Math Calculator API

A free, public REST API for computing percentages, fractions, derivatives, quadratic equations, standard deviation, slope, triangles, matrices, z-scores, binomial probability, normal distribution, and correlation. Returns structured JSON with step-by-step solutions and LaTeX notation.

v1CORS EnabledNo Auth RequiredRate Limited

Quick Start

Get started in seconds. Copy and paste this into your terminal to calculate 25% of 200:

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "percentage", "params": { "a": 25, "b": 200, "mode": "of" } }'

Response:

json

{
  "result": { "value": 50, "label": "25% of 200" },
  "steps": [
    "Convert percentage to decimal: 25 / 100 = 0.25",
    "Multiply by the number: 0.25 * 200 = 50"
  ],
  "latex": "\\frac{25}{100} \\times 200 = 50"
}

Key points:

All requests use POST with a JSON body
No authentication or API key required
CORS is enabled for browser-based requests
Rate limit: 60 requests per minute per IP
Every response includes step-by-step solutions and LaTeX notation

Base URL

https://mathcalculator.org/api/v1

All requests are made via POST to /api/v1/calculate with a JSON body. Machine-readable documentation is available at GET /api/v1/docs.

Rate Limiting

The API enforces a rate limit of 60 requests per minute per IP address using a sliding window. Exceeding the limit returns a 429 Too Many Requests response.

Header	Description
X-RateLimit-Limit	Maximum requests per window (60)
X-RateLimit-Remaining	Requests remaining in current window
X-RateLimit-Reset	Unix timestamp (seconds) when the window resets
Retry-After	Seconds to wait before retrying (only on 429 responses)

Request Format

json

POST /api/v1/calculate
Content-Type: application/json

{
  "type": "percentage | fraction | derivative | quadratic | standard-deviation | slope | triangle | matrix | z-score | binomial | normal-distribution | correlation",
  "params": { ... }
}

type (string, required) -- the calculator to use. One of 12 supported types.

params (object, required) -- parameters for the calculation. Shape varies by type (see sections below).

Response Format

json

{
  "result": { ... },
  "steps": ["Step 1", "Step 2", "..."],
  "latex": "\\frac{25}{100} \\times 200 = 50"
}

result -- the computed answer (shape depends on calculator type).

steps -- array of human-readable step-by-step explanations.

latex -- LaTeX string for rendering the solution.

Percentage Calculator

Five modes: of, is, change, difference, reverse.

Parameter	Type	Required	Description
a	number	Yes	First value (percentage for "of" mode, value for "is" mode, original for "change" mode)
b	number	Yes	Second value (number for "of" mode, total for "is" mode, new value for "change" mode)
mode	string	No	"of" \| "is" \| "change" \| "difference" \| "reverse" (default: "of")

Example: What is 25% of 200?

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "percentage", "params": { "a": 25, "b": 200, "mode": "of" } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "percentage",
    "params": { "a": 25, "b": 200, "mode": "of" }
})
data = response.json()
print(data["result"]["value"])  # 50

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "percentage",
    params: { a: 25, b: 200, mode: "of" }
  })
});
const data = await response.json();
console.log(data.result.value); // 50

Sample Response

json

{
  "result": { "value": 50, "label": "25% of 200" },
  "steps": [
    "Convert percentage to decimal: 25 / 100 = 0.25",
    "Multiply by the number: 0.25 * 200 = 50"
  ],
  "latex": "\\frac{25}{100} \\times 200 = 50"
}

Fraction Calculator

Operations: add, subtract, multiply, divide, simplify. Results are always returned in simplest form.

Parameter	Type	Required	Description
num1	integer	Yes	Numerator of first fraction
den1	integer	Yes	Denominator of first fraction (cannot be 0)
num2	integer	No	Numerator of second fraction (not needed for "simplify")
den2	integer	No	Denominator of second fraction (not needed for "simplify", cannot be 0)
operation	string	No	"add" \| "subtract" \| "multiply" \| "divide" \| "simplify" (default: "add")

Example: Add 1/3 + 1/6

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "fraction", "params": { "num1": 1, "den1": 3, "num2": 1, "den2": 6, "operation": "add" } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "fraction",
    "params": {
        "num1": 1, "den1": 3,
        "num2": 1, "den2": 6,
        "operation": "add"
    }
})
data = response.json()
print(data["result"]["display"])  # "1/2"

