Solve permutations and combinations without writing custom math.
Calculate permutations (P(n,r)) and combinations (C(n,r)) for any given values of n and r.
Try it — live request, no key required
No key required to try it. Get a key to use it in your app.
{
"status": "ok",
"error": null,
"data": {
"n": 10,
"r": 3,
"permutation": 720,
"combination": 120,
"formulas": {
"permutation": "P(n,r) = n! / (n-r)!",
"combination": "C(n,r) = n! / (r! × (n-r)!)"
}
}
}
About the Permutation & Combination Calculator API
Perfect for probability calculations, statistics problems, and combinatorial analysis in mathematics.
What people use it for
- Education
- Solve permutation and combination problems for homework and exams
- Probability
- Calculate odds and probabilities in statistics
- Programming
- Determine algorithm complexity and counting problems
- Game Design
- Calculate possible combinations for game mechanics
Ways to call it
One endpoint, many ways in — REST with JSON, XML, YAML and CSV, plus GraphQL and an MCP interface for AI agents.
- JSON
- Default REST response
- XML
- Markup format
- YAML
- Human-readable
- CSV
- Tabular export
- GraphQL
- Query language
- MCP
- For AI agents
Other ways to use Permutation & Combination Calculator
Same data, same APIVerve account, same credit balance — one key works on all of them.
Does a single request calculate both permutations and combinations?
Can I set the number of chosen items higher than the total items?
Are the mathematical formulas included on the Free plan?
Does the calculator accept decimal or negative numbers?
Which plan fits 50,000 combinatorial calculations a month?
Request parameters — GET /v1/permutationcombination
Sent in the query string. Premium parameters are accepted on every plan but only take effect on plans that include them. Anything not listed here is dropped rather than passed through.
Required
| Parameter | Type | Example | Description |
|---|---|---|---|
nRequired | integer | 10 | Total number of items range 0-170 |
rRequired | integer | 3 | Number of items to choose (must be <= n) range 0-170 |
curl "https://api.apiverve.com/v1/permutationcombination?n=10&r=3" \
-H "x-api-key: YOUR_API_KEY"Authentication
Send your key in the x-api-key header. That is the only auth step — no token exchange, and no per-endpoint scope to configure.
| Header | When | Value |
|---|---|---|
x-api-keyRequired | Every request | Your API key. Header names are case-insensitive, so X-API-Key is the same header. |
AuthorizationAlternate | Instead of the above | Bearer <key> — for clients that only expose bearer auth. Resolves to the same account and the same billing. |
A 401 means the key is missing, invalid or expired. A 403 means the key is valid but not permitted here — blocked by a key restriction or an IP allow-list. Running out of credits is a 429.
Response — GET /v1/permutationcombination
Every APIVerve endpoint returns the same three top-level keys, so one response handler covers your whole integration: status, error and data. Only data changes shape.
{
"status": "ok",
"error": null,
"data": {
"n": 10,
"r": 3,
"permutation": 720,
"combination": 120,
"formulas": {
"permutation": "P(n,r) = n! / (n-r)!",
"combination": "C(n,r) = n! / (r! × (n-r)!)"
}
}
}
Response fields
Paths are relative to data. Premium fields are absent rather than zeroed on plans that do not include them, so check for presence instead of comparing to 0.
| Field | Type | Example | Description |
|---|---|---|---|
n | number | 10 | Total number of items used in calculation |
r | number | 3 | Number of items chosen in calculation |
permutation | number | 720 | Calculated permutation P(n,r) result value |
combination | number | 120 | Calculated combination C(n,r) result value |
formulasPremium | object | {...} | Object containing mathematical formulas for permutation and combination |
permutationPremium | string | "P(n,r) = n! / (n-r)!" | Mathematical formula used for permutation calculation |
combinationPremium | string | "C(n,r) = n! / (r! × (n-r)!)" | Mathematical formula used for combination calculation |
Response headers
Every response carries your balance, so your own code always knows where it stands without polling anything. All four are exposed to browsers through CORS.
| Header | What it carries |
|---|---|
x-api-remaining-credits | Credits left in the current cycle |
x-api-credits-used | Credits spent in the current cycle |
x-api-max-credits | The allowance for the cycle |
x-api-version | Version of the endpoint that answered |
Errors
Read the HTTP status first, then error for the specific reason. The body names the parameter that has to change.
| Status | Meaning | What to do |
|---|---|---|
400 | Input was rejected | Read error; it names the parameter that has to change. |
401 | Key missing or invalid | Check the header name and the key value. |
403 | Key valid, but not permitted here | A key restriction or an IP allow-list — never a bad key. |
429 | Rate limited, or out of credits | Read error to tell them apart, then back off or top up. |
What a call costs — 2 credits per call
Credits are shared across every APIVerve API — one balance, one key, one bill. Failed requests never count against it, so a rejected input costs nothing.
| Plan | Per month | Credits | Permutation & Combination Calculator calls | Per 1,000 calls |
|---|---|---|---|---|
| Free | Free | 200 | 100 | Free |
| Starter | $29.99 | 200,000 | 100,000 | $0.30 |
| Pro | $99.99 | 1,000,000 | 500,000 | $0.20 |
| Mega | $299.99 | 4,000,000 | 2,000,000 | $0.15 |
Calls are what the credits buy at this API's rate — spend them here, on any of the other APIs, or across both. Nothing is reserved per endpoint.
