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Math API

20 endpoints for math workflows. Every call requires bearer authentication and uses the standard ToolsOnDuty response envelope.

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EndpointAPI key

expression *angleMode

POST/v1/math/evaluate1 credit / call

Expression evaluator

Safely evaluate a calculator expression (supports sin/cos/tan, sqrt, ln, log, exp, ^, %, !).

Parameter	Type	Required	Description
expression	string	Yes	Expression to evaluate, e.g. "sqrt(16)+2^3".
angleMode	string	No	deg \| rad. Default: deg.

Request

curl -X POST https://toolsonduty.com/api/v1/math/evaluate \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"expression":"sqrt(16)+2^3"}'

Response

{
  "ok": true,
  "data": {
    "result": 12
  }
}

POST/v1/math/average1 credit / call

Average / mean

Compute count, sum, mean, median, minimum and maximum for a list of numbers.

Parameter	Type	Required	Description
values	string	Yes	Array of numbers, e.g. [1,2,3].

Request

curl -X POST https://toolsonduty.com/api/v1/math/average \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"values":[1,2,3,4]}'

Response

{
  "ok": true,
  "data": {
    "count": 4,
    "sum": 10,
    "mean": 2.5,
    "median": 2.5,
    "minimum": 1,
    "maximum": 4
  }
}

POST/v1/math/percentage1 credit / call

Percentage calculations

Compute a percentage of a value, a part-of-whole ratio, or percentage change between two values.

Parameter	Type	Required	Description
mode	string	Yes	of \| ratio \| change.
a	number	Yes	mode=of: percentage; mode=ratio: part; mode=change: original value.
b	number	Yes	mode=of: value; mode=ratio: whole; mode=change: updated value.

Request

curl -X POST https://toolsonduty.com/api/v1/math/percentage \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"mode":"of","a":20,"b":150}'

Response

{
  "ok": true,
  "data": {
    "result": 30
  }
}

POST/v1/math/fraction1 credit / call

Fraction arithmetic

Add, subtract, multiply or divide two fractions and simplify the result.

Parameter	Type	Required	Description
firstNumerator	number	Yes	Numerator of the first fraction.
firstDenominator	number	Yes	Denominator of the first fraction.
secondNumerator	number	Yes	Numerator of the second fraction.
secondDenominator	number	Yes	Denominator of the second fraction.
operator	string	Yes	+ \| - \| * \| /.

Request

curl -X POST https://toolsonduty.com/api/v1/math/fraction \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"firstNumerator":1,"firstDenominator":2,"secondNumerator":1,"secondDenominator":3,"operator":"+"}'

Response

{
  "ok": true,
  "data": {
    "numerator": 5,
    "denominator": 6,
    "whole": 0,
    "remainder": 5,
    "decimal": 0.833
  }
}

POST/v1/math/statistics1 credit / call

Descriptive statistics

Compute mean, median, range, modes, variance and standard deviation (population and sample) for a list of numbers.

Parameter	Type	Required	Description
values	string	Yes	Array of numbers.

Request

curl -X POST https://toolsonduty.com/api/v1/math/statistics \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"values":[2,4,4,4,5,5,7,9]}'

Response

{
  "ok": true,
  "data": {
    "mean": 5,
    "populationStandardDeviation": 2
  }
}

POST/v1/math/ratio1 credit / call

Ratio simplification

Simplify a ratio of two whole numbers to lowest terms.

Parameter	Type	Required	Description
a	number	Yes	First whole number.
b	number	Yes	Second whole number.

Request

curl -X POST https://toolsonduty.com/api/v1/math/ratio \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"a":8,"b":12}'

Response

{
  "ok": true,
  "data": {
    "simplified": [
      2,
      3
    ]
  }
}

POST/v1/math/quadratic1 credit / call

Quadratic equation solver

Solve ax²+bx+c=0: discriminant, real or complex roots, and vertex.

