{
  "id": "confidence-interval-calculator",
  "version": "2.0.0",
  "name": "Confidence Interval Calculator",
  "shortName": "Confidence interval",
  "description": "Calculate a two-sided normal confidence interval and margin of error for a population mean.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "confidence interval",
    "margin of error",
    "sample mean",
    "standard error",
    "critical z score"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "migrated",
  "migratedDate": "2026-08-25",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/confidence-interval-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/confidence-interval-calculator/",
    "definition": "/calculator/confidence-interval-calculator/definition.json",
    "schema": "/calculator/confidence-interval-calculator/schema.json",
    "llms": "/calculator/confidence-interval-calculator/llms.txt",
    "legacyDefinition": "/calculator/confidence-interval-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/confidence-interval-calculator/?sampleSize=100&sampleMean=50&standardDeviation=10&confidenceLevel=95",
  "queryParameters": {
    "sampleSize": {
      "label": "Sample size (n)",
      "type": "number",
      "required": true,
      "default": 100
    },
    "sampleMean": {
      "label": "Sample mean (x̄)",
      "type": "number",
      "required": true,
      "default": 50
    },
    "standardDeviation": {
      "label": "Standard deviation (σ or s)",
      "type": "number",
      "required": true,
      "default": 10
    },
    "confidenceLevel": {
      "label": "Confidence level",
      "type": "select",
      "required": true,
      "default": 95
    }
  },
  "inputs": [
    {
      "id": "sampleSize",
      "label": "Sample size (n)",
      "type": "number",
      "required": true,
      "defaultValue": 100,
      "min": 1,
      "max": 1000000000,
      "step": 1,
      "width": "half"
    },
    {
      "id": "sampleMean",
      "label": "Sample mean (x̄)",
      "type": "number",
      "required": true,
      "defaultValue": 50,
      "step": 0.01,
      "width": "half"
    },
    {
      "id": "standardDeviation",
      "label": "Standard deviation (σ or s)",
      "type": "number",
      "required": true,
      "defaultValue": 10,
      "min": 0,
      "step": 0.01,
      "width": "half"
    },
    {
      "id": "confidenceLevel",
      "label": "Confidence level",
      "type": "select",
      "required": true,
      "defaultValue": 95,
      "options": [
        {
          "label": "80%",
          "value": 80
        },
        {
          "label": "85%",
          "value": 85
        },
        {
          "label": "90%",
          "value": 90
        },
        {
          "label": "95%",
          "value": 95
        },
        {
          "label": "98%",
          "value": 98
        },
        {
          "label": "99%",
          "value": 99
        },
        {
          "label": "99.9%",
          "value": 99.9
        }
      ],
      "width": "half"
    }
  ],
  "outputs": [
    {
      "id": "lowerBound",
      "label": "Lower bound",
      "format": "number",
      "primary": true,
      "digits": 6
    },
    {
      "id": "upperBound",
      "label": "Upper bound",
      "format": "number",
      "primary": true,
      "digits": 6
    },
    {
      "id": "interval",
      "label": "Confidence interval",
      "format": "text"
    },
    {
      "id": "marginOfError",
      "label": "Margin of error",
      "format": "number",
      "digits": 6
    },
    {
      "id": "standardError",
      "label": "Standard error",
      "format": "number",
      "digits": 6
    },
    {
      "id": "criticalZ",
      "label": "Critical z-score",
      "format": "number",
      "digits": 6
    }
  ],
  "formula": {
    "expression": "CI=x̄±z*·σ/√n; margin of error=z*·σ/√n."
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "sampleSize": 100,
        "sampleMean": 50,
        "standardDeviation": 10,
        "confidenceLevel": 95
      }
    }
  ],
  "sources": [
    {
      "label": "Calculator.net reference calculator",
      "url": "https://www.calculator.net/confidence-interval-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"
    },
    {
      "label": "NIST: confidence interval with known standard deviation",
      "url": "https://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm"
    }
  ]
}