ForHosting KIT · Math

Regular tetrahedron calculator

A regular tetrahedron with an edge of 2 has a volume of about 0.942809 and a surface area of 6.928203. Enter one edge and get volume, face area, total surface, height and both sphere radii, rounded to the decimals you choose. Free in your browser.

Free
Runs in your browser
No sign-up
Your data stays on your device

Run — free How it works & API

Use it from WebAPIEmailTelegramApp soon

Worked example

If you enter

Edge length a: 2
Decimal places: 6

You get

Volume: 0.942809
Face area: 1.732051
Surface area: 6.928203
Height: 1.632993

Volume, areas, height, R and r from edge a. Search intent: regular tetrahedron volume. No network calls or random seeds are required. Failed jobs are not billed.

Six measurements from a single edge

A regular tetrahedron is a solid made of four identical equilateral triangles, with all six edges the same length. Because the shape is fixed, one edge is enough to know everything else. Enter it and the calculator gives the volume, the area of one face, the total surface area of all four faces, the height, the circumradius and the inradius. With an edge of 2, one face covers about 1.732051 square units and the four together 6.928203, the height is 1.632993, and the radii of the outer and inner spheres are 1.224745 and 0.408248.

How the figures are worked out, and what to watch for

The volume is the edge cubed divided by six times the square root of 2, the circumradius is √6/4 times the edge and the inradius √6/12 times the edge. Two mix-ups are common: taking the area of one face for the area of the whole surface, which is four times larger, and swapping the two radii, when the outer one is always three times the inner one. Rounding each step by hand also makes the result drift; here every figure is rounded only once, to the decimals you pick.

What you can do with it

Teaching

Pinned goldens.

FAQ

What is the formula for the volume of a regular tetrahedron?

The volume is the edge cubed divided by six times the square root of 2, written a³/(6√2). With an edge of 2 that gives about 0.942809 cubic units.

What is the difference between the circumradius and the inradius?

The circumradius is the radius of the sphere through the four corners, √6/4 times the edge; the inradius belongs to the sphere touching the four faces, √6/12 times the edge. The first is always three times the second.

How are the results rounded?

You choose how many decimals you want. Each value is rounded once, half up, straight from the full-precision result, so rounding errors do not pile up from one figure to the next.

How does the volume change if I double the edge?

It becomes 8 times larger, because the volume depends on the cube of the edge. The two sphere radii, on the other hand, simply double, since they are fixed multiples of the edge.

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/regular-tetrahedron

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/regular-tetrahedron \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"side":2}'

const res = await fetch("https://api.kit.forhosting.com/math/regular-tetrahedron", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "side": 2
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/math/regular-tetrahedron",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "side": 2
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/regular-tetrahedron", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"side":2}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"side":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/regular-tetrahedron", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "side": 2
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "math.regular_tetrahedron",
  "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, automation, or teaching demos.

How it works

Volume, areas, height, R and r from edge a. V=a³/(6√2); R=√6/4 a; r=√6/12 a. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. 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, 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, automation, or teaching demos.

Inputs, limits and rounding

Optional decimals use half-up once. Outputs echo inputs. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. Provide required JSON fields. 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, 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, automation, or teaching demos.

When to use it

Use when search intent matches. Volume, areas, height, R and r from edge a. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. 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, 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, automation, or teaching demos.

Integration use cases

Quick check

Free widget.

Automation

Same JSON via API.

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