{
  "id": "z-score-calculator",
  "version": "2.0.0",
  "name": "Z-score Calculator",
  "shortName": "Z-score",
  "description": "Calculate a z-score, convert between z and normal probability, or find probability between two z-scores.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "z score",
    "standard score",
    "normal probability",
    "z table",
    "inverse normal",
    "normal distribution"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "migrated",
  "migratedDate": "2026-08-25",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/z-score-calculator.json",
    "qualifiedReview": "pending",
    "qualifiedReviewer": null,
    "qualifiedReviewDate": null,
    "formulaVersion": "2.0.0",
    "referenceCoverage": "references-listed",
    "releaseTestScope": "Catalog and regression checks are not a professional formula audit; consult release evidence.",
    "historicalMetadataDate": "2026-08-25",
    "historicalMetadataNotice": "The imported date is not evidence of a completed human review."
  },
  "urls": {
    "page": "/calculator/z-score-calculator/",
    "definition": "/calculator/z-score-calculator/definition.json",
    "schema": "/calculator/z-score-calculator/schema.json",
    "llms": "/calculator/z-score-calculator/llms.txt",
    "legacyDefinition": "/calculator/z-score-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/z-score-calculator/?mode=raw-score&rawScore=85&mean=75&standardDeviation=10",
  "queryParameters": {
    "mode": {
      "label": "Calculation",
      "type": "select",
      "required": true,
      "default": "raw-score"
    },
    "rawScore": {
      "label": "Raw score (x)",
      "type": "number",
      "required": true,
      "default": 85,
      "showWhen": {
        "field": "mode",
        "equals": "raw-score"
      }
    },
    "mean": {
      "label": "Population mean (μ)",
      "type": "number",
      "required": true,
      "default": 75,
      "showWhen": {
        "field": "mode",
        "equals": "raw-score"
      }
    },
    "standardDeviation": {
      "label": "Standard deviation (σ)",
      "type": "number",
      "required": true,
      "default": 10,
      "showWhen": {
        "field": "mode",
        "equals": "raw-score"
      }
    },
    "zValue": {
      "label": "Z-score",
      "type": "number",
      "required": true,
      "default": 1,
      "showWhen": {
        "field": "mode",
        "equals": "z-to-probability"
      }
    },
    "leftProbability": {
      "label": "Left-tail probability P(X<z)",
      "type": "number",
      "required": true,
      "default": 0.841344746,
      "showWhen": {
        "field": "mode",
        "equals": "probability-to-z"
      }
    },
    "leftZ": {
      "label": "Left z-score",
      "type": "number",
      "required": true,
      "default": -1,
      "showWhen": {
        "field": "mode",
        "equals": "between"
      }
    },
    "rightZ": {
      "label": "Right z-score",
      "type": "number",
      "required": true,
      "default": 1,
      "showWhen": {
        "field": "mode",
        "equals": "between"
      }
    }
  },
  "inputs": [
    {
      "id": "mode",
      "label": "Calculation",
      "type": "select",
      "required": true,
      "defaultValue": "raw-score",
      "options": [
        {
          "label": "Raw score to z-score",
          "value": "raw-score"
        },
        {
          "label": "Z-score to probabilities",
          "value": "z-to-probability"
        },
        {
          "label": "Left-tail probability to z-score",
          "value": "probability-to-z"
        },
        {
          "label": "Probability between two z-scores",
          "value": "between"
        }
      ],
      "width": "full"
    },
    {
      "id": "rawScore",
      "label": "Raw score (x)",
      "type": "number",
      "required": true,
      "defaultValue": 85,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "raw-score"
      },
      "width": "full"
    },
    {
      "id": "mean",
      "label": "Population mean (μ)",
      "type": "number",
      "required": true,
      "defaultValue": 75,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "raw-score"
      },
      "width": "half"
    },
    {
      "id": "standardDeviation",
      "label": "Standard deviation (σ)",
      "type": "number",
      "required": true,
      "defaultValue": 10,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "raw-score"
      },
      "width": "half"
    },
    {
      "id": "zValue",
      "label": "Z-score",
      "type": "number",
      "required": true,
      "defaultValue": 1,
      "step": 0.001,
      "showWhen": {
        "field": "mode",
        "equals": "z-to-probability"
      },
      "width": "full"
    },
    {
      "id": "leftProbability",
      "label": "Left-tail probability P(X<z)",
      "type": "number",
      "required": true,
      "defaultValue": 0.841344746,
      "min": 1e-9,
      "max": 0.999999999,
      "step": 0.0001,
      "showWhen": {
        "field": "mode",
        "equals": "probability-to-z"
      },
      "width": "full"
    },
    {
      "id": "leftZ",
      "label": "Left z-score",
      "type": "number",
      "required": true,
      "defaultValue": -1,
      "step": 0.001,
      "showWhen": {
        "field": "mode",
        "equals": "between"
      },
      "width": "half"
    },
    {
      "id": "rightZ",
      "label": "Right z-score",
      "type": "number",
      "required": true,
      "defaultValue": 1,
      "step": 0.001,
      "showWhen": {
        "field": "mode",
        "equals": "between"
      },
      "width": "half"
    }
  ],
  "outputs": [
    {
      "id": "zScore",
      "label": "Z-score",
      "format": "number",
      "primary": true,
      "digits": 6
    },
    {
      "id": "probabilityLess",
      "label": "P(X < z)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "probabilityGreater",
      "label": "P(X > z)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "probabilityMeanToZ",
      "label": "Area between mean and z",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "probabilityCentral",
      "label": "P(−|z| < X < |z|)",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "probabilityTwoTail",
      "label": "Outside ±|z|",
      "format": "percent",
      "digits": 6
    },
    {
      "id": "betweenProbability",
      "label": "Probability between bounds",
      "format": "percent",
      "digits": 6
    }
  ],
  "formula": {
    "expression": "z=(x−μ)/σ; probabilities use the standard-normal CDF Φ(z); inverse conversion uses z=Φ⁻¹(p)."
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "mode": "raw-score",
        "rawScore": 85,
        "mean": 75,
        "standardDeviation": 10,
        "zValue": 1,
        "leftProbability": 0.841344746,
        "leftZ": -1,
        "rightZ": 1
      }
    }
  ],
  "sources": [
    {
      "label": "Calculator.net reference calculator",
      "url": "https://www.calculator.net/z-score-calculator.html"
    }
  ]
}