Polygon centroid calculator
For a ring with corners at latitude 0 to 3 and longitude 0 to 4, the area-weighted centre is 1.5, 2: the balance point of the whole shape, not simply the mean of its corners. Handy for labels and map pins inside a zone. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Runs in your browser. Free, unlimited — your data never leaves this page.
The area-weighted centroid of a simple polygon is the balance point of a uniform lamina whose boundary is an ordered ring of vertices. On maps and in GIS pipelines that point is usually requested in WGS84 latitude and longitude: send the corners of a parcel, a campus outline, or a delivery zone and receive a single lat/lon pair that sits at the geometric center of area rather than at a naive average of the corner list. Students, survey helpers, and map tools get a deterministic oracle they can pin in tests.
What an area-weighted polygon centroid is and when to use it
In plane geometry the centroid of a polygonal region is the center of mass assuming constant density. It is not the same as the average of the vertex coordinates once the shape has more than three corners: a long thin arm can pull the vertex mean away from the bulk of the area, while the area-weighted formula integrates over the interior via the shoelace sums.
Practitioners search for a polygon centroid calculator when they need to place a label inside a plot, pick a map marker for a multi-sided zone, seed a routing demo from a closed boundary, or check homework that asks for the barycenter of a quadrilateral or irregular field. GIS and education tools often hand you latitude and longitude lists rather than Cartesian meters, so treating longitude as the planar x axis and latitude as y in decimal degrees is a common local approximation for small regions.
This landing targets that intent: ordered lat/lon vertices in, a single stable lat/lon centroid out. Search phrases cluster around polygon centroid, area-weighted centroid, center of a polygon from coordinates, and shoelace centroid calculator. Unlike a triangle-only average of three points, the algorithm here generalizes to n greater than or equal to three and reports signed area so you can see winding direction and catch degenerate flat rings.
Practical limits and everyday uses
Use the free browser polygon centroid calculator when you want an immediate check while editing a zone outline, verifying a classroom exercise, or placing a map pin without installing GIS software. Rings are capped at a generous maximum vertex count suitable for city blocks and campus footprints; keep regions modest if you rely on the planar degree approximation, because large continental polygons should use equal-area projections or geodesic libraries instead of raw lat/lon shoelace. Self-intersecting bow-tie polygons are not a supported product promise; feed simple non-self-intersecting rings for predictable centers.
Authors shipping SDKs can map lat and lon directly into map marker APIs or CSV exports without reimplementing shoelace in every language.
What you can do with it
Map labels and zone markers
Place a single pin at the area-weighted center of a multi-sided delivery zone, parcel, or campus outline from ordered lat/lon corners.
Homework and GIS classroom checks
Students and graders verify shoelace centroids for quadrilaterals and irregular polygons without a local geometry library.
FAQ
What formula does the polygon centroid calculator use?
The planar shoelace area-weighted centroid with x = longitude and y = latitude in decimal degrees.
Is the polygon centroid calculator free?
The browser tool runs free on your device.
Is this the same as averaging all vertices?
No. For triangles the two can coincide, but for general n-gons the area-weighted shoelace centroid differs from the plain vertex average. This product always uses the area-weighted formula.
Can I use it for large regions or whole countries?
It is best for modest areas such as plots, campuses or city blocks. Longitude and latitude are treated as flat x and y in degrees, so continent-sized shapes need an equal-area projection or a geodesic tool instead.
Why was my polygon rejected?
Usually because it has fewer than three corners, or because its area is zero or almost zero, as with points in a straight line. Coordinates outside the valid latitude or longitude ranges are refused too.
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/geo/polygon-centroid \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"vertices":[{"lat":0,"lon":0},{"lat":0,"lon":4},{"lat":3,"lon":4},{"lat":3,"lon":0}]}'const res = await fetch("https://api.kit.forhosting.com/geo/polygon-centroid", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"vertices": [
{
"lat": 0,
"lon": 0
},
{
"lat": 0,
"lon": 4
},
{
"lat": 3,
"lon": 4
},
{
"lat": 3,
"lon": 0
}
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geo/polygon-centroid",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"vertices": [
{
"lat": 0,
"lon": 0
},
{
"lat": 0,
"lon": 4
},
{
"lat": 3,
"lon": 4
},
{
"lat": 3,
"lon": 0
}
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/polygon-centroid", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"vertices":[{"lat":0,"lon":0},{"lat":0,"lon":4},{"lat":3,"lon":4},{"lat":3,"lon":0}]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"vertices":[{"lat":0,"lon":0},{"lat":0,"lon":4},{"lat":3,"lon":4},{"lat":3,"lon":0}]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/polygon-centroid", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"vertices": [
{
"lat": 0,
"lon": 0
},
{
"lat": 0,
"lon": 4
},
{
"lat": 3,
"lon": 4
},
{
"lat": 3,
"lon": 0
}
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geo.polygon_centroid",
"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 capability implements the classical planar shoelace centroid on decimal-degree coordinates, rejects rings with fewer than three vertices, and returns structured JSON with the centroid, signed planar area, and a normalized vertex echo.
What an area-weighted polygon centroid is and when to use it
Results are pure functions of the input ring: identical vertices always produce identical JSON with no model, no network geocoder, and no random seed involved in the path.
Input contract, validation, and the shoelace formulas used
Latitude must lie between minus ninety and ninety, longitude between minus one hundred eighty and one hundred eighty, and every coordinate must be a finite number or numeric string. If the ring is closed in the GeoJSON style with the first point repeated at the end, the duplicate closing vertex is dropped before counting. Zero or near-zero signed area fails because collinear or collapsed rings have no well-defined area-weighted center. Send a JSON object whose required field vertices is an array of objects, each carrying lat and lon in WGS84 decimal degrees. Aliases points, ring, and coordinates are accepted for the array; each vertex also accepts latitude or y for lat and longitude, lng, or x for lon. After normalization the engine requires at least three vertices; fewer than three vertices raises invalid_input with a clear message and is not charged. The planar signed area A is half the sum of cross products x_i y_{i+1} minus x_{i+1} y_i with x equal to lon and y equal to lat. The centroid longitude is one over six A times the sum of x_i plus x_{i+1} times each cross term, and the centroid latitude uses the analogous sum on the y coordinates. Successful responses echo vertex_count and the normalized vertices, return lat and lon for the centroid, include signed_area in degree squared units for diagnostics, and set method to area_weighted_shoelace so callers can assert the algorithm in continuous integration. There is no triangulation library and no external map tile service—only arithmetic on a Worker isolate shared with the free in-browser tool.
API usage, pricing, limits, and practical workflows
Use the prepaid API when a logistics dashboard, property platform, lesson generator, or test suite needs the same area-weighted contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Order vertices consistently around the boundary—clockwise or counter-clockwise both work; the sign of signed_area reflects winding. Pair this endpoint with triangle centroid tools when the shape is strictly three points and you only want the arithmetic mean of vertices, or with bearing and distance helpers when the next step is navigation from the computed center.
Integration use cases
Deterministic fixtures for geo pipelines
CI and SDK demos pin stable lat/lon centroids from known rings instead of reimplementing area-weighted formulas in every service.
Technical questions
How do I compute a polygon centroid from lat/lon vertices?
Send JSON with vertices as an array of {lat, lon} objects (at least three). The response returns lat and lon for the area-weighted centroid plus signed_area.
What happens if I send fewer than three vertices?
The request fails with invalid_input because a polygon centroid requires at least three ordered vertices. Those validation failures are not charged.