ForHosting KIT · Developer Utilities

Conical frustum calculator

A conical frustum, or truncated cone, is the solid left when a plane parallel to the base cuts a right circular cone short of the apex.

● BetaFree · in your browser

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

It is defined by two circular radii (the parallel bases) and the perpendicular height between those bases. Once those three measures are known, every classical metric of the solid is determined: the volume is one-third pi times height times the sum of the squared radii and their product; the slant height is the hypotenuse of the right triangle formed by the height and the absolute difference of the radii; the lateral surface is pi times the sum of the radii times the slant height; and the total surface area adds the areas of the two circular bases. Students meet these formulas in solid-geometry homework and contest problems; engineers, packaging designers, and makers need the same numbers for hoppers, lamp shades, buckets, funnels, and tapered tanks. This capacity accepts radius1, radius2, and height, rejects a negative radius on either base, and returns volume, slant height, lateral area, and total surface area as structured JSON. The same pure function powers the free browser widget and the prepaid API path, so a golden server example matches what a visitor runs locally with no network round trip and no language-model involvement.

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/geom/frustum-cone

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/geom/frustum-cone \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"radius1":3,"radius2":4,"height":5}'

const res = await fetch("https://api.kit.forhosting.com/geom/frustum-cone", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "radius1": 3,
    "radius2": 4,
    "height": 5
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/geom/frustum-cone",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "radius1": 3,
    "radius2": 4,
    "height": 5
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/frustum-cone", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"radius1":3,"radius2":4,"height":5}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"radius1":3,"radius2":4,"height":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/frustum-cone", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "radius1": 3,
  "radius2": 4,
  "height": 5
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "geom.frustum_cone",
  "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