Heptagon calculator
A side of 5 is all a regular heptagon needs: it gives a perimeter of 35, an area of about 90.847811 and interior angles of 128.571429° each. Useful for checking geometry homework or laying out seven-sided panels. Free in your browser.
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A regular heptagon is a seven-sided polygon whose sides and interior angles are all equal. From a single measurement—the side length—every other property follows from closed-form geometry. Each interior angle measures 900 divided by 7 degrees (about 128.571429), the seven interior angles sum to exactly 900 degrees, each exterior angle is 360 divided by 7 degrees, the perimeter is seven times the side, and the area is seven quarters of the side squared times the cotangent of pi over seven.
The geometry of a regular heptagon
Any regular polygon with n sides has interior angles that sum to (n minus 2) times 180 degrees, because the polygon can be triangulated into n minus 2 triangles from one vertex. For the heptagon, n equals seven, so the interior angles sum to 5 times 180, exactly 900 degrees, and since all seven angles are equal, each one measures 900 over 7—about 128.571429 degrees.
The exterior angle, the turn you make walking around the boundary, is 360 divided by 7, about 51.428571 degrees, and interior plus exterior always add to 180. The perimeter is trivially seven times the side length. The area is the interesting formula: split the heptagon into seven congruent isosceles triangles from the center, each with base s and height equal to the apothem s over (2 times the tangent of pi over 7).
Summing the triangles gives area equals (7/4) times s squared times the cotangent of pi over 7, which is also perimeter times apothem over 2. The numerical coefficient is about 3.633912, so a heptagon of side 5 has an area near 90.8478 square units. Unlike the general regular-polygon calculators that ask for an arbitrary side count, this capability fixes n at seven, so the angles are constants of the shape and only the side length scales the perimeter and area.
Practical tips, limits, and related searches
Keep the side within the published maximum of 1e15 so the squared term in the area formula stays well inside the double-precision range; realistically, heptagon problems live between millimeters and kilometers, so the cap is generous. Because area grows with the square of the side, doubling the side quadruples the area while the perimeter only doubles—useful intuition when estimating material for scaled designs. Remember that all results assume a regular heptagon: equal sides and equal angles.
If your shape is an irregular seven-sided polygon, its angles and area are not determined by one side length; you need vertex coordinates and a shoelace-formula tool instead, which is a different search intent served by sibling capabilities in this kit. For teaching, pair examples: side 1 exposes the raw constants (perimeter 7, area about 3.633912), side 10 scales them by ten and a hundred, and side 0 or minus 3 demonstrates the hard rejection path.
If you also need the inscribed or circumscribed circle radius, note that the apothem returned here is the inradius; the circumradius is s over (2 sin(pi/7)) and can be derived from the same inputs.
What you can do with it
Fabrication and design of seven-sided panels
Estimate edge material (perimeter) and surface material (area) for heptagonal tiles, tabletops, or gaskets directly from the planned side length.
FAQ
What is the interior angle of a regular heptagon?
Each interior angle is 900/7 degrees, about 128.571429°. The seven interior angles sum to exactly 900°, and each exterior angle is 360/7 ≈ 51.428571°.
What is the area formula of a regular heptagon?
Area = (7/4) · s² · cot(π/7), about 3.633912 times the side squared. It is equivalent to perimeter times apothem over two.
What happens if the side is zero or negative?
A polygon side must be a positive finite number; failed tasks are not charged.
Does this work for irregular heptagons?
No. The formulas assume a regular heptagon (equal sides and angles). Irregular seven-sided polygons need vertex coordinates and a shoelace-formula tool instead.
Is the heptagon calculator free?
The browser tool is free and runs locally.
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/heptagon \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"side":5}'const res = await fetch("https://api.kit.forhosting.com/math/heptagon", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"side": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/heptagon",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"side": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/heptagon", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"side":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"side":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/heptagon", 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": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.heptagon",
"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.
Limits
max_side | 1000000000000000 |
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 capability takes the side length, validates that it is a positive finite number, and returns all of these measurements as deterministic JSON. Students checking geometry homework, designers laying out seven-sided panels, and developers building measurement pipelines get one reproducible answer with no computer-algebra system: the same pure function runs in the free browser tool and in the prepaid API, so what you see locally is exactly what the API charges for.
How to call the API and what comes back
Values derived from transcendental functions are rounded to six decimals so the output is byte-stable across machines and CPU architectures; the angle sum stays an exact integer. Send a JSON body with one required field: side, the length of one side of the regular heptagon. It must be a finite number strictly greater than zero—integers and decimals are both fine, and numeric strings like "7.5" are coerced. The aliases side_length, length, and a are accepted for the same meaning. On success the response includes side (the normalized value), sides (always 7), interior_angle_deg (900/7, about 128.571429), interior_angle_sum_deg (exactly 900), exterior_angle_deg (360/7, about 51.428571), perimeter (7 times the side), apothem (s over 2 tan(pi/7)), and area ((7/4) s squared cot(pi/7)). Failed validation—a missing side, a non-numeric value, zero, or a negative length—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap while users learn the contract.
Integration use cases
Geometry homework: heptagon measurements from one side
Give students a side length and let them verify hand-computed interior angles, perimeter, and area against a deterministic API or the free browser result.
Test fixtures for geometry pipelines
Assert that a CAD or graphics pipeline produces the same heptagon constants (900/7 degree angles, 7s perimeter, 3.633912s^2 area) with a stable JSON oracle.