{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "https://askcalculators.com/calculator/z-score-calculator/schema.json",
  "title": "Z-score Calculator inputs",
  "description": "Calculate a z-score, convert between z and normal probability, or find probability between two z-scores.",
  "type": "object",
  "properties": {
    "mode": {
      "title": "Calculation",
      "type": "string",
      "default": "raw-score",
      "enum": [
        "raw-score",
        "z-to-probability",
        "probability-to-z",
        "between"
      ],
      "x-optionLabels": {
        "raw-score": "Raw score to z-score",
        "z-to-probability": "Z-score to probabilities",
        "probability-to-z": "Left-tail probability to z-score",
        "between": "Probability between two z-scores"
      }
    },
    "rawScore": {
      "title": "Raw score (x)",
      "type": "number",
      "default": 85,
      "x-step": 0.01,
      "x-showWhen": {
        "field": "mode",
        "equals": "raw-score"
      }
    },
    "mean": {
      "title": "Population mean (μ)",
      "type": "number",
      "default": 75,
      "x-step": 0.01,
      "x-showWhen": {
        "field": "mode",
        "equals": "raw-score"
      }
    },
    "standardDeviation": {
      "title": "Standard deviation (σ)",
      "type": "number",
      "default": 10,
      "minimum": 0.000001,
      "x-step": 0.01,
      "x-showWhen": {
        "field": "mode",
        "equals": "raw-score"
      }
    },
    "zValue": {
      "title": "Z-score",
      "type": "number",
      "default": 1,
      "x-step": 0.001,
      "x-showWhen": {
        "field": "mode",
        "equals": "z-to-probability"
      }
    },
    "leftProbability": {
      "title": "Left-tail probability P(X<z)",
      "type": "number",
      "default": 0.841344746,
      "minimum": 1e-9,
      "maximum": 0.999999999,
      "x-step": 0.0001,
      "x-showWhen": {
        "field": "mode",
        "equals": "probability-to-z"
      }
    },
    "leftZ": {
      "title": "Left z-score",
      "type": "number",
      "default": -1,
      "x-step": 0.001,
      "x-showWhen": {
        "field": "mode",
        "equals": "between"
      }
    },
    "rightZ": {
      "title": "Right z-score",
      "type": "number",
      "default": 1,
      "x-step": 0.001,
      "x-showWhen": {
        "field": "mode",
        "equals": "between"
      }
    }
  },
  "required": [
    "mode"
  ],
  "allOf": [
    {
      "if": {
        "properties": {
          "mode": {
            "const": "raw-score"
          }
        },
        "required": [
          "mode"
        ]
      },
      "then": {
        "required": [
          "rawScore"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "mode": {
            "const": "raw-score"
          }
        },
        "required": [
          "mode"
        ]
      },
      "then": {
        "required": [
          "mean"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "mode": {
            "const": "raw-score"
          }
        },
        "required": [
          "mode"
        ]
      },
      "then": {
        "required": [
          "standardDeviation"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "mode": {
            "const": "z-to-probability"
          }
        },
        "required": [
          "mode"
        ]
      },
      "then": {
        "required": [
          "zValue"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "mode": {
            "const": "probability-to-z"
          }
        },
        "required": [
          "mode"
        ]
      },
      "then": {
        "required": [
          "leftProbability"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "mode": {
            "const": "between"
          }
        },
        "required": [
          "mode"
        ]
      },
      "then": {
        "required": [
          "leftZ"
        ]
      }
    },
    {
      "if": {
        "properties": {
          "mode": {
            "const": "between"
          }
        },
        "required": [
          "mode"
        ]
      },
      "then": {
        "required": [
          "rightZ"
        ]
      }
    }
  ],
  "additionalProperties": false,
  "x-askcalculators": {
    "version": "2.0.0",
    "calculatorUrl": "https://askcalculators.com/calculator/z-score-calculator/",
    "queryExample": "https://askcalculators.com/calculator/z-score-calculator/?mode=raw-score&rawScore=85&mean=75&standardDeviation=10",
    "migrationStatus": "migrated",
    "reviewStatus": "pending",
    "pageStatus": "live",
    "workStatus": "pending",
    "migratedDate": "2026-08-25",
    "formula": {
      "expression": "z=(x−μ)/σ; probabilities use the standard-normal CDF Φ(z); inverse conversion uses z=Φ⁻¹(p)."
    },
    "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."
    },
    "outputs": {
      "zScore": {
        "title": "Z-score",
        "type": "number",
        "x-format": "number",
        "x-digits": 6,
        "x-primary": true
      },
      "probabilityLess": {
        "title": "P(X < z)",
        "type": "number",
        "x-format": "percent",
        "x-digits": 6
      },
      "probabilityGreater": {
        "title": "P(X > z)",
        "type": "number",
        "x-format": "percent",
        "x-digits": 6
      },
      "probabilityMeanToZ": {
        "title": "Area between mean and z",
        "type": "number",
        "x-format": "percent",
        "x-digits": 6
      },
      "probabilityCentral": {
        "title": "P(−|z| < X < |z|)",
        "type": "number",
        "x-format": "percent",
        "x-digits": 6
      },
      "probabilityTwoTail": {
        "title": "Outside ±|z|",
        "type": "number",
        "x-format": "percent",
        "x-digits": 6
      },
      "betweenProbability": {
        "title": "Probability between bounds",
        "type": "number",
        "x-format": "percent",
        "x-digits": 6
      }
    }
  }
}