.5,
        "current": 0.00025,
        "ratio": 0.5
      },
      "source": "hand calculation in content.mdx: equal resistors halve the voltage; OpenStax, University Physics Volume 2, §10.2 Resistors in Series and Parallel (series resistance R_S = R₁ + R₂ + …, the same current I = V ÷ R_S through each, and the drop across each V_i = I R_i; Example 10.2: 9 V across 90 Ω gives 0.1 A, 2 V across each 20 Ω and 1 V across the 10 Ω), https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel (retrieved 2026-10-02)"
    },
    {
      "given": {
        "vin": 12,
        "vout": 3.3,
        "r2": 10000
      },
      "expect": {
        "r1": 26363.636363636364
      },
      "source": "hand calculation in content.mdx: R1 = 10,000 × (12 − 3.3) ÷ 3.3; Python 3: 10000*(12-3.3)/3.3; OpenStax, University Physics Volume 2, §10.2 Resistors in Series and Parallel (series resistance R_S = R₁ + R₂ + …, the same current I = V ÷ R_S through each, and the drop across each V_i = I R_i; Example 10.2: 9 V across 90 Ω gives 0.1 A, 2 V across each 20 Ω and 1 V across the 10 Ω), https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel (retrieved 2026-10-02)"
    },
    {
      "given": {
        "vout": 2,
        "r1": 30,
        "r2": 60
      },
      "expect": {
        "vin": 3
      },
      "source": "hand calculation in content.mdx: Vin = 2 × 90 ÷ 60 = 3 V; OpenStax, University Physics Volume 2, §10.2 Resistors in Series and Parallel (series resistance R_S = R₁ + R₂ + …, the same current I = V ÷ R_S through each, and the drop across each V_i = I R_i; Example 10.2: 9 V across 90 Ω gives 0.1 A, 2 V across each 20 Ω and 1 V across the 10 Ω), https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel (retrieved 2026-10-02)"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 2, §10.2 Resistors in Series and Parallel (series resistance R_S = R₁ + R₂ + …, the same current I = V ÷ R_S through each, and the drop across each V_i = I R_i; Example 10.2: 9 V across 90 Ω gives 0.1 A, 2 V across each 20 Ω and 1 V across the 10 Ω). https://openstax.org/books/university-physics-volume-2/pages/10-2-resistors-in-series-and-parallel (retrieved 2026-10-02)"
  ],
  "related": [
    "ohms-law",
    "parallel-resistor",
    "voltage-drop"
  ],
  "changelog": []
}