{
  "id": "right-triangle-calculator",
  "version": "2.0.0",
  "name": "Right Triangle Calculator",
  "shortName": "Right triangle",
  "description": "Solve a right triangle from two known values and calculate all sides, acute angles, altitude, area, and perimeter.",
  "category": "Math & Statistics",
  "categorySlug": "math-statistics",
  "keywords": [
    "right triangle",
    "triangle sides and angles",
    "hypotenuse",
    "right triangle area",
    "trigonometry",
    "altitude"
  ],
  "status": "live",
  "workStatus": "pending",
  "reviewStatus": "pending",
  "migrationStatus": "migrated",
  "migratedDate": "2026-08-25",
  "engine": "native",
  "creator": null,
  "reviewer": null,
  "quality": {
    "availability": "live",
    "technicalReviewRecord": "/reviews/right-triangle-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/right-triangle-calculator/",
    "definition": "/calculator/right-triangle-calculator/definition.json",
    "schema": "/calculator/right-triangle-calculator/schema.json",
    "llms": "/calculator/right-triangle-calculator/llms.txt",
    "legacyDefinition": "/calculator/right-triangle-calculator.json"
  },
  "queryExample": "https://askcalculators.com/calculator/right-triangle-calculator/?mode=legs&legA=3&legB=4&angleUnit=degrees",
  "queryParameters": {
    "mode": {
      "label": "Known values",
      "type": "select",
      "required": true,
      "default": "legs"
    },
    "legA": {
      "label": "Leg a",
      "type": "number",
      "required": true,
      "default": 3,
      "showWhen": {
        "field": "mode",
        "equals": "legs"
      }
    },
    "legB": {
      "label": "Leg b",
      "type": "number",
      "required": true,
      "default": 4,
      "showWhen": {
        "field": "mode",
        "equals": "legs"
      }
    },
    "knownLeg": {
      "label": "Known leg a",
      "type": "number",
      "required": true,
      "default": 3,
      "showWhen": {
        "field": "mode",
        "equals": "leg-hypotenuse"
      }
    },
    "knownHypotenuse": {
      "label": "Hypotenuse c",
      "type": "number",
      "required": true,
      "default": 5,
      "showWhen": {
        "field": "mode",
        "equals": "leg-hypotenuse"
      }
    },
    "angleHypotenuse": {
      "label": "Hypotenuse c",
      "type": "number",
      "required": true,
      "default": 5,
      "showWhen": {
        "field": "mode",
        "equals": "hypotenuse-angle"
      }
    },
    "angleAlpha": {
      "label": "Angle α",
      "type": "number",
      "required": true,
      "default": 36.869897,
      "showWhen": {
        "field": "mode",
        "equals": "hypotenuse-angle"
      }
    },
    "angleLeg": {
      "label": "Leg a",
      "type": "number",
      "required": true,
      "default": 3,
      "showWhen": {
        "field": "mode",
        "equals": "leg-angle"
      }
    },
    "legAngleAlpha": {
      "label": "Angle α",
      "type": "number",
      "required": true,
      "default": 36.869897,
      "showWhen": {
        "field": "mode",
        "equals": "leg-angle"
      }
    },
    "areaInput": {
      "label": "Area",
      "type": "number",
      "required": true,
      "default": 6,
      "showWhen": {
        "field": "mode",
        "equals": "area-leg"
      }
    },
    "areaLeg": {
      "label": "Leg a",
      "type": "number",
      "required": true,
      "default": 3,
      "showWhen": {
        "field": "mode",
        "equals": "area-leg"
      }
    },
    "angleUnit": {
      "label": "Angle input unit",
      "type": "select",
      "required": true,
      "default": "degrees"
    }
  },
  "inputs": [
    {
      "id": "mode",
      "label": "Known values",
      "type": "select",
      "required": true,
      "defaultValue": "legs",
      "options": [
        {
          "label": "Two legs (a and b)",
          "value": "legs"
        },
        {
          "label": "One leg and hypotenuse",
          "value": "leg-hypotenuse"
        },
        {
          "label": "Hypotenuse and angle α",
          "value": "hypotenuse-angle"
        },
        {
          "label": "Leg a and angle α",
          "value": "leg-angle"
        },
        {
          "label": "Area and leg a",
          "value": "area-leg"
        }
      ],
      "width": "full"
    },
    {
      "id": "legA",
      "label": "Leg a",
      "type": "number",
