Hexagon area calculator
Get the area of a regular hexagon from one edge length, so side 6 gives 54√3, about 93.531, with a perimeter of 36 and a long diagonal of 12. The apothem and short diagonal arrive too. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Side
- 6
- Area
- 93.5307436087
- Perimeter
- 36
- Apothem
- 5.1961524227
- Long diagonal
- 12
A regular hexagon has six equal sides and six equal interior angles. Given only the side length, this calculator returns the enclosed area using the closed form A equals three times the square root of three over two, times side squared. Related perimeter, apothem, and long and short diagonals ship in the same response so one request covers the usual worksheet pack.
How regular hexagon area is computed from the side
Label the common side length of the regular hexagon as side (or s). A regular hexagon decomposes into six congruent equilateral triangles that meet at the center; each triangle has area equal to the square root of three over four times side squared. Multiplying by six yields the compact textbook formula area equals three times the square root of three over two times side squared.
Equivalently, the apothem equals the square root of three over two times side, the perimeter is six times side, and area also equals one half times perimeter times apothem—the same numeric result. Classic checks include side one, which yields area three root three over two (about 2.598), and side two, which scales by four to about 10.392. Because the path uses only multiplication and a single square root of three, it is deterministic, O(1), and free of iterative solvers.
The response also echoes perimeter, apothem, long diagonal (two times side, opposite vertices through the center), and short diagonal (side times root three, skipping one vertex) so a single call covers the metrics most worksheets ask for next to area.
Where hexagon area calculations show up in real work
Secondary-school and college geometry courses constantly ask for the area of a regular hexagon given only the side, and often for perimeter or apothem on the same problem set; a trusted calculator with a strict positive-side gate speeds homework grading and removes spreadsheet mistakes where someone multiplies side by six and stops.
Architecture, tiling, and manufacturing workflows size hexagonal floor tiles, honeycomb panels, nut and bolt head flats, and regular cell packing layouts from a single edge length; area feeds material estimates while apothem and diagonals help place centerlines and clearance circles. Game, graphics, and CAD libraries store regular hexagonal grids for maps, strategy boards, and procedural meshes; deterministic area and related metrics support collision proxies and layout math without a full computational-geometry stack.
Survey and sketch tools sometimes approximate flat regular panels as hexagons when only the side is measured; having a shared numeric oracle keeps field notes and office scripts aligned. If you later need irregular hexagon area from vertices, hexagonal pyramid volume, or a general regular n-gon, treat those as separate search intents rather than overloading this hexagon-area landing.
What you can do with it
Homework and exam checks
Compute regular hexagon area from side length, and reject zero or negative sides with a clear error.
Tiles, panels, and bolt flats
From a measured edge length, recover area, perimeter, and apothem for cut lists and material estimates.
FAQ
What formula does this calculator use?
area = (3 × √3 / 2) × side² for a regular hexagon. Perimeter is 6×side; apothem is (√3/2)×side.
What happens if the side length is zero or negative?
The side must be a positive finite number; the error message names the field.
Does this work for irregular hexagons?
No. This tool assumes a regular hexagon (all sides equal, all interior angles equal). Irregular polygons need vertex coordinates and a different method such as the shoelace formula.
What else is returned besides area?
Perimeter (6×side), apothem ((√3/2)×side), long diagonal (2×side), short diagonal (side×√3), the area formula string, and a method tag for logs and teaching UIs.
What does it cost?
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/geom/hexagon-area \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"side":6}'const res = await fetch("https://api.kit.forhosting.com/geom/hexagon-area", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"side": 6
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geom/hexagon-area",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"side": 6
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geom/hexagon-area", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"side":6}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"side":6}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geom/hexagon-area", 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": 6
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geom.hexagon_area",
"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
A missing, non-finite, zero, or negative side is rejected with a clear invalid_input error instead of a silent nonsense area. No network calls, no random sampling, and no floating-point surprises beyond ordinary IEEE-754 arithmetic on the numbers you provide.
How regular hexagon area is computed from the side
Huge magnitudes can still overflow IEEE-754 double range; when intermediates are non-finite the request fails with a clear overflow message instead of returning Infinity in JSON. That closed form matches analytic geometry textbooks and keeps automated graders aligned with hand computation on the same side length.
What you send and what you get back
Provide one required finite number: side is the length of any edge of the regular hexagon and must be strictly positive. Example checks: side six yields area fifty-four root three (about 93.531) with perimeter thirty-six; side one yields the unit regular hexagon area; a side of zero or minus two fails naming the field. Wire the free browser tool for quick sanity checks, then call the identical contract from scripts for bulk evaluation without reimplementing the three-root-three formula in every language. Optional precision is an integer from zero through fifteen decimal places (default twelve) for numeric fields in the response; aliases decimals and dp map to the same control. Missing fields, empty strings, non-numeric text, NaN, Infinity, zero, and any negative side are rejected with invalid_input and are not charged. On success the JSON response returns side, area, perimeter, apothem, long_diagonal, short_diagonal, formula_area describing the closed form, and method set to regular_hexagon_side_squared so logs and teaching UIs can document the algorithm. API pricing is the published base of $0.002 per successful item.
Where hexagon area calculations show up in real work
Because this capability is a pure parse engine, failed validation does not consume balance and successful runs stay at $0.002 per item.
Integration use cases
Hex grid games and CAD cells
Turn side length into area and diagonals for layout, packing, and collision proxies in browser or API.