{
  "id": "charles-law",
  "version": "a1c25d6a32da",
  "status": "published",
  "name": "Charles Law Calculator",
  "question": "How does Charles law work?",
  "summary": "Solves Charles’s law V₁/T₁ = V₂/T₂ for a gas at constant pressure: the new volume after a temperature change, or the temperature for a new volume, in liters, mL, °C, °F or kelvins.",
  "category": "chemistry",
  "subcategory": "gases",
  "url": "https://www.acalculator.org/chemistry/charles-law-calculator",
  "markdown": "https://www.acalculator.org/chemistry/charles-law-calculator.md",
  "kind": "function",
  "method": "V₁ ÷ T₁ = V₂ ÷ T₂ with T in kelvins: V₂ = V₁T₂ ÷ T₁; T₂ = T₁V₂ ÷ V₁; V₁ = V₂T₁ ÷ T₂; T₁ = T₂V₁ ÷ V₂.",
  "assumptions": [
    "The pressure and the amount of gas stay the same, and the gas is ideal.",
    "Temperatures are absolute: K = °C + 273.15; K = (°F + 459.67) × 5/9."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Which of the four values to work out from the other three.",
        "type": "string",
        "enum": [
          "v1",
          "t1",
          "v2",
          "t2"
        ]
      },
      "v1": {
        "title": "Volume V₁",
        "description": "The gas volume before the change.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "minimum": 1e-12,
        "maximum": 1000000000
      },
      "t1": {
        "title": "Temperature T₁",
        "description": "The gas temperature before the change; above absolute zero.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 0.000001,
        "maximum": 1000000000
      },
      "v2": {
        "title": "Volume V₂",
        "description": "The gas volume after the change.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "minimum": 1e-12,
        "maximum": 1000000000
      },
      "t2": {
        "title": "Temperature T₂",
        "description": "The gas temperature after the change; above absolute zero.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 0.000001,
        "maximum": 1000000000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The value worked out, to 6 significant figures.",
      "format": "text"
    },
    "v1L": {
      "label": "V₁ (L)",
      "description": "The volume before the change, in liters.",
      "format": "number"
    },
    "t1K": {
      "label": "T₁ (K)",
      "description": "The temperature before the change, in kelvins.",
      "format": "number"
    },
    "v2L": {
      "label": "V₂ (L)",
      "description": "The volume after the change, in liters.",
      "format": "number"
    },
    "t2K": {
      "label": "T₂ (K)",
      "description": "The temperature after the change, in kelvins.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "v2",
      "v1": "0.3 L",
      "t1": "10 °C",
      "v2": "0.321 L",
      "t2": "30 °C"
    },
    "outputs": {
      "result": "V₂ = 0.32119 L",
      "v1L": 0.3,
      "t1K": 283.15,
      "v2L": 0.3211901818823945,
      "t2K": 303.15
    },
    "text": "The answer is V₂ = 0.32119 L."
  },
  "examples": [
    {
      "given": {
        "find": "v2",
        "v1": 0.0003,
        "t1": 283.15,
        "t2": 303.15
      },
      "expect": {
        "v2L": 0.3211901818823945,
        "result": "V₂ = 0.32119 L"
      },
      "source": "OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (Charles’s law, V ÷ T constant), https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.6 Predicting Change in Volume with Temperature: 0.321 L; Python 3"
    },
    {
      "given": {
        "find": "t2",
        "v1": 0.00015,
        "t1": 273.15,
        "v2": 0.0001317
      },
      "expect": {
        "t2K": 239.8257,
        "result": "T₂ = 239.826 K (−33.3243 °C)"
      },
      "source": "OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (Charles’s law, V ÷ T constant), https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.7 Measuring Temperature with a Volume Change: 239.8 K (−33.4 °C); hand calculation in content.mdx"
    },
    {
      "given": {
        "find": "v2",
        "v1": 0.000405,
        "t1": 298,
        "t2": 467
      },
      "expect": {
        "v2L": 0.6346812080536913
      },
      "source": "OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (Charles’s law, V ÷ T constant), https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Check Your Learning after Example 9.6: 635 mL; Python 3"
    }
  ],
  "sources": [
    "OpenStax, Chemistry 2e, section 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law: Charles’s law, Examples 9.6 and 9.7 and the Check Your Learning after Example 9.6. CC BY 4.0, retrieved 2026-10-03. https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law",
    "NIST Special Publication 811, Appendix B.8: 1 ft³ = 0.028316846592 m³; 1 gal = 0.003785411784 m³; °F and °C to kelvins. Retrieved 2026-10-03. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8"
  ],
  "related": [
    "combined-gas-law",
    "ideal-gas-law",
    "partial-pressure"
  ],
  "changelog": []
}