Parameter	Type	Required	Description
a	number	Yes	Coefficient a (must not be zero).
b	number	Yes	Coefficient b.
c	number	Yes	Coefficient c.

Request

curl -X POST https://toolsonduty.com/api/v1/math/quadratic \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"a":1,"b":-3,"c":2}'

Response

{
  "ok": true,
  "data": {
    "discriminant": 1,
    "roots": [
      "2",
      "1"
    ],
    "vertexX": 1.5,
    "vertexY": -0.25
  }
}

POST/v1/math/power1 credit / call

Exponents and roots

Raise a number to a power, or compute its nth root.

Parameter	Type	Required	Description
mode	string	Yes	power \| root.
value	number	Yes	Base (mode=power) or radicand (mode=root).
n	number	Yes	Exponent (mode=power) or root degree, >=2 (mode=root).

Request

curl -X POST https://toolsonduty.com/api/v1/math/power \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"mode":"power","value":2,"n":10}'

Response

{
  "ok": true,
  "data": {
    "result": 1024
  }
}

POST/v1/math/round1 credit / call

Configurable rounding

Round a number to a given number of decimal places using nearest, up, down or truncate.

Parameter	Type	Required	Description
value	number	Yes	Value to round.
places	number	No	Decimal places, -10 to 10. Default: 0.
mode	string	No	nearest \| up \| down \| truncate. Default: nearest.

Request

curl -X POST https://toolsonduty.com/api/v1/math/round \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"value":3.14159,"places":2}'

Response

{
  "ok": true,
  "data": {
    "result": 3.14
  }
}

POST/v1/math/lcm1 credit / call

Least common multiple

Compute the least common multiple of a list of whole numbers.

Parameter	Type	Required	Description
values	string	Yes	Array of whole numbers (2+).

Request

curl -X POST https://toolsonduty.com/api/v1/math/lcm \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"values":[4,6]}'

Response

{
  "ok": true,
  "data": {
    "result": 12
  }
}

POST/v1/math/gcf1 credit / call

Greatest common factor

Compute the greatest common factor of a list of whole numbers.

Parameter	Type	Required	Description
values	string	Yes	Array of whole numbers (2+).

Request

curl -X POST https://toolsonduty.com/api/v1/math/gcf \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"values":[12,18]}'

Response

{
  "ok": true,
  "data": {
    "result": 6
  }
}

POST/v1/math/prime-factors1 credit / call

Prime factorization

Factorize a whole number (2 or more) into its prime factors with exponents.

Parameter	Type	Required	Description
value	number	Yes	Whole number, 2 or more.

Request

curl -X POST https://toolsonduty.com/api/v1/math/prime-factors \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"value":60}'

Response

{
  "ok": true,
  "data": {
    "factors": [
      {
        "prime": 2,
        "exponent": 2
      },
      {
        "prime": 3,
        "exponent": 1
      },
      {
        "prime": 5,
        "exponent": 1
      }
    ]
  }
}

POST/v1/math/random1 credit / call

Secure random integers

Generate secure random integers in an inclusive range, optionally without repeats.

Parameter	Type	Required	Description
minimum	number	Yes	Range minimum.
maximum	number	Yes	Range maximum.
count	number	No	How many to generate (1-1000). Default: 1.
unique	boolean	No	Disallow repeated values. Default: false.

Request

curl -X POST https://toolsonduty.com/api/v1/math/random \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"minimum":1,"maximum":100,"count":5}'

Response

{
  "ok": true,
  "data": {
    "values": [
      12,
      87,
      3,
      45,
      60
    ]
  }
}

POST/v1/math/probability1 credit / call

Probability calculations

Compute a single-event probability from favorable/total outcomes, or combine two independent probabilities with AND/OR.

Parameter	Type	Required	Description
mode	string	No	single \| combine. Default: single.
favorable	number	No	mode=single: favorable outcomes.
total	number	No	mode=single: total outcomes.
first	number	No	mode=combine: first probability (0-1).
second	number	No	mode=combine: second probability (0-1).
operation	string	No	mode=combine: and \| or. Default: and.

