{
    "name": "Pythagorean Theorem Calculator",
    "url": "https://calculators.geekmidst.com/calculators/pythagorean-theorem-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/pythagorean-theorem-calculator.md",
    "category": "Algebra, geometry & advanced math",
    "description": "Solve a² + b² = c² for the missing side of a right triangle, with the working shown and a check for whole-number Pythagorean triples.",
    "summary": "In a right triangle the square on the hypotenuse equals the sum of the squares on the other two sides: a² + b² = c².",
    "also_called": [
        "Hypotenuse calculator",
        "a² + b² = c² calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "solve",
            "label": "Find",
            "type": "segmented",
            "default": "hyp",
            "options": {
                "hyp": "Hypotenuse c",
                "leg": "A leg"
            }
        },
        {
            "name": "a",
            "label": "Leg a",
            "type": "number",
            "default": "5",
            "shown_when": {
                "solve": "hyp"
            }
        },
        {
            "name": "b",
            "label": "Leg b",
            "type": "number",
            "default": "12",
            "shown_when": {
                "solve": "hyp"
            }
        },
        {
            "name": "known_leg",
            "label": "Known leg",
            "type": "number",
            "default": "5",
            "shown_when": {
                "solve": "leg"
            }
        },
        {
            "name": "c",
            "label": "Hypotenuse c",
            "type": "number",
            "default": "13",
            "shown_when": {
                "solve": "leg"
            }
        }
    ],
    "outputs": [
        {
            "key": "result",
            "label": "Missing side",
            "format": "number"
        },
        {
            "key": "working",
            "label": "Working",
            "format": "text"
        },
        {
            "key": "triple",
            "label": "Whole-number Pythagorean triple?",
            "format": "text"
        }
    ],
    "formula": {
        "text": "c = √(a² + b²);  a = √(c² − b²)",
        "variables": {
            "a, b": "the legs (the sides that meet at the right angle)",
            "c": "the hypotenuse, opposite the right angle"
        }
    },
    "worked_example": {
        "inputs": {
            "solve": "hyp",
            "a": "5",
            "b": "12",
            "known_leg": "5",
            "c": "13"
        },
        "steps": [
            "Square the legs: 5² = 25 and 12² = 144.",
            "Add them: 25 + 144 = 169.",
            "Take the square root: c = √169 = 13."
        ],
        "result": "A right triangle with legs 5 and 12 has a hypotenuse of 13, so 5, 12, 13 is a Pythagorean triple."
    },
    "interpretation": "The hypotenuse is always the longest side. Builders use the 3-4-5 triple to check that a corner is square: mark 3 units along one side and 4 along the other, and the diagonal should be exactly 5.",
    "assumptions": [
        "The triangle has a 90° angle between legs a and b."
    ],
    "limitations": [
        "For triangles without a right angle use the law of cosines."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Which side is the hypotenuse?",
            "answer": "The side opposite the right angle. It is always the longest side."
        },
        {
            "question": "What is a Pythagorean triple?",
            "answer": "Three whole numbers that satisfy a² + b² = c², such as 3-4-5, 5-12-13 and 8-15-17. Multiples such as 6-8-10 also work."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Right Triangle Calculator",
            "url": "https://calculators.geekmidst.com/calculators/right-triangle-calculator"
        },
        {
            "name": "Distance Calculator",
            "url": "https://calculators.geekmidst.com/calculators/distance-calculator"
        },
        {
            "name": "Root Calculator",
            "url": "https://calculators.geekmidst.com/calculators/root-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}