ForHosting KIT · Math

Oblique cone volume calculator

A cone with radius 3 and perpendicular height 5 holds about 47.12389 cubic units, tilted or not. Enter the base radius and the height to get the volume and the base area, rounded to the decimals you pick. Free in your browser.

Free
Runs in your browser
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Your data stays on your device

Run — free How it works & API

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Worked example

If you enter

Radius: 3
Height: 5
Decimal places: 6

You get

Base area: 28.274334
Volume: 47.12389

Volume of circular cone with perpendicular height (oblique or right). Search intent: oblique cone volume. No network calls or random seeds are required. Failed jobs are not billed.

Why a leaning cone holds the same as an upright one

A circular cone has a round base and a single tip. When the tip sits straight above the centre of the base the cone is right; when it leans to one side the cone is oblique. The volume ignores that lean. What counts is the area of the base and the perpendicular height, the distance from the tip to the plane of the base measured at a right angle. The formula is V = (1/3)·π·r²·h: the base area times the height, divided by three. For radius 3 and height 5 the base area is about 28.274334 and the volume about 47.12389.

Where it is used, and the mistakes to avoid

Oblique cones turn up in geometry exercises, and the same calculation sizes funnels, hoppers, piles of sand or grain and decorative pieces whose tip is off-centre. The most frequent mistake is using the slanted side instead of the perpendicular height, which always gives too much volume. Others are entering the diameter where the radius belongs, which multiplies the result by four, and mixing units, such as a radius in centimetres with a height in metres. Keep both lengths in the same unit and the volume comes out in that unit cubed.

What you can do with it

Teaching

Pinned goldens.

FAQ

Does tilting a cone change its volume?

No. The volume depends only on the base radius and the perpendicular height, so an oblique cone holds exactly as much as a right cone with the same base and the same height.

Which height do I measure on an oblique cone?

The perpendicular height, meaning the straight distance from the tip down to the plane of the base, measured at a right angle. The slanted side is longer and would overstate the volume.

Why does the cone formula divide by three?

Because a cone fills one third of a cylinder with the same base and height. The calculator multiplies the base area, π times the radius squared, by the height and then takes one third of that product.

How many decimals does the result show?

As many as you ask for. The volume and the base area are rounded only once, from the exact value, so the example with 6 decimals gives 47.12389 with no error piling up along the way.

Related tools

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/math/oblique-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/math/oblique-cone \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"radius":3,"height":5}'

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

import os, requests

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

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

body := bytes.NewBufferString(`{"radius":3,"height":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/oblique-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

{
  "radius": 3,
  "height": 5
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "math.oblique_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.

Technical notes

The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos.

How it works

Volume of circular cone with perpendicular height (oblique or right). V = (1/3) π r² h. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos.

Inputs, limits and rounding

Optional decimals use half-up once. Optional output fields are omitted, never null. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Provide required JSON fields with DOM-safe names. Invalid types raise invalid_input. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks,

When to use it

Use when search intent matches. Volume of circular cone with perpendicular height (oblique or right). EN-only delivery; Nitro hydrates locales. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching demos. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. Use the same JSON from spreadsheets, CMS hooks, automation, or teaching

Integration use cases

Quick check

Free widget.

Automation

API same JSON.

Technical questions

Free?

Yes tier A.

Network?

No.

Bad input?

invalid_input.

API?

Yes.

Locales?

EN-only; Nitro hydrates.

Read the full KIT documentation →

Run — free