Regular dodecagon
A regular dodecagon with a side of 4 has an area of 179.138439 square units. From the side alone you get the area, 3·(2+√3)·s², the perimeter, 12·s, or the interior angle, always exactly 150°. Free in your browser.
- Free
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- Your data stays on your device
Run — free
Worked example
- Side
- 4
- Measurement
- Area
- Value
- 179.138439
The regular dodecagon calculator takes the side length of a twelve-sided regular polygon and returns the measurement you ask for: its area in square units, its perimeter in the same unit as the side, or its interior angle in degrees. The formulas are exact closed forms — the area is 3·(2+√3)·s², the perimeter is 12·s and the interior angle is 150° — so the result is deterministic, reproducible and safe to embed in drawings, bills of materials, cutting plans or geometry homework without ever opening a CAD tool or a spreadsheet.
One side length in, one exact measurement out
A regular dodecagon is fully determined by a single number: the length of one side. Because all twelve sides and all twelve interior angles are equal, every other property of the shape follows from that side through fixed formulas, with no measurement error and no approximation method to choose.
In every one of those cases what you know is the side, because that is what you cut or what you ordered, and what you need is one of these three numbers to price material, check a fit or write a specification.
Where it fits in a real workflow
Geometry lookups like this one tend to live at the boundaries of other systems. A quoting tool for a metal shop needs the area of a dodecagonal plate to price the sheet it is cut from; a CNC post-processor wants the perimeter to estimate cutting time; a math-learning app checks a student's answer for the interior angle. In each case the polygon math is a detail that should not be reimplemented — and re-derived, and re-tested — inside every product that touches it.
This capability runs on our global edge with no state between requests, so the same call works from a browser form, a batch script or a backend service. For other polygons, sibling capabilities cover the decagon and more.
What you can do with it
Price a dodecagonal part
Get the exact area of a twelve-sided plate, tabletop or floor plan from its side length to compute material cost and cutting waste.
Check geometry homework
Verify the area, perimeter or 150° interior angle of a regular dodecagon exercise with a deterministic reference value.
FAQ
What is a regular dodecagon?
A polygon with twelve equal sides and twelve equal interior angles of 150° each. This capability only handles the regular case.
How many decimal places does the result have?
Six by default. You can set the decimals field to any integer from 0 to 12; rounding is half-up and deterministic.
Why is each interior angle of a regular dodecagon 150°?
Every regular polygon follows the rule (n−2)·180° divided by n. With twelve sides that gives exactly 150°, whatever the side length, so the angle is never rounded and the decimals setting does not touch it.
Where does the dodecagon area formula come from?
Split the shape into twelve identical isosceles triangles meeting at the centre, each with a central angle of 30°. Adding their areas gives 3·(2+√3)·s², and that coefficient, about 11.196152, is exact rather than measured.
What can I use a dodecagon calculator for?
For any twelve-sided object whose side you know because you cut or ordered it: the area of a plate, tabletop or floor plan to estimate material, the perimeter to estimate cutting time, or the angle to check homework.
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/math/dodecagon \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"side":4,"measurement":"area"}'const res = await fetch("https://api.kit.forhosting.com/math/dodecagon", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"side": 4,
"measurement": "area"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/dodecagon",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"side": 4,
"measurement": "area"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/dodecagon", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"side":4,"measurement":"area"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"side":4,"measurement":"area"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/dodecagon", 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": 4,
"measurement": "area"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.dodecagon",
"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
One side length in, one exact measurement out
You send the side length and the name of the measurement you want — area, perimeter or interior_angle — and you receive exactly one value, labelled with its unit: square units for the area, the same unit you gave for the perimeter, and degrees for the angle. This matters when the dodecagon is a real object: a tabletop, a gazebo floor, a clock face, a coin blank or the cross-section of a turned part. The API does that conversion in a single deterministic call, with no file kept and nothing to install.
How the numbers are computed
The three formulas come from splitting the dodecagon into twelve identical isosceles triangles that meet at the centre, each with a central angle of 30°. Results are rounded half-up to a fixed number of decimal places — six by default, adjustable between zero and twelve through the optional decimals field — so the same input always produces byte-identical output on any machine, which is what makes the value safe to store, compare and cache. Summing their areas gives the closed form A = 3·(2+√3)·s², which is what the endpoint evaluates — the coefficient 3·(2+√3) ≈ 11.196152 is exact, not measured. The perimeter is simply 12·s, and the interior angle follows the general polygon rule (n−2)·180°/n, which for n = 12 gives exactly 150° with no rounding at all. The side length itself must be a positive finite number; zero, negatives, NaN, infinities and non-numeric values are rejected with an invalid_input error, and rejected calls are never billed.
Where it fits in a real workflow
The exact code that serves the API also runs free on this page in your browser, which means you can verify a value by hand before you wire the call into anything, and you only pay — $0.002 per request — when you automate it.
Integration use cases
Estimate cutting time
Use the perimeter returned by the API to feed feed-rate calculations for saws, lasers and CNC routers cutting dodecagon outlines.
Technical questions
What does it cost?
$0.002 per request. It is also free to run in your browser on this page.
Which measurements can I request?
Area (square units), perimeter (same unit as the side) and interior_angle (degrees, always exactly 150).
What formula is used for the area?
A = 3·(2+√3)·s², an exact closed form derived from the twelve triangles that compose the dodecagon.
What input is rejected?
A side length that is zero, negative, non-numeric or not finite is rejected with an invalid_input error, and the call is not billed.