Truncated cube calculator
Enter one edge length and get the volume and surface area of a truncated cube: an edge of 1 gives a volume of 13.599663291074 and a surface of 32.434664363615. Handy for checking textbook answers or sizing a 3D model. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Edge
- 1
- Volume
- 13.5996632911
- Surface area
- 32.4346643636
- Faces
- 14
- Edges
- 36
A truncated cube is the Archimedean solid obtained by cutting every vertex of a cube until the original square faces become regular octagons and equilateral triangles appear where the vertices used to be. Students, 3D designers, and exam writers need its volume and total surface area from a single shared edge length when sizing solids, checking textbook answers, or scripting parametric models. This truncated cube calculator accepts one edge length, applies the closed formulas V equals (21 plus 14 times square root of two) over three times a cubed and S equals two times (6 plus 6 times square root of two plus square root of three) times a squared, and returns both metrics with the solid’s fixed face, edge, and vertex counts.
What a truncated cube is and which formulas fix volume and surface
Start from a cube and truncate (cut off) each of the eight vertices by the same depth until the original square faces become regular octagons and new equilateral triangular faces appear at the former vertices. The resulting convex polyhedron is the truncated cube, one of the thirteen Archimedean solids: all faces are regular polygons, and the vertex figure is the same at every vertex. It has fourteen faces in total—six regular octagons and eight equilateral triangles—thirty-six equal edges, and twenty-four identical vertices.
Because every edge has the same length a after a uniform truncation, a single positive length completely determines the solid up to congruence. The classical closed formulas used in solid-geometry tables are volume V equals (21 plus 14 times the square root of two) divided by three, times a cubed, and total surface area S equals two times the quantity (6 plus 6 times the square root of two plus the square root of three), times a squared.
Those expressions come from summing the areas of six regular octagons of side a and eight equilateral triangles of side a, plus the known volume of the fully truncated cube in terms of edge length. When a is zero the solid collapses and both volume and surface area are zero; when a is positive both grow as a cubed and a squared respectively. Negative a has no interpretation as a geometric edge length, so this capability refuses it rather than taking an absolute value that would hide a data-entry bug.
Where truncated cube measurements come in handy
Classrooms and tutoring platforms use a truncated cube calculator so learners can check volume and surface area for arbitrary non-negative edge lengths without mixing the octagon and triangle face formulas by hand. Exam-prep generators need a deterministic oracle that marks negative edges as invalid input instead of silently reflecting the absolute value or inventing a positive volume. Failed validation does not consume balance.
Compared with a plain cube calculator, this landing targets the narrower search intent of the truncated cube alone, so SEO pages do not compete for ordinary cube volume queries while still serving the exact scalars designers and students ask for when they type truncated cube into a search box and need volume plus surface area from edge length.
What you can do with it
CAD and parametric design notebooks
Compute volume and surface area for truncated-cube cells in scripts that size decorative polyhedra, packaging shells, or clearance envelopes.
Exam generators and LMS auto-grading
Mark solid-geometry items with a deterministic oracle that rejects negative edges and pins twelve-decimal goldens for volume and surface area.
FAQ
Which formulas does the calculator use?
Volume V = (21 + 14√2)/3 · a³.
What happens if the edge is negative?
A truncated cube requires a non-negative edge length; negative values are rejected and those calls are not charged.
Is the truncated cube calculator free?
The browser tool runs free on your device.
How does a truncated cube differ from a regular cube?
A regular cube has six square faces. A truncated cube has six regular octagons and eight equilateral triangles (14 faces, 36 edges, 24 vertices) after cutting off the cube’s vertices uniformly.
What happens to the volume if I double the edge?
The volume grows eight times and the surface area four times, because volume depends on the edge cubed and surface on the edge squared. An edge of 1 gives 13.599663291074, so an edge of 2 gives eight times that.
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
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/truncated-cube \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"edge":2}'const res = await fetch("https://api.kit.forhosting.com/geom/truncated-cube", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"edge": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/truncated-cube",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"edge": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/truncated-cube", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"edge":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"edge":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/truncated-cube", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"edge": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.truncated_cube",
"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
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
Negative edges are rejected with invalid_input so automation never treats a sign error as a physical solid. The free browser path and the paid API path share the same pure module, so classroom checks and production pipelines always agree on twelve-decimal rounding. At $0.002 per successful API call there is no model spend and no outbound network—only analytic arithmetic on one finite scalar.
What a truncated cube is and which formulas fix volume and surface
Reporting volume, surface_area, and the topology triple faces, edges, vertices matches textbook language and CAD notebooks without forcing clients to re-derive face counts from memory.
Input contract, response shape, and error behaviour
Example: edge equals one yields volume approximately thirteen point six zero zero and surface area approximately thirty-two point four three five in consistent cubic and square units. Edge equals two scales volume by eight and surface area by four because of the a cubed and a squared dependence. Keep requests small, pin the rounded volume and surface area in automated tests, and you get reproducible Archimedean metrics for homework, LMS plugins, and edge workers without standing up a full solid-geometry library. POST a JSON body with one required field edge: a finite number or numeric string for the common edge length of the truncated cube. Aliases a, side, edge_length, and length are accepted and mapped to the same parameter so notebook cells and form widgets can keep their local naming. Missing, empty, or non-finite values fail with invalid_input naming the field. On success the body echoes edge rounded to twelve decimal places, volume, surface_area, faces set to fourteen, edges set to thirty-six, vertices set to twenty-four, method set to truncated_cube, and two formula strings for display next to the answer: V = (21 + 14√2)/3 · a³ and S = 2(6 + 6√2 + √3) · a². Pair the response with your own renderer if you need a 3D mesh of the truncated cube; this endpoint returns scalars and topology only and does not emit meshes, unit conversions, or midradius or circumradius.
Where a truncated cube calculator API earns its keep
CAD, digital-fabrication, and parametric-design notebooks often size Archimedean cells, packaging shells, or decorative polyhedra; calling a tiny parse API avoids pulling a computer-algebra system for two closed multiplications.
Integration use cases
Classroom checks of truncated-cube metrics
Let students submit an edge length and verify volume V=(21+14√2)/3·a³ and surface S=2(6+6√2+√3)·a² against textbook Archimedean solid tables.
Technical questions
How do I compute truncated cube volume and surface area?
Send a finite non-negative edge length as edge (aliases a, side, edge_length, length). The API returns volume, surface_area, faces, edges, vertices, and the closed formulas used.