Request

curl -X POST https://toolsonduty.com/api/v1/math/probability \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"mode":"single","favorable":1,"total":6}'

Response

{
  "ok": true,
  "data": {
    "probability": 0.1667,
    "percentage": 16.67
  }
}

POST/v1/math/combinatorics1 credit / call

Permutations and combinations

Compute nPr (permutations) and nCr (combinations) for n items choosing r.

Parameter	Type	Required	Description
n	number	Yes	Total items.
r	number	Yes	Items chosen (0 <= r <= n).

Request

curl -X POST https://toolsonduty.com/api/v1/math/combinatorics \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"n":5,"r":2}'

Response

{
  "ok": true,
  "data": {
    "permutations": 20,
    "combinations": 10
  }
}

POST/v1/math/pythagorean1 credit / call

Right-triangle solver

Solve for the missing side, area and perimeter of a right triangle given two known sides.

Parameter	Type	Required	Description
firstSide	number	Yes	First known side.
secondSide	number	Yes	Second known side (or hypotenuse when mode=leg).
mode	string	No	hypotenuse \| leg. Default: hypotenuse.

Request

curl -X POST https://toolsonduty.com/api/v1/math/pythagorean \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"firstSide":3,"secondSide":4}'

Response

{
  "ok": true,
  "data": {
    "missingSide": 5,
    "area": 6,
    "perimeter": 12
  }
}

POST/v1/math/logarithm1 credit / call

Logarithm calculator

Compute a custom-base logarithm along with the natural (ln) and common (log10) logarithm.

Parameter	Type	Required	Description
argument	number	Yes	Value to take the logarithm of (must be > 0).
base	number	Yes	Logarithm base (must be > 0 and not 1).

Request

curl -X POST https://toolsonduty.com/api/v1/math/logarithm \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"argument":8,"base":2}'

Response

{
  "ok": true,
  "data": {
    "value": 3,
    "naturalLog": 2.079,
    "commonLog": 0.903
  }
}

POST/v1/math/fibonacci1 credit / call

Fibonacci generator

Generate a bounded Fibonacci-style safe-integer sequence.

Parameter	Type	Required	Description
count	number	Yes	Number of values from 1 to 1,000.
first	number	No	First integer. Default: 0.
second	number	No	Second integer. Default: 1.

Request

curl -X POST https://toolsonduty.com/api/v1/math/fibonacci \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"count":8}'

Response

{
  "ok": true,
  "data": {
    "values": [
      0,
      1,
      1,
      2,
      3,
      5,
      8,
      13
    ]
  }
}

POST/v1/math/truth-table1 credit / call

Truth table generator

Generate a Boolean truth table for !, &&, ||, ^ and parentheses with up to eight variables.

Parameter	Type	Required	Description
expression	string	Yes	Boolean expression, e.g. (A && B) \|\| !C.

Request

curl -X POST https://toolsonduty.com/api/v1/math/truth-table \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"expression":"A && B"}'

Response

{
  "ok": true,
  "data": {
    "expression": "A && B",
    "variables": [
      "A",
      "B"
    ],
    "rows": [
      {
        "values": {
          "A": false,
          "B": false
        },
        "result": false
      }
    ]
  }
}

POST/v1/math/roman1 credit / call

Roman numeral math

Add, subtract, multiply or divide canonical Roman numerals with results from 1 to 3999.

Parameter	Type	Required	Description
first	string	Yes	First Roman numeral.
operator	string	Yes	+ \| - \| * \| /.
second	string	Yes	Second Roman numeral.

Request

curl -X POST https://toolsonduty.com/api/v1/math/roman \
  -H "Authorization: ******" \
  -H "Content-Type: application/json" \
  -d '{"first":"XIV","operator":"+","second":"IX"}'

Response

{
  "ok": true,
  "data": {
    "first": 14,
    "second": 9,
    "result": 23,
    "roman": "XXIII"
  }
}