ForHosting KIT · Developer Utilities

Compound rule of three calculator

A compound rule of three problem asks for one unknown when several quantities change at once and each quantity is either directly or inversely proportional to that unknown.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Students meet this model in middle-school arithmetic, vocational exams, and shop-floor planning: more workers produce more pieces (direct), but more workers finish a job in fewer days (inverse). A simple cross-multiply handles one pair; the compound form multiplies every direct ratio of sought over given and every inverse ratio of given over sought, then scales the known magnitude. This compound rule of three calculator accepts that known magnitude as value plus two or more labeled factors, each with a given value, a sought value, and a relation of direct or inverse, and returns the unknown together with the product of ratios and a filled-in setup string. The free browser path and the API share one pure module, so homework checks and automation never disagree. Failed validation is not billed; successful calls use the published $0.002 base price.

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/algebra/compound-rule-of-three

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/algebra/compound-rule-of-three \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"value":240,"factors":[{"name":"workers","given":8,"sought":12,"relation":"direct"},{"name":"days","given":6,"sought":4,"relation":"direct"},{"name":"hours","given":5,"sought":6,"relation":"direct"}]}'

const res = await fetch("https://api.kit.forhosting.com/algebra/compound-rule-of-three", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "value": 240,
    "factors": [
      {
        "name": "workers",
        "given": 8,
        "sought": 12,
        "relation": "direct"
      },
      {
        "name": "days",
        "given": 6,
        "sought": 4,
        "relation": "direct"
      },
      {
        "name": "hours",
        "given": 5,
        "sought": 6,
        "relation": "direct"
      }
    ]
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/algebra/compound-rule-of-three",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "value": 240,
    "factors": [
        {
            "name": "workers",
            "given": 8,
            "sought": 12,
            "relation": "direct"
        },
        {
            "name": "days",
            "given": 6,
            "sought": 4,
            "relation": "direct"
        },
        {
            "name": "hours",
            "given": 5,
            "sought": 6,
            "relation": "direct"
        }
    ]
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/algebra/compound-rule-of-three", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"value":240,"factors":[{"name":"workers","given":8,"sought":12,"relation":"direct"},{"name":"days","given":6,"sought":4,"relation":"direct"},{"name":"hours","given":5,"sought":6,"relation":"direct"}]}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"value":240,"factors":[{"name":"workers","given":8,"sought":12,"relation":"direct"},{"name":"days","given":6,"sought":4,"relation":"direct"},{"name":"hours","given":5,"sought":6,"relation":"direct"}]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/algebra/compound-rule-of-three", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "value": 240,
  "factors": [
    {
      "name": "workers",
      "given": 8,
      "sought": 12,
      "relation": "direct"
    },
    {
      "name": "days",
      "given": 6,
      "sought": 4,
      "relation": "direct"
    },
    {
      "name": "hours",
      "given": 5,
      "sought": 6,
      "relation": "direct"
    }
  ]
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "algebra.compound_rule_of_three",
  "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_items 12

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 →