Call it from cURL — GET /v1/permutationcombination
No SDK to install — this is a plain HTTPS call to /v1/permutationcombination with your key in the x-api-key header. Swap in a real key and it runs as-is.
curl "https://api.apiverve.com/v1/permutationcombination" \
-H "x-api-key: YOUR_API_KEY"Resources
Also published for
Only the languages APIVerve ships a client for are listed — the rest call the endpoint directly over HTTPS.
Call it from Node.js — GET /v1/permutationcombination
Install the Node.js SDK, then call the Permutation & Combination Calculator API with your key. The client wraps the same HTTPS request, so anything it returns is what the endpoint returns.
npm install @apiverve/permutationcombinationconst res = await fetch("https://api.apiverve.com/v1/permutationcombination", {
headers: { "x-api-key": "YOUR_API_KEY" },
});
const { data } = await res.json();
console.log(data);Resources
Also published for
Only the languages APIVerve ships a client for are listed — the rest call the endpoint directly over HTTPS.
Call it from Python — GET /v1/permutationcombination
No SDK to install — this is a plain HTTPS call to /v1/permutationcombination with your key in the x-api-key header. Swap in a real key and it runs as-is.
import requests
res = requests.get(
"https://api.apiverve.com/v1/permutationcombination",
headers={"x-api-key": "YOUR_API_KEY"},
)
print(res.json()["data"])Resources
Also published for
Only the languages APIVerve ships a client for are listed — the rest call the endpoint directly over HTTPS.
Call it from C# / .NET — GET /v1/permutationcombination
Install the C# / .NET SDK, then call the Permutation & Combination Calculator API with your key. The client wraps the same HTTPS request, so anything it returns is what the endpoint returns.
dotnet add package APIVerve.API.PermutationCombinationCalculatorusing var client = new HttpClient();
client.DefaultRequestHeaders.Add("x-api-key", "YOUR_API_KEY");
var json = await client.GetStringAsync("https://api.apiverve.com/v1/permutationcombination");
Console.WriteLine(json);Resources
Also published for
Only the languages APIVerve ships a client for are listed — the rest call the endpoint directly over HTTPS.
Call it from Go — GET /v1/permutationcombination
No SDK to install — this is a plain HTTPS call to /v1/permutationcombination with your key in the x-api-key header. Swap in a real key and it runs as-is.
req, _ := http.NewRequest("GET", "https://api.apiverve.com/v1/permutationcombination", nil)
req.Header.Set("x-api-key", "YOUR_API_KEY")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))Resources
Also published for
Only the languages APIVerve ships a client for are listed — the rest call the endpoint directly over HTTPS.
Call it from PHP — GET /v1/permutationcombination
No SDK to install — this is a plain HTTPS call to /v1/permutationcombination with your key in the x-api-key header. Swap in a real key and it runs as-is.
$ch = curl_init("https://api.apiverve.com/v1/permutationcombination");
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ["x-api-key: YOUR_API_KEY"]);
$response = curl_exec($ch);
echo $response;Resources
Also published for
Only the languages APIVerve ships a client for are listed — the rest call the endpoint directly over HTTPS.
Call it from Ruby — GET /v1/permutationcombination
No SDK to install — this is a plain HTTPS call to /v1/permutationcombination with your key in the x-api-key header. Swap in a real key and it runs as-is.
require "net/http"
uri = URI("https://api.apiverve.com/v1/permutationcombination")
req = Net::HTTP::Get.new(uri)
req["x-api-key"] = "YOUR_API_KEY"
res = Net::HTTP.start(uri.hostname, uri.port, use_ssl: true) { |h| h.request(req) }
puts res.bodyResources
Also published for
Only the languages APIVerve ships a client for are listed — the rest call the endpoint directly over HTTPS.
Zero-code embed — one snippet, no backend
Drop an interactive Permutation & Combination Calculator form onto any page. The widget calls the API for you, so no key ever appears in your markup and there is nothing to deploy.
Changelog — Permutation & Combination Calculator API
Every change to this endpoint, newest first. Breaking changes ship as a new version and the previous one keeps serving — response fields are added, never removed or retyped in place, so an integration written against v1 keeps working.
Entries are picked up from dated catalog snapshots, so the first one appears after the next snapshot that moves something. A period where nothing changed produces no entry — silence is a valid changelog for the Permutation & Combination Calculator API.
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