{
  "slug": "standard-deviation",
  "title": "Standard Deviation Calculator",
  "heading": "Standard Deviation Calculator",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/standard-deviation",
  "summary": "Population and sample standard deviation.",
  "description": "Computes mean, variance, and standard deviation (both sample and population) from a number list.",
  "formula": null,
  "dateModified": "2026-10-03",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=standard-deviation",
  "inputs": [
    {
      "id": "list",
      "label": "Numbers",
      "kind": "text",
      "hint": null,
      "default": "10, 12, 23, 23, 16, 23, 21, 16"
    }
  ],
  "outputs": [
    {
      "id": "sampleSd",
      "label": "Sample SD",
      "format": "decimal",
      "hint": null,
      "primary": true
    },
    {
      "id": "popSd",
      "label": "Population SD",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "variance",
      "label": "Sample variance",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "mean",
      "label": "Mean",
      "format": "decimal",
      "hint": null,
      "primary": false
    }
  ],
  "worked_example": {
    "inputs": [
      "Numbers: 10, 12, 23, 23, 16, 23, 21, 16"
    ],
    "outputs": [
      "Sample SD: 5.2372",
      "Population SD: 4.899",
      "Sample variance: 27.4286",
      "Mean: 18"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter numbers.",
      "Read your sample sd on the right — it updates as you type.",
      "Hit Share to keep the scenario or send it to someone."
    ]
  },
  "scenarios": [
    {
      "name": "Conservative",
      "description": "Lower-end numbers — what if things land soft?",
      "values": {
        "list": "10, 12, 23, 23, 16, 23, 21, 16"
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "list": "10, 12, 23, 23, 16, 23, 21, 16"
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "list": "10, 12, 23, 23, 16, 23, 21, 16"
      }
    }
  ],
  "limitations": [
    "Results are rounded for display; the underlying calculation keeps full precision.",
    "Very large or very small inputs may hit floating-point limits in the browser.",
    "Inputs outside the accepted range are clamped rather than rejected."
  ],
  "faq": [
    {
      "q": "How does the standard deviation calculator work?",
      "a": "Computes mean, variance, and standard deviation (both sample and population) from a number list."
    },
    {
      "q": "What do I need to enter?",
      "a": "Just one value: numbers. Each field starts with a sensible default, so you can change one number at a time and watch the result move."
    },
    {
      "q": "What does the sample sd result mean?",
      "a": "It is returned as a decimal number and updates live as you edit the inputs, so you can compare two or three versions of a scenario in a few seconds."
    },
    {
      "q": "Is this calculator free, and do I need an account?",
      "a": "Yes, it's free, and no account is required. Nothing you type is stored on our servers — the maths runs entirely in your browser."
    },
    {
      "q": "How accurate is the result?",
      "a": "It applies the standard formula exactly, so the arithmetic is precise. Results are rounded for display; the underlying calculation keeps full precision."
    },
    {
      "q": "Who is this tool for?",
      "a": "It's built for students, developers, and anyone who needs the answer right now without setting up a spreadsheet."
    }
  ],
  "related": [
    "https://www.revenuelab.fyi/toolbox/average"
  ],
  "license": "CC-BY-4.0",
  "citation": "RevenueLab — Standard Deviation Calculator (https://www.revenuelab.fyi/toolbox/standard-deviation)"
}