Hendecagon apothem calculator
Turn the measured side of a regular 11-sided polygon into its apothem, the distance from the centre to the middle of each edge, so side 1 gives 1 ÷ (2·tan(π/11)) and a perimeter of 11. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Side
- 1
- Apothem
- 1.7028436194
- Circumradius
- 1.7747327664
- Perimeter
- 11
- Area
- 9.3656399069
A regular hendecagon is the eleven-sided polygon with equal sides and equal interior angles. When you know only the common side length and need the apothem—the perpendicular distance from the center to any side, equal to the inradius of the inscribed circle—the standard regular-polygon identity divides that side by twice the tangent of pi over eleven. You do not need eleven vertex coordinates, a full radius survey, or a general computer-algebra session.
What regular-hendecagon apothem from side length means and how the numbers work
A regular hendecagon has eleven equal sides and eleven equal interior angles. Each interior angle measures one thousand four hundred forty over eleven degrees, about one hundred thirty point nine degrees. Its apothem is the inradius: the radius of the inscribed circle, equal to the perpendicular distance from the geometric center to the midpoint of any side.
Once the figure is known to be regular, a single positive side length s fixes the entire shape up to similarity scaling. The standard apothem identity for any regular n-gon is side over two times the tangent of pi over n. For n equals eleven that becomes apothem equals s divided by two times tan of pi over eleven.
The central half-angle is one hundred eighty over eleven degrees, so the solver evaluates tan of pi over eleven once and divides—no angle-mode ambiguity, no iterative approximation, and no need to place eleven vertices in the plane. Circumradius follows as s over two times sin of pi over eleven; perimeter is eleven times the side; area is one-half times perimeter times apothem. For a unit side the apothem is one over two tan of pi over eleven; scale linearly with s for any other positive side.
Every step is elementary arithmetic on one scalar: no iteration, no sampling, no wall-clock dependence, and no dependence on floating Date or network state. Compared with an area-from-apothem landing, this path matches surveys and drafting notes where the edge length is the measured quantity rather than the inradius. Compared with a general n-gon calculator, this landing is dedicated to the hendecagon search intent and the familiar side-over-two-tan form textbooks quote for the side-to-apothem path when n is eleven.
What you can do with it
Decorative layouts and planters measured by edge length
Turn a measured side of a regular hendecagon into center-to-side distance for layout, paint, planting, or fabric planning without reconstructing every radius by hand.
Game, CAD, and mesh inradius stored by side
Validate a regular hendecagon pad or compute the inscribed radius when the scene graph stores edge length rather than apothem.
FAQ
What is the apothem of a regular hendecagon with side s?
a = s / (2·tan(π/11)). This calculator evaluates that closed form and also returns circumradius s/(2·sin(π/11)), perimeter 11s, and area (1/2)·P·a.
Why must the side length be positive?
A non-positive side does not define a positive finite regular hendecagon.
How is this different from a hendecagon area-from-apothem tool?
An area-from-apothem tool takes the inradius and returns area. This one takes side length and returns the apothem (plus related metrics). Same regular hendecagon geometry, different measured input and different search intent.
Is the hendecagon apothem calculator free?
The browser tool is free and runs locally.
What else does the result include besides the apothem?
The circumradius, which is the side over twice the sine of π/11, the perimeter of eleven sides, and the area, half the perimeter times the apothem. Together they let you cross-check a drawing in one pass.
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/hendecagon-apothem \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"side":1}'const res = await fetch("https://api.kit.forhosting.com/geom/hendecagon-apothem", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"side": 1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/hendecagon-apothem",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"side": 1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/hendecagon-apothem", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"side":1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"side":1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/hendecagon-apothem", 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": 1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.hendecagon_apothem",
"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
This hendecagon apothem calculator accepts a single positive side length, returns the apothem together with circumradius, perimeter, and area for cross-checks, and rejects zero or negative sides with invalid_input instead of inventing a meaningless number. The same pure solve function powers the free browser tool and the prepaid API path, so homework checks, grading scripts, landscaping takeoffs, decorative-layout estimators, and production pipelines all see the same deterministic JSON every time.
What regular-hendecagon apothem from side length means and how the numbers work
Degenerate inputs—zero, negative, missing, or non-finite side—do not form a positive finite regular hendecagon, so this tool returns invalid_input rather than zero or NaN.
How to call the API and what comes back
Use it from geometry homework pipelines, decorative eleven-sided layout or planter takeoff scripts when only the edge is known, game-level tooling for hendecagon pads stored by side length, interview-prep sandboxes, or any workflow that needs a reproducible regular hendecagon apothem without installing a computer-algebra package on every machine. Round-trip checks are easy: after solving, confirm apothem equals side over two tan of pi over eleven within floating tolerance, that circumradius equals side over two sin of pi over eleven, that perimeter equals eleven times side, and that area equals one-half times perimeter times apothem after the same rounding policy. Send a JSON body with one required field. Field side is the positive finite length of each edge of the regular hendecagon; aliases s and side_length are accepted so form UIs and scripts can keep their preferred names. On success the response echoes side, returns apothem as the inradius from center to a side, circumradius as the distance from center to a vertex, perimeter as eleven times that side, area as one-half times perimeter times apothem, method set to regular_hendecagon_from_side, and a short formula block documenting the closed forms including the general n-gon pattern and the specialized eleven-side expressions. Failed validation—missing the field, a non-finite value, a non-positive side, or a side outside published limits—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item. Pair success cases such as side one and side two with a deliberate zero or negative side to verify clients handle invalid_input cleanly.
Practical tips, limits, and related searches
When teaching, prefer paired examples: side one for the pure one-over-two-tan constant; side two so students can verify that apothem scales linearly with s (twice the unit-side apothem); and side zero or negative to demonstrate the hard rejection path that protects callers from non-positive geometry. If you already know the apothem instead and need area, use the companion hendecagon area from apothem path so each search intent stays on its own SEO landing without cannibalizing the other. For flat-to-flat decorative tiles, hardware blanks, or playground figures, remember that the full width across flats is twice the apothem returned here, so you can convert a measured edge into the across-flats dimension in one step. Keep the side length inside the published positive range up to one trillion so intermediate products stay finite in IEEE double precision on the Worker and in the browser. Units are whatever you pass—metres, feet, or game units—as long as you interpret lengths in that unit and area in the square of that unit; the API does not convert units for you. Because the formula only needs the side, students can recompute s over two tan of pi over eleven by hand for small integers and match the API line by line after rounding. This landing targets people searching for a hendecagon apothem calculator, eleven-sided polygon inradius from side length tool, or regular hendecagon apothem from side; it is not the area-from-apothem hendecagon calculator, not a general n-gon solver with a variable side count—use the regular polygon or polygon apothem calculator when n is not eleven—and it is not a hendecagonal prism volume or hendecagonal pyramid tool. Prefer this endpoint when the figure is known regular and only the side length is measured. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when users type impossible sides while learning the contract.
Integration use cases
Homework and exam checks from a measured side
Give students a positive side length; compare their hand-computed hendecagon apothem, circumradius, perimeter, and area against a deterministic API or free browser result.
Technical questions
What inputs does the hendecagon apothem calculator need?
Only one positive finite number: side (aliases s, side_length). Zero, negative, missing, or non-finite values return invalid_input.