{
  "id": "dilution",
  "version": "91f17c63fee0",
  "status": "published",
  "name": "Dilution Calculator",
  "question": "How much stock for this dilution?",
  "summary": "Solves the dilution equation C₁V₁ = C₂V₂ for the stock volume, the final volume or either concentration, and gives the solvent to add and the dilution factor.",
  "category": "chemistry",
  "subcategory": "solutions",
  "url": "https://www.acalculator.org/chemistry/dilution-calculator",
  "markdown": "https://www.acalculator.org/chemistry/dilution-calculator.md",
  "kind": "formulas",
  "method": "C₁ × V₁ = C₂ × V₂; solvent to add = V₂ − V₁; dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁.",
  "assumptions": [
    "Both concentrations use the same unit (mol/L, mmol/L, % or mg/mL). The volumes may be in any units.",
    "Only solvent is added, so the amount of solute does not change.",
    "Volumes add up: the final volume is the stock volume plus the solvent volume. For mixtures such as alcohol and water this is only approximate."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "c1": {
        "title": "Stock concentration (C₁)",
        "description": "The concentration of the stock solution you start from.",
        "type": "number",
        "exclusiveMinimum": 0
      },
      "v1": {
        "title": "Stock volume (V₁)",
        "description": "The volume of stock solution to use.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "exclusiveMinimum": 0
      },
      "c2": {
        "title": "Final concentration (C₂)",
        "description": "The concentration you want after diluting, in the same unit as the stock concentration.",
        "type": "number",
        "exclusiveMinimum": 0
      },
      "v2": {
        "title": "Final volume (V₂)",
        "description": "The total volume after diluting: stock plus solvent.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "exclusiveMinimum": 0
      }
    }
  },
  "solve": {
    "fillAny": 3,
    "variables": [
      "c1",
      "v1",
      "c2",
      "v2"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "c1": {
      "label": "Stock concentration (C₁)",
      "description": "The concentration of the stock solution you start from.",
      "format": "number"
    },
    "v1": {
      "label": "Stock volume (V₁)",
      "description": "The volume of stock solution to use.",
      "format": "quantity"
    },
    "c2": {
      "label": "Final concentration (C₂)",
      "description": "The concentration you want after diluting, in the same unit as the stock concentration.",
      "format": "number"
    },
    "v2": {
      "label": "Final volume (V₂)",
      "description": "The total volume after diluting: stock plus solvent.",
      "format": "quantity"
    },
    "solvent": {
      "label": "Solvent to add",
      "description": "The volume of solvent to add to the stock: V₂ − V₁. Shown only when the final volume is larger.",
      "format": "quantity",
      "unit": "mL"
    },
    "factor": {
      "label": "Dilution factor",
      "description": "How many times the stock is diluted: C₁ ÷ C₂, which equals V₂ ÷ V₁.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "c1": 1,
      "c2": 0.1,
      "v2": 0.0001
    },
    "outputs": {
      "v1": 0.00001,
      "solvent": 0.00009,
      "factor": 10
    },
    "text": "To make 100 mL at 0.1 from a stock at 1, use 10 mL of stock."
  },
  "examples": [
    {
      "given": {
        "c1": 1,
        "c2": 0.1,
        "v2": 0.0001
      },
      "expect": {
        "v1": 0.00001,
        "solvent": 0.00009,
        "factor": 10
      },
      "source": "hand calculation in content.mdx: V₁ = 0.1 × 100 ÷ 1 = 10 mL; solvent = 100 − 10 = 90 mL; factor = 1 ÷ 0.1 = 10",
      "tolerance": 1e-12
    },
    {
      "given": {
        "c1": 12,
        "v1": 0.000025,
        "v2": 0.00025
      },
      "expect": {
        "c2": 1.2,
        "factor": 10
      },
      "source": "hand calculation in content.mdx: C₂ = 12 × 25 ÷ 250 = 1.2 M",
      "tolerance": 1e-12
    },
    {
      "given": {
        "c1": 70,
        "v1": 0.0001,
        "c2": 25
      },
      "expect": {
        "v2": 0.00028,
        "solvent": 0.00018,
        "factor": 2.8
      },
      "source": "hand calculation in content.mdx: V₂ = 70 × 100 ÷ 25 = 280 mL; solvent = 280 − 100 = 180 mL",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "IUPAC Compendium of Chemical Terminology (the Gold Book), amount concentration: c = n ÷ V. https://doi.org/10.1351/goldbook.A00295",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 US gallon = 3.785411784 L and 1 US fluid ounce = 29.5735295625 mL. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "molarity",
    "percentage"
  ],
  "changelog": []
}