{
    "name": "Big Number Calculator",
    "url": "https://calculators.geekmidst.com/calculators/big-number-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/big-number-calculator.md",
    "category": "Mathematics",
    "description": "Add, subtract, multiply, divide, raise to powers and take remainders of numbers with thousands of digits, exactly and without rounding errors.",
    "summary": "Ordinary calculators keep about 15 to 16 significant digits. This one works on every digit you enter, so 2¹⁰⁰ or a 50-digit product comes out exactly.",
    "also_called": [
        "Large number calculator",
        "Arbitrary-precision 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": "a",
            "label": "X",
            "type": "textarea",
            "default": "2"
        },
        {
            "name": "op",
            "label": "Operation",
            "type": "select",
            "default": "pow",
            "options": {
                "add": "X + Y",
                "sub": "X − Y",
                "mul": "X × Y",
                "div": "X ÷ Y",
                "pow": "X to the power Y",
                "mod": "X mod Y (remainder)"
            }
        },
        {
            "name": "b",
            "label": "Y",
            "type": "textarea",
            "default": "100"
        },
        {
            "name": "dp",
            "label": "Decimal places for division",
            "type": "number",
            "default": "20",
            "optional": true
        }
    ],
    "outputs": [
        {
            "key": "result",
            "label": "Result",
            "format": "text"
        },
        {
            "key": "exactness",
            "label": "Precision",
            "format": "text"
        },
        {
            "key": "int_digits",
            "label": "Digits before the decimal point",
            "format": "integer"
        },
        {
            "key": "approx",
            "label": "Approximately",
            "format": "text"
        }
    ],
    "formula": {
        "text": "Each number is held as an integer of any length with a decimal scale: X = m ÷ 10ˢ. Addition, subtraction, multiplication and whole powers are exact; division rounds half up at the chosen decimal place",
        "variables": {
            "m": "all the digits as one integer",
            "s": "the number of decimal places"
        }
    },
    "worked_example": {
        "inputs": {
            "a": "2",
            "op": "pow",
            "b": "100",
            "dp": "20"
        },
        "steps": [
            "2¹⁰ = 1024, so 2¹⁰⁰ = 1024¹⁰, about 1.27 × 10³⁰.",
            "Multiplying out with every digit kept gives 1,267,650,600,228,229,401,496,703,205,376.",
            "That is 31 digits; ordinary double-precision arithmetic keeps only the first 16 or so (1.267650600228229 × 10³⁰)."
        ],
        "result": "2¹⁰⁰ = 1267650600228229401496703205376 exactly."
    },
    "interpretation": "Use this when the last digits matter: checking cryptography or number-theory examples, exact factorial-sized products, or showing that 0.1 + 0.2 is exactly 0.3 in decimal.",
    "assumptions": [
        "Mod uses truncated division, so the remainder has the sign of X (as in most programming languages)."
    ],
    "limitations": [
        "Results are limited to about 200,000 digits.",
        "Powers must be whole numbers; roots and logarithms are not supported."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why does my phone show 0.30000000000000004 for 0.1 + 0.2?",
            "answer": "Most software stores numbers in binary floating point, where 0.1 has no exact representation. This calculator stores decimal digits exactly."
        },
        {
            "question": "How precise is division?",
            "answer": "Division gives as many decimal places as you ask for, up to 1,000, rounded half up; the result is marked exact when the division terminates."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Scientific Notation Calculator",
            "url": "https://calculators.geekmidst.com/calculators/scientific-notation-calculator"
        },
        {
            "name": "Rounding Calculator",
            "url": "https://calculators.geekmidst.com/calculators/rounding-calculator"
        },
        {
            "name": "Long Division Calculator",
            "url": "https://calculators.geekmidst.com/calculators/long-division-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}