Regular polygon perimeter
A regular hexagon with sides of 2 has a perimeter of 12, because every side is equal and the total is simply the number of sides times their length. Enter both and get the full boundary in the same unit. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Sides
- 6
- Side length
- 2
- Perimeter
- 12
A regular polygon is a closed plane figure whose sides are all equal and whose interior angles are all equal. Once you know how many sides it has and the length of one side, the perimeter is a single multiply: the side count times the side length. This regular polygon perimeter calculator accepts an integer number of sides of three or more and a finite non-negative side length, then returns the exact boundary length P equals n times s. Students checking homework, CNC and craft planners sizing frames, survey tools converting a measured edge into total fence length, and exam generators that need a deterministic oracle all reach for the same closed form.
What a regular polygon perimeter means and why P = n × s
A regular polygon is a convex n-sided figure whose sides are all the same length and whose interior angles are all equal. Because every edge is identical, the distance around the figure collapses to a product rather than a sum of mixed lengths: if the polygon has n sides and each side has length s, the perimeter is exactly n times s. That identity is exact for every integer n of three or more and every non-negative finite s.
There is no trigonometric reduction, no apothem, and no circumradius in the perimeter itself; those quantities appear only when you also want area or a radius. In classroom language the perimeter is the length of the boundary: walk along every edge once and you have travelled n times s.
In manufacturing and layout the same number is the total linear material for a closed regular frame, the cut length of trim around a regular window, or the fence length enclosing a regular bed when a tape measure already gave one side. Keeping the contract to two inputs and one primary output makes the calculator a fast check beside a diagram, a two-field form, or a one-line step in a larger geometry pipeline.
When s is positive the result scales linearly, so doubling the side doubles the perimeter with no hidden constants beyond the integer n that defines the figure.
Where a regular polygon perimeter calculator earns its keep
Geometry homework and entrance exams often ask for the perimeter of a regular polygon given only the side count and the side length. Learners flip factor errors when they multiply by the wrong n, treat an irregular figure as regular, or confuse perimeter with area; a deterministic oracle that always multiplies the given n by s catches those slips before a tutor spends a session on arithmetic.
Craft, laser-cut, and CNC workflows that cut regular n-gon panels or frames need the total edge length for material estimates once the design freezes a side size. Landscape and event planners who lay regular stages, garden beds, or game boards convert a measured side into total border or rope length without opening a full CAD suite. Exam-prep generators and LMS auto-graders need a tiny closed-form checker that rejects a side count below three as invalid rather than silently returning a two-times-s result that a buggy grader might accept.
What you can do with it
Classroom and homework checks
Students enter a side count and a side length and verify that the perimeter is exactly n times s, catching wrong-factor mistakes before they reach a tutor.
Craft, CNC, and material estimates
Convert a frozen design side into total edge length for frames, trim, laser paths, or stock cut lists around a regular n-sided panel.
LMS and exam auto-grading
Mark regular-polygon perimeter items with a deterministic oracle that rejects n below three and never invents area or apothem when only P = n × s is required.
FAQ
What happens if the side count is less than three?
A polygon needs at least three sides, so two sides, one side, or zero are rejected and are not billed.
Does this calculator also return area or apothem?
Use other geometry capabilities if you need area, apothem, diagonals, or circumradius.
How do I find the perimeter of a regular pentagon?
Multiply 5 by the length of one side. A regular pentagon with sides of 6 has a perimeter of 30, and the same rule works for any regular polygon, whatever its number of sides.
What unit is the perimeter given in?
The same unit you used for the side. A side in centimetres gives a perimeter in centimetres and a side in metres gives metres; nothing is converted along the way.
Can the number of sides be a decimal?
No. The side count must be a whole number of three or more, because a polygon cannot have a fraction of a side. A decimal count is rejected instead of producing a meaningless result.
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/regular-polygon-perimeter \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"sides":6,"side_length":2}'const res = await fetch("https://api.kit.forhosting.com/math/regular-polygon-perimeter", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"sides": 6,
"side_length": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/regular-polygon-perimeter",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"sides": 6,
"side_length": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/regular-polygon-perimeter", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"sides":6,"side_length":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"sides":6,"side_length":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/regular-polygon-perimeter", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"sides": 6,
"side_length": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.regular_polygon_perimeter",
"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
Side counts below three, missing fields, and a negative side fail with invalid_input and are not billed.
What a regular polygon perimeter means and why P = n × s
This endpoint answers only that boundary question. It does not compute area, diagonals, circumradius, or apothem; those are separate intents and separate landings. When s is zero the mathematical perimeter is zero, which this API returns honestly rather than inventing a minimum size.
Input contract, response shape, and error behaviour
Non-integers and a count above the published maximum also fail. A regular pentagon with side six yields perimeter thirty. Units are caller-defined: if you send centimetres you get centimetres of perimeter; if you send metres you get metres. The calculator does not convert units, draw the polygon, or estimate waste factors for cutting stock. Pair the numeric result with your own unit labels and drawings. POST a JSON body with two required fields. The field sides is an integer greater than or equal to three and at most one million; aliases n and n_sides mean the same thing. The field side_length is a finite non-negative number giving the length of each equal edge; aliases side, s, and length are accepted so clients that already use short geometry names do not need a rename layer. Each field may arrive as a JSON number or as a numeric string. Empty strings, missing fields, Infinity, and NaN fail with invalid_input naming the problem. On success the body includes the echoed sides count, the echoed side_length rounded to twelve decimal places for stable goldens, perimeter equal to n times that side with the same rounding, and formula set to a short string that restates P equals n times s with the n that was used. Example: sides equals six and side_length equals two yields perimeter twelve, because six times two is twelve.
Where a regular polygon perimeter calculator earns its keep
Engineering notebooks and spreadsheet replacements can call this endpoint as a two-field step when a larger script already holds side lengths for several regular polygons and only the perimeter question needs a dedicated, SEO-clear name. In all of those settings the value is not exotic mathematics: it is a stable contract, clear errors, and a search intent that matches how people actually query for regular polygon perimeter from side count and side length at $0.002 per successful API call.
Technical questions
How do I calculate the perimeter of a regular polygon?
Send an integer sides count of three or more and a finite non-negative side_length. The API returns perimeter = n × s, plus the echoed inputs and the formula string P = n × s.
Which units does the regular polygon perimeter calculator use?
Any consistent linear unit you choose. If side_length is in centimetres, perimeter is in centimetres; the API does not convert units.
What does the regular polygon perimeter calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.