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "fraction",
    params: { num1: 1, den1: 3, num2: 1, den2: 6, operation: "add" }
  })
});
const data = await response.json();
console.log(data.result.display); // "1/2"

Sample Response

json

{
  "result": { "numerator": 1, "denominator": 2, "display": "1/2" },
  "steps": [
    "Find the LCD of 3 and 6: LCD = 6",
    "Convert: 1*2/6 + 1*1/6 = 2/6 + 1/6",
    "Add numerators: (2 + 1) / 6 = 3/6",
    "Simplify by dividing by GCD (3): 1/2"
  ],
  "latex": "\\frac{1}{3} + \\frac{1}{6} = \\frac{1}{2}"
}

Derivative Calculator

Symbolic differentiation powered by mathjs. Supports higher-order derivatives up to 10th order.

Parameter	Type	Required	Description
expression	string	Yes	Mathematical expression (e.g. "x^3 + 2x^2 - 5x"). Max 500 characters.
variable	string	No	Variable to differentiate with respect to (default: "x")
order	integer	No	Derivative order, 1-10 (default: 1)

Example: Derivative of x^3 + 2x^2 - 5x

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "derivative", "params": { "expression": "x^3 + 2*x^2 - 5*x", "variable": "x" } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "derivative",
    "params": {
        "expression": "x^3 + 2*x^2 - 5*x",
        "variable": "x"
    }
})
data = response.json()
print(data["result"]["derivative"])  # "3 * x ^ 2 + 4 * x - 5"

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "derivative",
    params: { expression: "x^3 + 2*x^2 - 5*x", variable: "x" }
  })
});
const data = await response.json();
console.log(data.result.derivative); // "3 * x ^ 2 + 4 * x - 5"

Sample Response

json

{
  "result": {
    "derivative": "3 * x ^ 2 + 4 * x - 5",
    "order": 1
  },
  "steps": [
    "1st derivative: 3 * x ^ 2 + 4 * x - 5"
  ],
  "latex": "\\frac{d}{dx}\\left[x^3 + 2*x^2 - 5*x\\right] = 3 * x ^ 2 + 4 * x - 5"
}

Quadratic Equation Solver

Solves ax² + bx + c = 0. Returns roots (real or complex), discriminant, vertex, and axis of symmetry.

Parameter	Type	Required	Description
a	number	Yes	Coefficient of x-squared (must not be 0)
b	number	Yes	Coefficient of x
c	number	Yes	Constant term

Example: Solve x² - 5x + 6 = 0

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "quadratic", "params": { "a": 1, "b": -5, "c": 6 } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "quadratic",
    "params": { "a": 1, "b": -5, "c": 6 }
})
data = response.json()
roots = data["result"]["roots"]
print(f"x1 = {roots['x1']}, x2 = {roots['x2']}")  # x1 = 3, x2 = 2

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "quadratic",
    params: { a: 1, b: -5, c: 6 }
  })
});
const data = await response.json();
console.log(data.result.roots); // { x1: 3, x2: 2, type: "two-real" }

Sample Response

json

{
  "result": {
    "roots": { "x1": 3, "x2": 2, "type": "two-real" },
    "discriminant": 1,
    "vertex": { "x": 2.5, "y": -0.25 },
    "axisOfSymmetry": 2.5
  },
  "steps": [
    "Standard form: 1x^2 + -5x + 6 = 0",
    "Discriminant: b^2 - 4ac = -5^2 - 4*1*6 = 1",
    "sqrt(discriminant) = 1",
    "x1 = (--5 + 1) / (2 * 1) = 3",
    "x2 = (--5 - 1) / (2 * 1) = 2",
    "Vertex: (2.5, -0.25)"
  ],
  "latex": "x = \\frac{--5 \\pm \\sqrt{1}}{2}"
}

Standard Deviation Calculator

Calculate mean, variance, and standard deviation for a data set. Supports both population and sample standard deviation.

