{
  "id": "serial-dilution",
  "version": "c9c29d115c26",
  "status": "published",
  "name": "Serial Dilution Calculator",
  "question": "Serial dilution: what is in each tube?",
  "summary": "Plans a serial dilution: the concentration in every tube, the total dilution factor, and how much sample and diluent go in each tube for a chosen factor per step and final volume.",
  "category": "biology",
  "subcategory": "lab",
  "url": "https://www.acalculator.org/biology/serial-dilution-calculator",
  "markdown": "https://www.acalculator.org/biology/serial-dilution-calculator.md",
  "kind": "function",
  "method": "Tube k = C₀ ÷ Fᵏ; total dilution factor = Fⁿ; sample moved each step = V ÷ F; diluent in each tube = V − V ÷ F.",
  "assumptions": [
    "Every step uses the same dilution factor F and the same final volume V.",
    "Each tube is mixed well before its sample is moved on, and volumes add up.",
    "The concentration keeps the unit of the starting concentration (M, mg/mL, cells/mL)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "c0": {
        "title": "Starting concentration",
        "description": "The concentration of the stock or culture before the first step, in any unit (M, mg/mL, cells/mL).",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1e+30
      },
      "f": {
        "title": "Dilution factor per step",
        "description": "How many times each step dilutes the tube before it: 10 for a 1:10 (ten-fold) series.",
        "type": "number",
        "exclusiveMinimum": 1,
        "maximum": 1000000
      },
      "n": {
        "title": "Number of dilution steps",
        "description": "How many tubes the series makes after the stock.",
        "type": "integer",
        "minimum": 1,
        "maximum": 30
      },
      "v": {
        "title": "Final volume in each tube",
        "description": "The total volume in each tube after mixing: sample plus diluent.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "exclusiveMinimum": 0,
        "maximum": 1
      }
    }
  },
  "outputs": {
    "final": {
      "label": "Concentration in the last tube",
      "description": "The starting concentration ÷ (dilution factor per step) ^ steps, in the starting unit.",
      "format": "number"
    },
    "total": {
      "label": "Total dilution factor",
      "description": "(Dilution factor per step) ^ steps: how many times the last tube is diluted from the stock.",
      "format": "number"
    },
    "transfer": {
      "label": "Sample to move each step",
      "description": "The volume taken from one tube into the next: final volume ÷ dilution factor per step.",
      "format": "quantity",
      "unit": "mL"
    },
    "diluent": {
      "label": "Diluent in each tube",
      "description": "The diluent put in each tube before the sample: final volume − sample moved.",
      "format": "quantity",
      "unit": "mL"
    },
    "tubes": {
      "label": "Each tube",
      "description": "Every tube in order, with its dilution from the stock and its concentration.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "c0": 1000000,
      "f": 10,
      "n": 6,
      "v": "10 mL"
    },
    "outputs": {
      "final": 1,
      "total": 1000000,
      "transfer": 0.000001,
      "diluent": 0.000009,
      "tubes": "Tube 1: 1:10 of the stock, 100000; Tube 2: 1:100 of the stock, 10000; Tube 3: 1:1000 of the stock, 1000; Tube 4: 1:10000 of the stock, 100; Tube 5: 1:100000 of the stock, 10; Tube 6: 1:1000000 of the stock, 1"
    },
    "text": "After 6 steps of 1:10, the last tube holds 1, a total dilution of 1,000,000."
  },
  "examples": [
    {
      "given": {
        "c0": 1000000,
        "f": 10,
        "n": 6,
        "v": 0.00001
      },
      "expect": {
        "final": 1,
        "total": 1000000,
        "transfer": 0.000001,
        "diluent": 0.000009
      },
      "source": "OpenStax, Microbiology, section 9.1 How Microbes Grow (1.0 mL of culture into 9.0 mL of broth is a dilution factor of 10, or 1:10; a second 1.0 mL into 9.0 mL makes 1:100 of the original culture), CC BY 4.0, https://openstax.org/books/microbiology/pages/9-1-how-microbes-grow (retrieved 2026-10-03); hand calculation in content.mdx: 1,000,000 ÷ 10⁶ = 1; 10 mL ÷ 10 = 1 mL of sample and 9 mL of diluent",
      "tolerance": 1e-12
    },
    {
      "given": {
        "c0": 1,
        "f": 10,
        "n": 2,
        "v": 0.00001
      },
      "expect": {
        "final": 0.01,
        "total": 100,
        "transfer": 0.000001,
        "diluent": 0.000009,
        "tubes": "Tube 1: 1:10 of the stock, 0.1; Tube 2: 1:100 of the stock, 0.01"
      },
      "source": "OpenStax, Microbiology, section 9.1 How Microbes Grow (1.0 mL of culture into 9.0 mL of broth is a dilution factor of 10, or 1:10; a second 1.0 mL into 9.0 mL makes 1:100 of the original culture), CC BY 4.0, https://openstax.org/books/microbiology/pages/9-1-how-microbes-grow (retrieved 2026-10-03)",
      "tolerance": 1e-12
    },
    {
      "given": {
        "c0": 2,
        "f": 2,
        "n": 5,
        "v": 0.000001
      },
      "expect": {
        "final": 0.0625,
        "total": 32,
        "transfer": 5e-7,
        "diluent": 5e-7
      },
      "source": "OpenStax, Microbiology, section 9.1 How Microbes Grow (1.0 mL of culture into 9.0 mL of broth is a dilution factor of 10, or 1:10; a second 1.0 mL into 9.0 mL makes 1:100 of the original culture), CC BY 4.0, https://openstax.org/books/microbiology/pages/9-1-how-microbes-grow (retrieved 2026-10-03); hand calculation in content.mdx: 2 ÷ 2⁵ = 2 ÷ 32 = 0.0625; 1 mL ÷ 2 = 0.5 mL",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, Microbiology, section 9.1 How Microbes Grow (serial dilutions for plate counts: 1.0 mL of culture into 9.0 mL of broth is a dilution factor of 10, or 1:10; the next 1.0 mL into 9.0 mL is 1:100 of the original culture; plates of 30 to 300 colonies), CC BY 4.0, retrieved 2026-10-03. https://openstax.org/books/microbiology/pages/9-1-how-microbes-grow"
  ],
  "related": [
    "dilution",
    "molarity"
  ],
  "changelog": []
}