BrainyCalc Docs — Mathematics

API Reference

Mathematics

12 deterministic math tools covering arithmetic, algebra, statistics, geometry, and trigonometry. All tools use the math_* prefix and return verified, reproducible results.

math_evaluate math_percentage math_statistics math_quadratic math_gcd_lcm math_prime_factors math_power_root math_permutations_combinations math_simplify_fraction math_geometry math_trigonometry math_logarithm

math_evaluate

Safely evaluates an arithmetic expression string. Supports +, −, *, /, %, ^, and parentheses.

arithmetic

Parameter	Type	Required	Description
`expression`	string	required	Arithmetic expression, e.g. `(12 + 8) * 3 / 2`

Request / Response

// Request
{ "expression": "(12 + 8) * 3 / 2" }

// Response
{
  "expression": "(12 + 8) * 3 / 2",
  "result": 30
}

math_percentage

Percentage of, what percent is, percentage change, and percentage difference — four modes in one tool.

percentages

Parameter	Type	Required	Description
`mode`	enum	required	`percentage_of` · `what_percent_is` · `percentage_change` · `percentage_difference`
`a`	number	required	First number
`b`	number	required	Second number

Request / Response

// "What is 15% of 200?"
{ "mode": "percentage_of", "a": 15, "b": 200 }

{ "mode": "percentage_of", "inputA": 15, "inputB": 200, "result": 30 }

math_statistics

Descriptive statistics for a dataset: count, sum, mean, median, mode, min, max, range, variance, and standard deviation.

statistics

Parameter	Type	Required	Description
`numbers`	number[]	required	Non-empty array of numbers to analyze

Request / Response

{ "numbers": [4, 8, 6, 5, 3, 2, 8, 9, 2, 5] }

{
  "count": 10, "sum": 52, "mean": 5.2,
  "median": 5, "mode": [2, 5, 8],
  "min": 2, "max": 9, "range": 7,
  "variance": 5.16, "stdDev": 2.2716
}

math_quadratic

Solves ax² + bx + c = 0. Returns real roots, a single root, or complex conjugate roots depending on the discriminant.

algebra

Parameter	Type	Required	Description
`a`	number	required	Coefficient a (must not be zero)
`b`	number	required	Coefficient b
`c`	number	required	Coefficient c

Request / Response

// Solve x² - 5x + 6 = 0
{ "a": 1, "b": -5, "c": 6 }

{
  "type": "two_real_roots",
  "discriminant": 1,
  "root1": 3,
  "root2": 2
}

Return types

two_real_roots when discriminant > 0 · one_real_root when = 0 · complex_roots when < 0

math_gcd_lcm

Calculates the Greatest Common Divisor (GCD) and Least Common Multiple (LCM) for two integers.

number theory

Parameter	Type	Required	Description
`a`	number	required	First integer
`b`	number	required	Second integer

Request / Response

{ "a": 48, "b": 18 }

{ "a": 48, "b": 18, "gcd": 6, "lcm": 144 }

math_prime_factors

Returns the prime factorization of an integer and whether the number itself is prime.

number theory

Parameter	Type	Required	Description
`number`	number	required	Positive integer to factorize

Request / Response

{ "number": 360 }

{
  "number": 360,
  "isPrime": false,
  "factors": [2, 2, 2, 3, 3, 5]
}

math_power_root

Computes powers (baseⁿ) or nth roots (ⁿ√base) of a number.

arithmetic

Parameter	Type	Required	Description
`base`	number	required	Base value
`exponent`	number	required	Exponent or root index
`mode`	enum	optional	`power` (default) or `root`

Request / Response

// Cube root of 27
{ "base": 27, "exponent": 3, "mode": "root" }

{ "base": 27, "rootIndex": 3, "result": 3 }

math_permutations_combinations

Calculates Factorial (n!), Permutations (nPr), and Combinations (nCr) in a single tool.

combinatorics

Parameter	Type	Required	Description
`n`	number	required	Total set size
`r`	number	optional	Sub-selection size (required for nPr and nCr)
`mode`	enum	optional	`nCr` (default) · `nPr` · `factorial`

Request / Response

// How many ways to choose 3 from 10?
{ "n": 10, "r": 3, "mode": "nCr" }

{ "n": 10, "r": 3, "nCr": 120 }

math_simplify_fraction

Reduces a fraction to its lowest terms and converts it to a mixed number and decimal.

fractions

Parameter	Type	Required	Description
`numerator`	number	required	Numerator
`denominator`	number	required	Denominator (must not be zero)

Request / Response

{ "numerator": 18, "denominator": 12 }

{
  "original": "18/12",
  "simplified": "3/2",
  "mixedFraction": "1 1/2",
  "decimal": 1.5
}

math_geometry

Area, perimeter, volume, and surface area for circle, rectangle, triangle, sphere, and cylinder.

geometry

Parameter	Type	Required	Description
`shape`	enum	required	`circle` · `rectangle` · `triangle` · `sphere` · `cylinder`
`dimensions`	object	required	Shape-specific dimension keys: `radius`, `length`, `width`, `height`, `base`

Request / Response

// Cylinder volume & surface area
{
  "shape": "cylinder",
  "dimensions": { "radius": 5, "height": 10 }
}

{
  "volume": 785.3982,
  "surfaceArea": 471.2389
}

math_trigonometry

sin, cos, tan, asin, acos, and atan — accepts degrees or radians.

trigonometry

Parameter	Type	Required	Description
`func`	enum	required	`sin` · `cos` · `tan` · `asin` · `acos` · `atan`
`angleValue`	number	required	Angle value (or input for inverse functions)
`unit`	enum	optional	`deg` (default) or `rad`

Request / Response

{ "func": "sin", "angleValue": 45, "unit": "deg" }

{
  "func": "sin", "angleValue": 45,
  "unit": "deg", "result": 0.707107
}

math_logarithm

Computes logarithm of a value in any base, including natural log (base e).

algebra

Parameter	Type	Required	Description
`value`	number	required	Positive number to take the log of
`base`	number	optional	Logarithm base (default 10). Pass `e` or `2.71828...` for natural log.

Request / Response

{ "value": 1000, "base": 10 }

{ "value": 1000, "base": 10, "result": 3 }