Parameter	Type	Required	Description
values	string \| number[]	Yes	Comma-separated numbers (e.g. "10,20,30") or array (e.g. [10,20,30]). Minimum 2 values.
type	string	No	"population" \| "sample" (default: "population")

Example: Population standard deviation of [10, 20, 30, 40, 50]

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "standard-deviation", "params": { "values": [10, 20, 30, 40, 50], "type": "population" } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "standard-deviation",
    "params": {
        "values": [10, 20, 30, 40, 50],
        "type": "population"
    }
})
data = response.json()
print(data["result"]["standardDeviation"])  # 14.142135624

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "standard-deviation",
    params: { values: [10, 20, 30, 40, 50], type: "population" }
  })
});
const data = await response.json();
console.log(data.result.standardDeviation); // 14.142135624

Sample Response

json

{
  "result": {
    "mean": 30,
    "variance": 200,
    "standardDeviation": 14.142135624,
    "count": 5,
    "type": "population"
  },
  "steps": [
    "Values: [10, 20, 30, 40, 50] (n = 5)",
    "Mean: (10 + 20 + 30 + 40 + 50) / 5 = 30",
    "Squared differences from mean: [400, 100, 0, 100, 400]",
    "Sum of squared differences: 1000",
    "Population variance: 1000 / 5 = 200",
    "Standard deviation: sqrt(200) = 14.142135624"
  ],
  "latex": "\\sigma = \\sqrt{\\frac{\\sum(x_i - \\bar{x})^2}{N}} = 14.142135624"
}

Slope Calculator

Calculate slope, y-intercept, distance, and line equation from two points.

Parameter	Type	Required	Description
x1	number	Yes	x-coordinate of first point
y1	number	Yes	y-coordinate of first point
x2	number	Yes	x-coordinate of second point
y2	number	Yes	y-coordinate of second point

Example: Slope between (1, 2) and (4, 8)

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "slope", "params": { "x1": 1, "y1": 2, "x2": 4, "y2": 8 } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "slope",
    "params": { "x1": 1, "y1": 2, "x2": 4, "y2": 8 }
})
data = response.json()
print(data["result"]["slope"])     # 2
print(data["result"]["equation"])  # "y = 2x + 0"

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "slope",
    params: { x1: 1, y1: 2, x2: 4, y2: 8 }
  })
});
const data = await response.json();
console.log(data.result.slope);    // 2
console.log(data.result.equation); // "y = 2x + 0"

Sample Response

json

{
  "result": {
    "slope": 2,
    "yIntercept": 0,
    "distance": 6.708203933,
    "equation": "y = 2x + 0"
  },
  "steps": [
    "Point 1: (1, 2)",
    "Point 2: (4, 8)",
    "Rise: 6, Run: 3",
    "Slope (m): 6 / 3 = 2",
    "y-intercept (b): 2 - 2 * 1 = 0",
    "Equation: y = 2x + 0",
    "Distance: sqrt(3^2 + 6^2) = 6.708203933"
  ],
  "latex": "m = \\frac{y_2 - y_1}{x_2 - x_1} = \\frac{6}{3} = 2"
}

Triangle Calculator

Calculate area (Heron's formula), perimeter, and angles of a triangle given three side lengths.

Parameter	Type	Required	Description
a	number	Yes	Length of side a (must be positive)
b	number	Yes	Length of side b (must be positive)
c	number	Yes	Length of side c (must be positive)

Example: Triangle with sides 3, 4, 5

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "triangle", "params": { "a": 3, "b": 4, "c": 5 } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "triangle",
    "params": { "a": 3, "b": 4, "c": 5 }
})
data = response.json()
print(data["result"]["area"])       # 6
print(data["result"]["perimeter"])  # 12

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "triangle",
    params: { a: 3, b: 4, c: 5 }
  })
});
const data = await response.json();
console.log(data.result.area);      // 6
console.log(data.result.perimeter); // 12

Sample Response

json

{
  "result": {
    "area": 6,
    "perimeter": 12,
    "semiPerimeter": 6,
    "angles": { "A": 36.8698976, "B": 53.1301024, "C": 90 }
  },
  "steps": [
    "Sides: a = 3, b = 4, c = 5",
    "Perimeter: 3 + 4 + 5 = 12",
    "Semi-perimeter (s): 12 / 2 = 6",
    "Area (Heron's formula): sqrt(6 * 3 * 2 * 1) = 6",
    "Angle A: 36.87 degrees",
    "Angle B: 53.13 degrees",
    "Angle C: 90 degrees"
  ],
  "latex": "A = \\sqrt{s(s-a)(s-b)(s-c)} = 6"
}

Matrix Calculator

Matrix operations: determinant, transpose, or inverse. Supports matrices up to 5x5.

