Averages, spread, chi-square, regression, primes, factorials, probability, areas and distances
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Calculates the arithmetic mean (average) of a list of numbers by summing all values and dividing by the count. (cost: 1 credit)
array, required, list of numeric values, no unit, no default
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Authorization (optional, not in the config above): Optional. Bearer <key> for more than the free daily allowance; free key from POST https://ukdata.reliness.co.uk/keysCalculates the arithmetic mean (average) of a list of numbers by summing all values and dividing by the count. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| numbers | any | array, required, list of numeric values, no unit, no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"numbers": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array, required, list of numeric values, no unit, no default"
}
}
}Calculates the area of geometric shapes including circle (πr²), triangle (½×base×height), rectangle (length×width), and square (side²). Returns area in square units. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| shape | string | string, required, shape type (circle/triangle/rectangle/square), no unit, no default |
| measurements | string | object, required, shape-specific measurements (radius/base/height/length/width/side), appropriate units, no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"shape": {
"type": "string",
"description": "string, required, shape type (circle/triangle/rectangle/square), no unit, no default"
},
"measurements": {
"type": "string",
"description": "object, required, shape-specific measurements (radius/base/height/length/width/side), appropriate units, no default"
}
}
}Calculates the smaller angle in degrees between the hour and minute hands of an analog clock given the time. Returns angle between 0 and 180 degrees. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| hour | string | integer, required, hour value (0-23 or 1-12) |
| minute | string | integer, required, minute value (0-59) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"hour": {
"type": "string",
"description": "integer, required, hour value (0-23 or 1-12)"
},
"minute": {
"type": "string",
"description": "integer, required, minute value (0-59)"
}
}
}Calculates the great-circle distance between two geographic points using the Haversine formula. Returns distance in kilometers, miles, or nautical miles. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| lat1 | number | string | number, required, latitude of first point, decimal degrees, no default |
| lat2 | number | string | number, required, latitude of second point, decimal degrees, no default |
| lon1 | number | string | number, required, longitude of first point, decimal degrees, no default |
| lon2 | number | string | number, required, longitude of second point, decimal degrees, no default |
| unit | string | string, optional, unit of measurement (km/miles/nautical), no unit, default km |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"lat1": {
"type": [
"number",
"string"
],
"description": "number, required, latitude of first point, decimal degrees, no default"
},
"lat2": {
"type": [
"number",
"string"
],
"description": "number, required, latitude of second point, decimal degrees, no default"
},
"lon1": {
"type": [
"number",
"string"
],
"description": "number, required, longitude of first point, decimal degrees, no default"
},
"lon2": {
"type": [
"number",
"string"
],
"description": "number, required, longitude of second point, decimal degrees, no default"
},
"unit": {
"type": "string",
"description": "string, optional, unit of measurement (km/miles/nautical), no unit, default km"
}
}
}Calculates the median (middle value) of a list of numbers. For even-length lists, returns the average of the two middle values. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| numbers | any | array of numbers, required, list of numeric values to find the median of |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"numbers": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of numbers, required, list of numeric values to find the median of"
}
}
}Calculates the population standard deviation of a list of numbers using the standard formula: sqrt(Σ(x - μ)² / N). (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| numbers | any | array, required, list of numeric values, no unit, no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"numbers": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array, required, list of numeric values, no unit, no default"
}
}
}Performs a Chi-Square test for independence on a 2x2 contingency table. Returns the chi-square statistic, p-value, and whether to reject the null hypothesis at the given significance level. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| contingency_table | string | 2D array, required, 2x2 table of observed frequencies [[a, b], [c, d]] |
| significance_level | number | string | number, required, significance level for the test (e.g., 0.05 for 5%) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"contingency_table": {
"type": "string",
"description": "2D array, required, 2x2 table of observed frequencies [[a, b], [c, d]]"
},
"significance_level": {
"type": [
"number",
"string"
],
"description": "number, required, significance level for the test (e.g., 0.05 for 5%)"
}
}
}Calculates the cosine similarity between two vectors, returning a value between -1 and 1 where 1 indicates identical direction. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| vector_a | any | array of numbers, required, the first vector |
| vector_b | any | array of numbers, required, the second vector (must be same length as vector_a) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"vector_a": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of numbers, required, the first vector"
},
"vector_b": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of numbers, required, the second vector (must be same length as vector_a)"
}
}
}Creates a histogram by counting the frequency of data points falling into specified bins or ranges. Returns the frequency count for each bin. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| bins | string | integer or array, required, number of bins or array of bin edges |
| data | any | array of numbers, required, data points to create histogram from |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"bins": {
"type": "string",
"description": "integer or array, required, number of bins or array of bin edges"
},
"data": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of numbers, required, data points to create histogram from"
}
}
}Calculates the probability of rolling a specific sum with a given number of dice, each with a specified number of faces. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| num_dice | string | integer, required, number of dice to roll |
| num_faces | string | integer, required, number of faces on each die |
| target_sum | string | integer, required, the desired sum to calculate probability for |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"num_dice": {
"type": "string",
"description": "integer, required, number of dice to roll"
},
"num_faces": {
"type": "string",
"description": "integer, required, number of faces on each die"
},
"target_sum": {
"type": "string",
"description": "integer, required, the desired sum to calculate probability for"
}
}