      "required": true,
      "defaultValue": 3,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "legs"
      },
      "width": "half"
    },
    {
      "id": "legB",
      "label": "Leg b",
      "type": "number",
      "required": true,
      "defaultValue": 4,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "legs"
      },
      "width": "half"
    },
    {
      "id": "knownLeg",
      "label": "Known leg a",
      "type": "number",
      "required": true,
      "defaultValue": 3,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "leg-hypotenuse"
      },
      "width": "half"
    },
    {
      "id": "knownHypotenuse",
      "label": "Hypotenuse c",
      "type": "number",
      "required": true,
      "defaultValue": 5,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "leg-hypotenuse"
      },
      "width": "half"
    },
    {
      "id": "angleHypotenuse",
      "label": "Hypotenuse c",
      "type": "number",
      "required": true,
      "defaultValue": 5,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "hypotenuse-angle"
      },
      "width": "half"
    },
    {
      "id": "angleAlpha",
      "label": "Angle α",
      "type": "number",
      "required": true,
      "defaultValue": 36.869897,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "hypotenuse-angle"
      },
      "width": "half"
    },
    {
      "id": "angleLeg",
      "label": "Leg a",
      "type": "number",
      "required": true,
      "defaultValue": 3,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "leg-angle"
      },
      "width": "half"
    },
    {
      "id": "legAngleAlpha",
      "label": "Angle α",
      "type": "number",
      "required": true,
      "defaultValue": 36.869897,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "leg-angle"
      },
      "width": "half"
    },
    {
      "id": "areaInput",
      "label": "Area",
      "type": "number",
      "required": true,
      "defaultValue": 6,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "area-leg"
      },
      "width": "half"
    },
    {
      "id": "areaLeg",
      "label": "Leg a",
      "type": "number",
      "required": true,
      "defaultValue": 3,
      "min": 0.000001,
      "step": 0.01,
      "showWhen": {
        "field": "mode",
        "equals": "area-leg"
      },
      "width": "half"
    },
    {
      "id": "angleUnit",
      "label": "Angle input unit",
      "type": "select",
      "required": true,
      "defaultValue": "degrees",
      "options": [
        {
          "label": "Degrees",
          "value": "degrees"
        },
        {
          "label": "Radians",
          "value": "radians"
        }
      ],
      "width": "full"
    }
  ],
  "outputs": [
    {
      "id": "sideA",
      "label": "Leg a",
      "format": "number",
      "primary": true,
      "digits": 6
    },
    {
      "id": "sideB",
      "label": "Leg b",
      "format": "number",
      "digits": 6
    },
    {
      "id": "hypotenuse",
      "label": "Hypotenuse c",
      "format": "number",
      "digits": 6
    },
    {
      "id": "angleAlphaResult",
      "label": "Angle α",
      "format": "number",
      "digits": 6,
      "suffix": "°"
    },
    {
      "id": "angleBetaResult",
      "label": "Angle β",
      "format": "number",
      "digits": 6,
      "suffix": "°"
    },
    {
      "id": "altitude",
      "label": "Altitude to hypotenuse",
      "format": "number",
      "digits": 6
    },
    {
      "id": "area",
      "label": "Area",
      "format": "number",
      "digits": 6
    },
    {
      "id": "perimeter",
      "label": "Perimeter",
      "format": "number",
      "digits": 6
    }
  ],
  "formula": {
    "expression": "a²+b²=c²; α=atan(a/b); β=90°−α; area=ab/2; altitude h=ab/c."
  },
  "examples": [
    {
      "label": "Reproducible default-input example (not a personal recommendation)",
      "inputs": {
        "mode": "legs",
        "legA": 3,
        "legB": 4,
        "knownLeg": 3,
        "knownHypotenuse": 5,
        "angleHypotenuse": 5,
        "angleAlpha": 36.869897,
        "angleLeg": 3,
        "legAngleAlpha": 36.869897,
        "areaInput": 6,
        "areaLeg": 3,
        "angleUnit": "degrees"
      }
    }
  ],
  "sources": [
    {
      "label": "Calculator.net reference calculator",
      "url": "https://www.calculator.net/right-triangle-calculator.html"
    }
  ]
}