{
  "id": "cube-root",
  "version": "cdf5c837b0e1",
  "status": "published",
  "name": "Cube Root Calculator",
  "question": "What is the cube root of a number?",
  "summary": "Finds the real cube root of any number, or the number from its cube root.",
  "category": "math",
  "subcategory": "arithmetic",
  "url": "https://www.acalculator.org/math/cube-root-calculator",
  "markdown": "https://www.acalculator.org/math/cube-root-calculator.md",
  "kind": "function",
  "method": "r = ∛x: the real number r with r³ = x.",
  "assumptions": [
    "Real numbers only. Every real number has exactly one real cube root, with the same sign.",
    "A whole number of up to 100 digits is read exactly: the perfect-cube check and the root of a perfect cube are exact at any such size.",
    "The simplified radical form is shown for whole numbers up to 10¹⁸ in size, and for every perfect cube.",
    "A decimal is read as a 64-bit float; a cube root within float error of a whole number is shown as that whole number."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "value": {
        "title": "Number (x)",
        "description": "The number to take the cube root of. A whole number keeps every digit.",
        "type": "string",
        "maxLength": 150
      },
      "answer": {
        "title": "Or its cube root",
        "description": "Leave the number empty and type a cube root to get the number back.",
        "type": "number"
      }
    }
  },
  "outputs": {
    "root": {
      "label": "Cube root",
      "description": "The real number that, cubed, gives the number.",
      "format": "number"
    },
    "number": {
      "label": "Number (x)",
      "description": "The number, with every digit as typed (or worked out from the root).",
      "format": "text"
    },
    "simplified": {
      "label": "Simplified radical form",
      "description": "For a whole number, ∛x written as k∛s with s as small as possible (∛16 = 2∛2).",
      "format": "text"
    },
    "perfect": {
      "label": "Perfect cube?",
      "description": "For a whole number, whether it is the cube of a whole number.",
      "format": "boolean"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "value": "8"
    },
    "outputs": {
      "root": 2,
      "number": "8",
      "simplified": "2",
      "perfect": true
    },
    "text": "The cube root of 8 is 2."
  },
  "examples": [
    {
      "given": {
        "value": "8"
      },
      "expect": {
        "root": 2,
        "perfect": true,
        "simplified": "2"
      },
      "source": "hand calculation in content.mdx: 2³ = 8; OpenStax, Intermediate Algebra 2e, §8.1 Simplify Expressions with Roots. https://openstax.org/books/intermediate-algebra-2e/pages/8-1-simplify-expressions-with-roots"
    },
    {
      "given": {
        "value": "-125"
      },
      "expect": {
        "root": -5,
        "simplified": "−5"
      },
      "source": "hand calculation in content.mdx: (−5)³ = −125; OpenStax, Intermediate Algebra 2e, §8.1 Simplify Expressions with Roots. https://openstax.org/books/intermediate-algebra-2e/pages/8-1-simplify-expressions-with-roots"
    },
    {
      "given": {
        "value": "1000000"
      },
      "expect": {
        "root": 100
      },
      "source": "hand calculation in content.mdx: 100³ = 1,000,000; OpenStax, Intermediate Algebra 2e, §8.1 Simplify Expressions with Roots. https://openstax.org/books/intermediate-algebra-2e/pages/8-1-simplify-expressions-with-roots"
    },
    {
      "given": {
        "value": "2"
      },
      "expect": {
        "root": 1.2599210498948732,
        "simplified": "∛2",
        "perfect": false
      },
      "source": "hand calculation in content.mdx: ∛2 = 1.25992105…; Python 3: 2 ** (1 / 3) = 1.2599210498948732; OpenStax, Intermediate Algebra 2e, §8.1 Simplify Expressions with Roots. https://openstax.org/books/intermediate-algebra-2e/pages/8-1-simplify-expressions-with-roots"
    },
    {
      "given": {
        "answer": 3
      },
      "expect": {
        "number": "27"
      },
      "source": "hand calculation in content.mdx: 3³ = 27; OpenStax, Intermediate Algebra 2e, §8.1 Simplify Expressions with Roots. https://openstax.org/books/intermediate-algebra-2e/pages/8-1-simplify-expressions-with-roots"
    }
  ],
  "sources": [
    "OpenStax, Intermediate Algebra 2e, §8.1 Simplify Expressions with Roots. https://openstax.org/books/intermediate-algebra-2e/pages/8-1-simplify-expressions-with-roots"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-28",
      "note": "A whole number is read exactly (BigInt) up to 100 digits; perfect-cube check and radical form (up to 10^18) added."
    },
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    }
  ]
}