Parameter	Type	Required	Description
matrixA	number[][]	Yes	Matrix as 2D array of numbers (e.g. [[1,2],[3,4]]). Max 5x5.
operation	string	No	"determinant" \| "transpose" \| "inverse" (default: "determinant")

Example: Determinant of a 2x2 matrix

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "matrix", "params": { "matrixA": [[1, 2], [3, 4]], "operation": "determinant" } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "matrix",
    "params": {
        "matrixA": [[1, 2], [3, 4]],
        "operation": "determinant"
    }
})
data = response.json()
print(data["result"]["determinant"])  # -2

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "matrix",
    params: { matrixA: [[1, 2], [3, 4]], operation: "determinant" }
  })
});
const data = await response.json();
console.log(data.result.determinant); // -2

Sample Response

json

{
  "result": { "determinant": -2, "operation": "determinant" },
  "steps": [
    "Input matrix (2x2): [[1, 2], [3, 4]]",
    "det = (1 * 4) - (2 * 3)",
    "det = 4 - 6 = -2"
  ],
  "latex": "\\det(A) = -2"
}

Example: Inverse of a 2x2 matrix

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "matrix", "params": { "matrixA": [[4, 7], [2, 6]], "operation": "inverse" } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "matrix",
    "params": {
        "matrixA": [[4, 7], [2, 6]],
        "operation": "inverse"
    }
})
data = response.json()
print(data["result"]["matrix"])  # [[0.6, -0.7], [-0.2, 0.4]]

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "matrix",
    params: { matrixA: [[4, 7], [2, 6]], operation: "inverse" }
  })
});
const data = await response.json();
console.log(data.result.matrix); // [[0.6, -0.7], [-0.2, 0.4]]

Sample Response

json

{
  "result": { "matrix": [[0.6, -0.7], [-0.2, 0.4]], "operation": "inverse" },
  "steps": [
    "Input matrix (2x2): [[4, 7], [2, 6]]",
    "Determinant = 10",
    "For 2x2: A^(-1) = (1/det) * [[d, -b], [-c, a]]",
    "A^(-1) = (1/10) * [[6, -7], [-2, 4]]",
    "Result: [[0.6, -0.7], [-0.2, 0.4]]"
  ],
  "latex": "A^{-1} = \\begin{pmatrix} 0.6 & -0.7 \\\\ -0.2 & 0.4 \\end{pmatrix}"
}

Z-Score Calculator

Calculate the z-score (standard score) and approximate percentile for a value given a mean and standard deviation.

Parameter	Type	Required	Description
value	number	Yes	The observed value (x)
mean	number	Yes	Population mean (mu)
stddev	number	Yes	Population standard deviation (sigma, must be positive)

Example: Z-score for value 85, mean 70, stddev 10

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "z-score", "params": { "value": 85, "mean": 70, "stddev": 10 } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "z-score",
    "params": { "value": 85, "mean": 70, "stddev": 10 }
})
data = response.json()
print(data["result"]["zScore"])      # 1.5
print(data["result"]["percentile"])  # 93.32

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "z-score",
    params: { value: 85, mean: 70, stddev: 10 }
  })
});
const data = await response.json();
console.log(data.result.zScore);     // 1.5
console.log(data.result.percentile); // 93.32

Sample Response

json

{
  "result": {
    "zScore": 1.5,
    "percentile": 93.319279891,
    "value": 85,
    "mean": 70,
    "stddev": 10
  },
  "steps": [
    "Value (x): 85",
    "Mean (mu): 70",
    "Standard deviation (sigma): 10",
    "Z-score: (x - mu) / sigma = (85 - 70) / 10 = 1.5",
    "Percentile (approx): 93.32%"
  ],
  "latex": "z = \\frac{x - \\mu}{\\sigma} = \\frac{85 - 70}{10} = 1.5"
}

Binomial Probability Calculator

Calculate the probability of exactly k successes in n independent Bernoulli trials, plus cumulative probability P(X <= k), expected value, and variance.

