{
  "id": "standard-deviation-calculator",
  "version": "2.0.0",
  "name": "Standard Deviation Calculator",
  "shortName": "Standard deviation",
  "description": "Calculate population or sample standard deviation, variance, mean, sum, standard error, and margin of error.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "standard deviation",
    "variance",
    "sample statistics",
    "population statistics",
    "standard error",
    "margin of error"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "new",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/standard-deviation-calculator.json",
    "qualifiedReview": "pending",
    "qualifiedReviewer": null,
    "qualifiedReviewDate": null,
    "formulaVersion": "2.0.0",
    "referenceCoverage": "references-listed",
    "releaseTestScope": "Flagship reference cases are specified in scripts/test-v20-1.mjs; consult release evidence for executed results.",
    "historicalMetadataDate": "2026-08-25",
    "historicalMetadataNotice": "The imported date is not evidence of a completed human review."
  },
  "urls": {
    "page": "/calculator/standard-deviation-calculator/",
    "definition": "/calculator/standard-deviation-calculator/definition.json",
    "schema": "/calculator/standard-deviation-calculator/schema.json",
    "llms": "/calculator/standard-deviation-calculator/llms.txt",
    "legacyDefinition": "/calculator/standard-deviation-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/standard-deviation-calculator/?values=10%2C+12%2C+23%2C+23%2C+16%2C+23%2C+21%2C+16&sample=0&confidenceLevel=95",
  "queryParameters": {
    "values": {
      "label": "Numbers",
      "type": "text",
      "required": true,
      "default": "10, 12, 23, 23, 16, 23, 21, 16"
    },
    "sample": {
      "label": "Treat the values as a sample",
      "type": "checkbox",
      "required": false,
      "default": false
    },
    "confidenceLevel": {
      "label": "Confidence level for margin of error",
      "type": "select",
      "required": true,
      "default": 95
    }
  },
  "inputs": [
    {
      "id": "values",
      "label": "Numbers",
      "type": "text",
      "required": true,
      "defaultValue": "10, 12, 23, 23, 16, 23, 21, 16",
      "placeholder": "10, 12, 23, 23",
      "help": "Separate values with commas, spaces, or semicolons.",
      "width": "full"
    },
    {
      "id": "sample",
      "label": "Treat the values as a sample",
      "type": "checkbox",
      "defaultValue": false,
      "width": "full"
    },
    {
      "id": "confidenceLevel",
      "label": "Confidence level for margin of error",
      "type": "select",
      "required": true,
      "defaultValue": 95,
      "options": [
        {
          "label": "80%",
          "value": 80
        },
        {
          "label": "90%",
          "value": 90
        },
        {
          "label": "95%",
          "value": 95
        },
        {
          "label": "98%",
          "value": 98
        },
        {
          "label": "99%",
          "value": 99
        }
      ],
      "width": "full"
    }
  ],
  "outputs": [
    {
      "id": "standardDeviation",
      "label": "Standard deviation",
      "format": "number",
      "primary": true,
      "digits": 6
    },
    {
      "id": "variance",
      "label": "Variance",
      "format": "number",
      "digits": 6
    },
    {
      "id": "mean",
      "label": "Mean",
      "format": "number",
      "digits": 6
    },
    {
      "id": "sum",
      "label": "Sum",
      "format": "number",
      "digits": 6
    },
    {
      "id": "count",
      "label": "Count",
      "format": "integer"
    },
    {
      "id": "standardError",
      "label": "Standard error",
      "format": "number",
      "digits": 6
    },
    {
      "id": "marginOfError",
      "label": "Margin of error",
      "format": "number",
      "digits": 6
    }
  ],
  "formula": {
    "expression": "Population: σ = √[Σ(x − μ)²/n]; sample: s = √[Σ(x − x̄)²/(n − 1)]; margin = z·s/√n."
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "values": "10, 12, 23, 23, 16, 23, 21, 16",
        "sample": false,
        "confidenceLevel": 95
      }
    }
  ],
  "sources": [
    {
      "label": "Calculator.net reference calculator",
      "url": "https://www.calculator.net/standard-deviation-calculator.html"
    },
    {
      "label": "NIST: confidence limits for the mean; assumptions and t versus z",
      "url": "https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm"
    }
  ]
}