}Computes the Euclidean distance between two points in a 2D plane using the formula: sqrt((x2-x1)² + (y2-y1)²). (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| point_a | any | array of two numbers, required, coordinates of first point [x, y] |
| point_b | any | array of two numbers, required, coordinates of second point [x, y] |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"point_a": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of two numbers, required, coordinates of first point [x, y]"
},
"point_b": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of two numbers, required, coordinates of second point [x, y]"
}
}
}Calculates the factorial of a non-negative integer n, which is the product of all positive integers less than or equal to n. Returns n! = n × (n-1) × ... × 1. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| number | string | integer, required, non-negative integer to calculate factorial of |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"number": {
"type": "string",
"description": "integer, required, non-negative integer to calculate factorial of"
}
}
}Generates the first n numbers in the Fibonacci sequence, where each number is the sum of the two preceding ones, starting with 0 and 1. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| n | string | integer, required, number of Fibonacci numbers to generate (must be positive) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"n": {
"type": "string",
"description": "integer, required, number of Fibonacci numbers to generate (must be positive)"
}
}
}Computes the greatest common divisor (GCD) of two non-negative integers using the Euclidean algorithm. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| a | string | integer, required, the first non-negative integer |
| b | string | integer, required, the second non-negative integer |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"a": {
"type": "string",
"description": "integer, required, the first non-negative integer"
},
"b": {
"type": "string",
"description": "integer, required, the second non-negative integer"
}
}
}Checks if a number is a power of two (2^n for some non-negative integer n). (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| num | string | integer, required, the number to check |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"num": {
"type": "string",
"description": "integer, required, the number to check"
}
}
}Checks if a positive integer is a prime number (only divisible by 1 and itself). Returns false for numbers less than 2. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| num | string | integer, required, the number to test for primality, no units, no default |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"num": {
"type": "string",
"description": "integer, required, the number to test for primality, no units, no default"
}
}
}Computes the least common multiple (LCM) of two positive integers using the relationship LCM(a,b) = (a × b) / GCD(a,b). (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| a | string | integer, required, the first positive integer |
| b | string | integer, required, the second positive integer |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"a": {
"type": "string",
"description": "integer, required, the first positive integer"
},
"b": {
"type": "string",
"description": "integer, required, the second positive integer"
}
}
}Predicts the y-value for a given x-value using simple linear regression (least squares method) fitted to the provided data points. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| target_x | number | string | number, required, the x-value for which to predict y |
| x_values | any | array of numbers, required, the x-coordinates of data points |
| y_values | any | array of numbers, required, the y-coordinates of data points (same length as x_values) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"target_x": {
"type": [
"number",
"string"
],
"description": "number, required, the x-value for which to predict y"
},
"x_values": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of numbers, required, the x-coordinates of data points"
},
"y_values": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of numbers, required, the y-coordinates of data points (same length as x_values)"
}
}
}Calculates the number of permutations P(n,k) = n!/(n-k)! representing ordered arrangements of k elements selected from n elements. Returns the count as an integer. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| k | string | integer, required, number of elements to select (must be 0 ≤ k ≤ n) |
| n | string | integer, required, total number of elements (must be non-negative) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"k": {
"type": "string",
"description": "integer, required, number of elements to select (must be 0 ≤ k ≤ n)"
},
"n": {
"type": "string",
"description": "integer, required, total number of elements (must be non-negative)"
}
}
}Calculates the area of a polygon given its vertices using the shoelace formula (also known as the surveyor's formula). (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| vertices | any | array of [x, y] coordinate pairs, required, the vertices of the polygon in order |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"vertices": {
"anyOf": [
{
"type": "array",
"items": {
"type": "string"
}
},
{
"type": "string"
}
],
"description": "array of [x, y] coordinate pairs, required, the vertices of the polygon in order"
}
}
}Calculates the probability of rolling a specific value consecutively for a given number of rolls on a die with specified sides using the formula (1/num_sides)^num_rolls. Returns probability as a decimal between 0 and 1. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| num_rolls | string | integer, required, number of consecutive rolls (must be positive) |
| num_sides | string | integer, required, number of sides on the die (must be positive) |
| target_value | string | integer, required, the target value to roll (must be between 1 and num_sides) |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"num_rolls": {
"type": "string",
"description": "integer, required, number of consecutive rolls (must be positive)"
},
"num_sides": {
"type": "string",
"description": "integer, required, number of sides on the die (must be positive)"
},
"target_value": {
"type": "string",
"description": "integer, required, the target value to roll (must be between 1 and num_sides)"
}
}
}Computes the real and complex roots of a quadratic equation ax² + bx + c = 0 using the quadratic formula. Returns both roots or indicates if no real solutions exist. (cost: 1 credit)
| Argument | Type | Description |
|---|---|---|
| a | number | string | number, required, coefficient of x² term (must be non-zero) |
| b | number | string | number, required, coefficient of x term |
| c | number | string | number, required, constant term |
{
"type": "object",
"$schema": "http://json-schema.org/draft-07/schema#",
"properties": {
"a": {
"type": [
"number",
"string"
],
"description": "number, required, coefficient of x² term (must be non-zero)"
},
"b": {
"type": [
"number",
"string"
],
"description": "number, required, coefficient of x term"
},
"c": {
"type": [
"number",
"string"
],
"description": "number, required, constant term"
}
}
}We read every tool's name, description and inputs the way the model will, looking for instructions hidden from you. A clean result means no warning signs, not a guarantee. Scanned Nov 7, 2026.