ForHosting KIT · Developer Utilities

Bayes theorem calculator

The Bayes theorem calculator turns a prior probability, a sensitivity (true positive rate), and a false-positive rate into the posterior probability of a hypothesis after observing evidence.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

This is the standard binary update used in diagnostic reasoning, quality-control alarms, spam filters sketches, and classroom problems about rare diseases and imperfect tests. You supply three numbers on the closed unit interval: how common the hypothesis is before seeing the test, how often the evidence appears when the hypothesis is true, and how often the evidence appears when the hypothesis is false. The engine returns the posterior P(H given E), the marginal evidence probability P(E), the specificity one minus the false-positive rate, and the positive likelihood ratio when it is finite. Any probability outside zero to one is rejected with invalid_input rather than clamped, so bad spreadsheets and off-by-one percent values cannot silently corrupt a result. Arithmetic is pure deterministic floating-point with no network, randomness, or clock dependency, so the same triple always yields the same JSON. Explore free in the browser, or call the API at $0.002 per successful request when you need reproducible Bayesian fixtures in CI, teaching demos, or automated decision pipelines.

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/bayes-theorem

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/bayes-theorem \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"prior":0.01,"sensitivity":0.99,"false_positive_rate":0.05}'

const res = await fetch("https://api.kit.forhosting.com/prob/bayes-theorem", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "prior": 0.01,
    "sensitivity": 0.99,
    "false_positive_rate": 0.05
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/prob/bayes-theorem",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "prior": 0.01,
    "sensitivity": 0.99,
    "false_positive_rate": 0.05
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/prob/bayes-theorem", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"prior":0.01,"sensitivity":0.99,"false_positive_rate":0.05}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"prior":0.01,"sensitivity":0.99,"false_positive_rate":0.05}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/prob/bayes-theorem", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "prior": 0.01,
  "sensitivity": 0.99,
  "false_positive_rate": 0.05
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "prob.bayes_theorem",
  "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.

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