ForHosting KIT · Developer Utilities

Poisson probability calculator

The Poisson distribution models how many discrete events occur in a fixed interval when arrivals are independent and the average rate is constant.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Call centers track tickets per hour, reliability engineers count failures per month, and analysts measure clicks, defects, or rare biological events with the same two parameters: a non-negative rate lambda and an integer count k. This calculator returns the exact Poisson probability of observing k events, the cumulative probability of at most k events, and the theoretical mean and variance (both equal to lambda). Negative rates and negative counts are rejected with a clear validation error so malformed queueing or counting models never produce silent nonsense numbers. The arithmetic is fully deterministic, runs free in your browser, and is available over the API at $0.002 per successful request.

How to use it

Enter your values in the form above. The tool checks them before calculating and shows the result on the same page.

Check your inputs

Use the labels and units shown next to each field. If something is missing or outside the allowed range, the page points to the field to fix.

Use it again or automate it

Use the browser tool for individual checks and the API when you need the same capability in an automated workflow.

What you can do with it

Get an answer now

Enter one set of values and see the result without building a spreadsheet or script.

Compare scenarios

Change one value at a time and rerun the calculation to understand what affects the result.

Automate repeated work

Use the API when the same calculation needs to run inside your product or workflow.

FAQ

How do I use this capability?

Complete the fields above and run it on this page. The form highlights anything that needs attention.

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/prob/poisson-distribution

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/prob/poisson-distribution \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"lambda":2.5,"k":3}'

const res = await fetch("https://api.kit.forhosting.com/prob/poisson-distribution", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "lambda": 2.5,
    "k": 3
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/prob/poisson-distribution",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "lambda": 2.5,
    "k": 3
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/prob/poisson-distribution", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"lambda":2.5,"k":3}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"lambda":2.5,"k":3}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/prob/poisson-distribution", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "lambda": 2.5,
  "k": 3
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "prob.poisson_distribution",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Limits

`max_lambda`	1000
`max_k`	10000

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Read the full KIT documentation →

Run — free