Parameter	Type	Required	Description
n	integer	Yes	Number of trials (0-170)
k	integer	Yes	Number of successes (0 to n)
p	number	Yes	Probability of success per trial (0 to 1)

Example: P(X = 3) for n=10 trials, p=0.5

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "binomial", "params": { "n": 10, "k": 3, "p": 0.5 } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "binomial",
    "params": { "n": 10, "k": 3, "p": 0.5 }
})
data = response.json()
print(data["result"]["probability"])  # 0.1171875
print(data["result"]["cumulative"])   # 0.171875

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "binomial",
    params: { n: 10, k: 3, p: 0.5 }
  })
});
const data = await response.json();
console.log(data.result.probability); // 0.1171875
console.log(data.result.cumulative);  // 0.171875

Sample Response

json

{
  "result": {
    "probability": 0.1171875,
    "cumulative": 0.171875,
    "expectedValue": 5,
    "variance": 2.5,
    "stddev": 1.5811388301,
    "n": 10, "k": 3, "p": 0.5
  },
  "steps": [
    "n (trials): 10, k (successes): 3, p (probability): 0.5",
    "C(n,k) = C(10,3) = 120",
    "P(X = 3) = C(10,3) * 0.5^3 * 0.5^7 = 0.1171875",
    "P(X <= 3) = 0.171875",
    "Expected value: n * p = 10 * 0.5 = 5",
    "Variance: n * p * (1 - p) = 2.5",
    "Standard deviation: sqrt(variance) = 1.5811388301"
  ],
  "latex": "P(X = 3) = \\binom{10}{3} \\cdot 0.5^{3} \\cdot 0.5^{7} = 0.1171875"
}

Normal Distribution Calculator

Evaluate the probability density function (PDF) and cumulative distribution function (CDF) for a normal distribution at a given point.

Parameter	Type	Required	Description
mean	number	Yes	Mean of the distribution (mu)
stddev	number	Yes	Standard deviation (sigma, must be positive)
x	number	Yes	Point at which to evaluate

Example: PDF and CDF for x=75, mean=70, stddev=10

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "normal-distribution", "params": { "mean": 70, "stddev": 10, "x": 75 } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "normal-distribution",
    "params": { "mean": 70, "stddev": 10, "x": 75 }
})
data = response.json()
print(data["result"]["pdf"])  # 0.0352065327
print(data["result"]["cdf"])  # 0.6914624613

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "normal-distribution",
    params: { mean: 70, stddev: 10, x: 75 }
  })
});
const data = await response.json();
console.log(data.result.pdf); // 0.0352065327
console.log(data.result.cdf); // 0.6914624613

Sample Response

json

{
  "result": {
    "pdf": 0.0352065327,
    "cdf": 0.6914624613,
    "zScore": 0.5,
    "mean": 70,
    "stddev": 10,
    "x": 75
  },
  "steps": [
    "Mean (mu): 70",
    "Standard deviation (sigma): 10",
    "Value (x): 75",
    "Z-score: (75 - 70) / 10 = 0.5",
    "PDF: f(x) = (1 / (sigma * sqrt(2*pi))) * e^(-z^2/2) = 0.0352065327",
    "CDF: P(X <= 75) = 0.6914624613"
  ],
  "latex": "f(x) = \\frac{1}{10\\sqrt{2\\pi}} e^{-\\frac{1}{2}\\left(\\frac{75 - 70}{10}\\right)^2} = 0.0352065327"
}

Correlation Calculator

Compute Pearson correlation coefficient (r), R-squared, and linear regression line (slope and intercept) for paired data sets.

Parameter	Type	Required	Description
xValues	number[]	Yes	Array of x-values (at least 2, max 1000)
yValues	number[]	Yes	Array of y-values (same length as xValues)

Example: Correlation between [1,2,3,4,5] and [2,4,5,4,5]

curl

bash

curl -X POST https://mathcalculator.org/api/v1/calculate \
  -H "Content-Type: application/json" \
  -d '{ "type": "correlation", "params": { "xValues": [1,2,3,4,5], "yValues": [2,4,5,4,5] } }'

Python

python

import requests

response = requests.post("https://mathcalculator.org/api/v1/calculate", json={
    "type": "correlation",
    "params": {
        "xValues": [1, 2, 3, 4, 5],
        "yValues": [2, 4, 5, 4, 5]
    }
})
data = response.json()
print(data["result"]["r"])         # 0.7745966692
print(data["result"]["rSquared"])  # 0.6

