Every request is made against:

https://math.tools/api/numbers

Every endpoint on this page requires a Sanctum personal access token — there is no free or anonymous tier. Subscribing to one of the plans below issues one automatically; sign in first if you haven't already. Manage or cancel an existing subscription from your subscriptions page. Send your token as a bearer token on every request:

Authorization: Bearer <your-token>

A missing or invalid token returns a 401:

{
  "error": { "code": 401, "message": "Unauthorized" }
}

A trivia fact about a number, if one is known — otherwise a fact derived from its number-theory properties (triangle, cube, square, and several classes of prime).

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 11,
    "fact": "11 is the fifth prime and first palindromic multi-digit number"
  }
}

One or more random integers in a range.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "numbers": [9, 4, 8, 4, 3],
    "min": 1,
    "max": 10,
    "requested": 5,
    "returned": 5
  }
}

Today's number of the day and its full set of properties, facts, and number systems — the same daily pick shown on the /numbers/number-of-the-day/ page.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "nod": {
      "category": {
        "name": "Number of the day",
        "description": "Number of the day and its properties, facts and anything else you may want to know about.",
        "background": ""
      },
      "numbers": {
        "number": "27982",
        "uuid": "27982",
        "id": "27982",
        "names": { "nominal": { "name": "nominal", "description": "Nominal", "value": 27982, "display": "27982" }, "...": "..." },
        "bases": { "binary": { "name": "binary", "description": "Base 2 (Binary)", "value": "110110101001110", "display": "110110101001110" }, "...": "..." },
        "numerals": { "roman": { "name": "roman", "description": "27982 in Roman numerals", "value": "...", "display": "..." }, "...": "..." },
        "general-facts": { "odd": { "name": "odd", "description": "Is 27982 an odd number?", "value": false, "display": "27982 is not an odd number" }, "...": "..." },
        "prime-facts": { "prime": { "name": "prime", "description": "Is 27982 a prime number?", "value": false, "display": "27982 is not a prime number" }, "...": "..." },
        "recreational": { "reverse": { "name": "reverse", "description": "Number 27982 reversed", "value": "28972", "display": "28972" }, "...": "..." },
        "category": "nod"
      }
    }
  }
}

Spells a number out in words. Also available at /api/numbers/words (identical response).

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 2342,
    "language": "en_US",
    "result": "two thousand three hundred forty-two",
    "cardinal": "two thousand three hundred forty-two"
  }
}

The English ordinal form of a number (1st, 2nd, 3rd, ...), with the same thousands-separator formatting as every other spelled-out number on this page. English only — there is no lang parameter.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 2342,
    "result": "2,342nd",
    "ordinal": "2,342nd"
  }
}

Spells a number out as a currency amount.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 1345456654,
    "language": "en_US",
    "result": "one billion three hundred forty-five million four hundred fifty-six thousand six hundred fifty-four dollars",
    "currency": "one billion three hundred forty-five million four hundred fifty-six thousand six hundred fifty-four dollars"
  }
}

Converts a base-10 number to a Roman numeral.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 4568367,
    "system": "roman",
    "result": "DLXVMMMCCCLXVII"
  }
}

Converts a base-10 number to a Chinese numeral.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 4568367,
    "system": "chinese",
    "result": "伍拾萬陸萬捌仟叄佰陸拾柒"
  }
}

Converts a base-10 number to an Egyptian numeral.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 4568367,
    "system": "egyptian",
    "result": "𓁨𓁨𓁨𓁨𓆐𓆐𓆐𓆐𓆐𓂲𓇃𓍤𓎋𓐀"
  }
}

Converts a base-10 number to a Babylonian (sexagesimal) numeral — returned as plain comma-separated base-60 digits (e.g. "1,1,1"), not a cuneiform-glyph rendering.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 3661,
    "system": "babylonian",
    "result": "1,1,1"
  }
}

Converts a base-10 number to a Mayan (vigesimal) numeral, using the real Unicode Mayan Numerals block (U+1D2E0-U+1D2F3).

The greatest common factor (GCF/GCD) of two or more numbers.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "numbers": [12, 18, 24],
    "answer": 6
  }
}

The least common multiple (LCM) of two or more numbers.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "numbers": [4, 6],
    "answer": 12
  }
}

The first N prime numbers.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "count": 5,
    "numbers": [2, 3, 5, 7, 11]
  }
}

The first N composite numbers.

The first N palindromic numbers.

A slice of the digits of pi.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "from": 0,
    "to": 100,
    "result": "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679",
    "number": "pi"
  }
}

Converts a number from any base to any other base (2-64).

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 88,
    "base": { "from": 10, "to": 12 },
    "answer": "74"
  }
}

Converts a number to binary (base 2). Shorthand for /api/numbers/base?to=2.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 32,
    "base": { "from": 10, "to": 2 },
    "answer": "100000"
  }
}

Converts a number to octal (base 8). Shorthand for /api/numbers/base?to=8.

Converts a number to hexadecimal (base 16). Shorthand for /api/numbers/base?to=16.

Is this number prime?

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": { "number": 17, "answer": true }
}

Is this a composite number (a positive integer with a factor other than 1 and itself)?

Is this number odd?

Is this number even?

The prime factorization of a number, as a list of {factor, times} pairs.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": {
    "number": 60,
    "answer": [
      { "factor": 2, "times": 2 },
      { "factor": 3, "times": 1 },
      { "factor": 5, "times": 1 }
    ],
    "prime-factors": [
      { "factor": 2, "times": 2 },
      { "factor": 3, "times": 1 },
      { "factor": 5, "times": 1 }
    ]
  }
}

Is this number a palindrome (reads the same forwards and backwards)?

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": { "number": 456654, "answer": true }
}

Is this a triangle number?

Is this a perfect square?

Is this a perfect cube?

Is this a perfect number (equal to the sum of its proper divisors)?

Is this a known Mersenne prime?

Is this a known Fermat prime?

Is this a known Fibonacci prime?

Is this a known Pell prime?

Is this a known partition prime?

Is this an abundant number (its proper divisors sum to more than the number itself)?

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": { "number": 12, "answer": true }
}

Is this a deficient number (its proper divisors sum to less than the number itself)?

Is this number squarefree (not divisible by any perfect square other than 1 — equivalently, no repeated prime factors)?

Euler's totient function φ(n): how many integers from 1 to n are coprime with n. Requires n ≥ 1.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": { "number": 36, "answer": 12 }
}

How many positive divisors n has, including 1 and n itself. Requires n ≥ 1.

The sum of all positive divisors of n, including n itself. Requires n ≥ 1.

The sum of n's proper divisors (every divisor except n itself) — equal to n for a perfect number, greater for an abundant number, less for a deficient one. Requires n ≥ 1.

Are a and b coprime (their only common positive divisor is 1)? The only endpoint on this page that takes two numbers instead of one.

Example response

{
  "success": { "total": 1 },
  "copyright": { "copyright": "2019-26 https://math.tools" },
  "contents": { "a": 8, "b": 15, "answer": true }
}