{
  "id": "combined-gas-law",
  "version": "212825213a5b",
  "status": "published",
  "name": "Combined Gas Law Calculator",
  "question": "How do I use the combined gas law?",
  "summary": "Solves the combined gas law P₁V₁/T₁ = P₂V₂/T₂ for any one of pressure, volume or temperature before or after a change, in atm, kPa, mmHg, L, °C or K.",
  "category": "chemistry",
  "subcategory": "gases",
  "url": "https://www.acalculator.org/chemistry/combined-gas-law-calculator",
  "markdown": "https://www.acalculator.org/chemistry/combined-gas-law-calculator.md",
  "kind": "formulas",
  "method": "P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂, with T in kelvins. For example V₂ = P₁V₁T₂ ÷ (T₁P₂).",
  "assumptions": [
    "The gas is ideal and its amount does not change (no gas leaks in or out).",
    "Temperatures are absolute: °C + 273.15 = K, and (°F + 459.67) × 5/9 = K.",
    "Pressures are absolute pressures, not gauge readings."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "p1": {
        "title": "Pressure P₁",
        "description": "The gas pressure before the change (absolute, not gauge).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "pressure",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "v1": {
        "title": "Volume V₁",
        "description": "The gas volume before the change.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "t1": {
        "title": "Temperature T₁",
        "description": "The gas temperature before the change; above absolute zero.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "p2": {
        "title": "Pressure P₂",
        "description": "The gas pressure after the change (absolute, not gauge).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "pressure",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "v2": {
        "title": "Volume V₂",
        "description": "The gas volume after the change.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "t2": {
        "title": "Temperature T₂",
        "description": "The gas temperature after the change; above absolute zero.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      }
    }
  },
  "solve": {
    "fillAny": 5,
    "variables": [
      "p1",
      "v1",
      "t1",
      "p2",
      "v2",
      "t2"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "p1": {
      "label": "Pressure P₁",
      "description": "The gas pressure before the change (absolute, not gauge).",
      "format": "quantity"
    },
    "v1": {
      "label": "Volume V₁",
      "description": "The gas volume before the change.",
      "format": "quantity"
    },
    "t1": {
      "label": "Temperature T₁",
      "description": "The gas temperature before the change; above absolute zero.",
      "format": "quantity"
    },
    "p2": {
      "label": "Pressure P₂",
      "description": "The gas pressure after the change (absolute, not gauge).",
      "format": "quantity"
    },
    "v2": {
      "label": "Volume V₂",
      "description": "The gas volume after the change.",
      "format": "quantity"
    },
    "t2": {
      "label": "Temperature T₂",
      "description": "The gas temperature after the change; above absolute zero.",
      "format": "quantity"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "p1": 15502725,
      "v1": 0.0132,
      "t1": 300.15,
      "p2": 317147.25,
      "t2": 310.15
    },
    "outputs": {
      "v2": 0.6667368552145653
    },
    "text": "A gas at 153 atm, 13.2 L and 27 °C is at 3.13 atm, 666.7 L and 37 °C after the change."
  },
  "examples": [
    {
      "given": {
        "p1": 15502725,
        "v1": 0.0132,
        "t1": 300.15,
        "p2": 317147.25,
        "t2": 310.15
      },
      "expect": {
        "v2": 0.6667368552145653
      },
      "source": "OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.10 Using the Combined Gas Law: about 667 L (the book rounds to 300 K and 310 K); hand calculation in content.mdx with 273.15"
    },
    {
      "given": {
        "p1": 360000,
        "v1": 0.00035,
        "t1": 297.15,
        "v2": 0.00035,
        "t2": 323.15
      },
      "expect": {
        "p2": 391499.2428066633
      },
      "source": "OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.5 Predicting Change in Pressure with Temperature: about 390 kPa; hand calculation in content.mdx"
    },
    {
      "given": {
        "p1": 101325,
        "v1": 0.00015,
        "t1": 273.15,
        "p2": 101325,
        "v2": 0.0001317
      },
      "expect": {
        "t2": 239.82569999999998
      },
      "source": "OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, 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": {
        "p1": 99991.77631578948,
        "v1": 0.0003,
        "t1": 283.15,
        "p2": 99991.77631578948,
        "t2": 303.15
      },
      "expect": {
        "v2": 0.00032119018188239446
      },
      "source": "OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, 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; hand calculation in content.mdx"
    }
  ],
  "sources": [
    "OpenStax, Chemistry 2e, section 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law: P₁V₁/T₁ = P₂V₂/T₂; Examples 9.5, 9.6, 9.7 and 9.10. CC BY 4.0, retrieved 2026-10-02. 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.9: 1 standard atmosphere = 101,325 Pa exactly; 1 psi = 6,894.757 Pa. Retrieved 2026-10-02. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9"
  ],
  "related": [
    "molarity",
    "dilution",
    "mole"
  ],
  "changelog": []
}