JavaScript

javascript

const response = await fetch("https://mathcalculator.org/api/v1/calculate", {
  method: "POST",
  headers: { "Content-Type": "application/json" },
  body: JSON.stringify({
    type: "correlation",
    params: { xValues: [1, 2, 3, 4, 5], yValues: [2, 4, 5, 4, 5] }
  })
});
const data = await response.json();
console.log(data.result.r);        // 0.7745966692
console.log(data.result.rSquared); // 0.6

Sample Response

json

{
  "result": {
    "r": 0.7745966692,
    "rSquared": 0.6,
    "slope": 0.6,
    "intercept": 2.2,
    "n": 5,
    "meanX": 3,
    "meanY": 4
  },
  "steps": [
    "n = 5",
    "Mean of x: 3, Mean of y: 4",
    "SS_xx = 10, SS_yy = 6, SS_xy = 6",
    "Pearson r = 6 / sqrt(60) = 0.7745966692",
    "R-squared = 0.6",
    "Regression slope (b) = 0.6",
    "Regression intercept (a) = 2.2",
    "Regression line: y = 0.6x + 2.2"
  ],
  "latex": "r = \\frac{\\sum(x_i - \\bar{x})(y_i - \\bar{y})}{\\sqrt{\\sum(x_i - \\bar{x})^2 \\cdot \\sum(y_i - \\bar{y})^2}} = 0.7745966692"
}

Error Handling

Errors return a JSON object with an error field and an appropriate HTTP status code.

Status	Meaning	When
400	Bad Request	Invalid JSON, missing fields, validation errors, unsupported type
429	Too Many Requests	Rate limit exceeded (60 req/min per IP)

400 Bad Request -- Missing type

json

// Request: POST /api/v1/calculate  { "params": { "a": 1 } }

{ "error": "Missing required field \"type\"." }

400 Bad Request -- Unsupported type

json

// Request: { "type": "integral", "params": {} }

{
  "error": "Unsupported calculator type \"integral\". Supported types: percentage, fraction, derivative, quadratic, standard-deviation, slope, triangle, matrix, z-score, binomial, normal-distribution, correlation."
}

400 Bad Request -- Validation error

json

// Request: { "type": "percentage", "params": { "a": "abc", "b": 100 } }

{ "error": "Parameters \"a\" and \"b\" must be valid numbers." }

400 Bad Request -- Invalid JSON

json

// Request body is not valid JSON

{ "error": "Invalid JSON body." }

429 Rate Limit Exceeded

json

// Headers: Retry-After: 23

{ "error": "Too many requests. Please try again later." }

Tip: Always check for the error field in the response body. When rate-limited, use the Retry-After header to determine when to retry.

mathcalculator.org

Math Calculator API

Table of Contents

Quick Start

Base URL

Rate Limiting

Request Format

Response Format

Percentage Calculator

Example: What is 25% of 200?

Sample Response

Fraction Calculator

Example: Add 1/3 + 1/6

Sample Response

Derivative Calculator

Example: Derivative of x^3 + 2*x^2 - 5*x

Sample Response

Quadratic Equation Solver

Example: Solve x² - 5x + 6 = 0

Sample Response

Standard Deviation Calculator

Example: Population standard deviation of [10, 20, 30, 40, 50]

Sample Response

Slope Calculator

Example: Slope between (1, 2) and (4, 8)

Sample Response

Triangle Calculator

Example: Triangle with sides 3, 4, 5

Sample Response

Matrix Calculator

Example: Determinant of a 2x2 matrix

Sample Response

Example: Inverse of a 2x2 matrix

Sample Response

Z-Score Calculator

Example: Z-score for value 85, mean 70, stddev 10

Sample Response

Binomial Probability Calculator

Example: P(X = 3) for n=10 trials, p=0.5

Sample Response

Normal Distribution Calculator

Example: PDF and CDF for x=75, mean=70, stddev=10

Sample Response

Correlation Calculator

Example: Correlation between [1,2,3,4,5] and [2,4,5,4,5]

Sample Response

Error Handling

400 Bad Request -- Missing type

400 Bad Request -- Unsupported type

400 Bad Request -- Validation error

400 Bad Request -- Invalid JSON

429 Rate Limit Exceeded

Example: Derivative of x^3 + 2x^2 - 5x