Geographic polygon area
A one-degree box at the equator with corners (0, 0), (0, 1), (1, 1) and (1, 0) covers 12363.71814518 km² on a mean-Earth sphere: a true surface area from map corners, not flat coordinate units. 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.
This geographic polygon area calculator takes an ordered ring of latitude and longitude vertices and returns the spherical surface area of that polygon in square meters on a mean-Earth sphere. Unlike a flat Cartesian shoelace area in abstract x-y units, this tool treats the Earth as a sphere of radius R (default 6,371,008.8 m, the IUGG mean radius) and applies a Chamberlain–Duquette style ring sum so the result is a real-world area you can report in m² or km². You need at least three distinct vertices; a closing repeat of the first point is optional and is dropped automatically. The path is fully deterministic: no network calls, no sampling, and no date-dependent shortcuts.
What the spherical area means and what you get
A geographic polygon is an ordered sequence of points on the Earth expressed as latitude and longitude in decimal degrees. Planar formulas that treat those numbers as plain x-y coordinates ignore the sphere: they can be useful for tiny local sketches, but they do not report true surface area in square meters.
This calculator models the planet as a sphere of radius R and evaluates a ring sum that accumulates longitude steps weighted by the sine of latitude at each vertex—the Chamberlain–Duquette construction used widely in GIS stacks such as Mapbox geojson-area and Turf area for spherical rings. The absolute value of that sum times R squared over two is the unsigned surface area in square meters. Self-intersecting or multi-ring multipolygons are outside this contract: feed a single simple ordered ring.
If you need planar shoelace on abstract coordinates, use the dedicated planar polygon tool; this page answers only the geographic spherical case suitable for maps, land parcels, and spherical demos that must quote SI area units.
Where geographic polygon area fits in mapping, survey, and software
Analysts and developers reach for spherical polygon area when a property boundary, flood zone, or delivery region is defined by GPS corners and the stakeholder asks for square meters or hectares, not abstract coordinate units. Students and teachers use a known ring—such as a one-degree box near the equator—to check homework against GIS software without installing a full desktop stack.
Product teams embed the same contract when a mobile app captures a fence-walk of lat/lon points and must show area immediately, or when a backend job validates uploaded GeoJSON rings before storage. Pair it with rhumb or great-circle distance helpers when you also need path lengths on the same sphere, and with planar shoelace when the problem is pure Euclidean geometry rather than geography.
What you can do with it
Parcel and fence-walk area
Turn ordered GPS corners of a field, lot, or delivery zone into square meters for reports and quotes.
GIS ring validation
Sanity-check GeoJSON-style rings from exporters against a second spherical area before publishing maps.
FAQ
What does the geographic polygon area calculator cost?
It is free in your browser on this page.
How is the area computed?
On a sphere of radius R, a Chamberlain–Duquette style sum S = Σ (λ_{i+1} − λ_{i−1}) sin φ_i over the ordered ring gives area = |S|·R²/2 in square meters (φ latitude, λ longitude in radians).
What if I supply fewer than three distinct vertices?
A polygon surface needs at least three distinct corners after an optional closing duplicate is dropped.
Is this the same as planar shoelace area?
No. Planar shoelace treats coordinates as flat x-y units. This tool models a sphere and returns real surface area in m² from geographic lat/lon.
Can I change the Earth radius?
The default is 6371008.8 m (IUGG mean Earth radius). Results scale with R².
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-area \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"vertices":[[0,0],[0,1],[1,1],[1,0]]}'const res = await fetch("https://api.kit.forhosting.com/geo/polygon-area", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"vertices": [
[
0,
0
],
[
0,
1
],
[
1,
1
],
[
1,
0
]
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/geo/polygon-area",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"vertices": [
[
0,
0
],
[
0,
1
],
[
1,
1
],
[
1,
0
]
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/geo/polygon-area", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"vertices":[[0,0],[0,1],[1,1],[1,0]]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"vertices":[[0,0],[0,1],[1,1],[1,0]]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/geo/polygon-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
{
"vertices": [
[
0,
0
],
[
0,
1
],
[
1,
1
],
[
1,
0
]
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "geo.polygon_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.
Limits
lat_min | -90 |
lat_max | 90 |
lon_min | -180 |
lon_max | 180 |
max_vertices | 10000 |
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
What spherical polygon area means and what the response contains
The response includes the vertex count n, how many of those vertices are distinct, area_m2, a convenient area_km2 companion, the signed_area_m2 (orientation-sensitive), a clockwise or counterclockwise orientation label, the radius_m used, the unit tag m2, a short formula reminder, the precision applied, and the normalized vertex list as lat/lon objects. Degenerate rings that collapse to fewer than three distinct points after dropping a trailing closer are rejected with invalid_input rather than returning a silent zero that could look like a real plot.
How vertices, radius, and precision are read so results stay reproducible
A trailing vertex that duplicates the first within a tiny degree epsilon is treated as closed-ring notation and removed before the area sum, so you can paste rings from GIS exporters that repeat the start point. Latitude must lie in [−90, 90] and longitude in [−180, 180]; out-of-range or non-finite coordinates fail clearly so a bad spreadsheet cell does not become a wrong square-kilometer figure. Longitudes are unwrapped along the ring so edges that cross the antimeridian do not inject spurious ±2π jumps into the sum. The preferred field is vertices: an ordered array of at least three points. Each point may be a [lat, lon] pair or a {lat, lon} object; aliases latitude for lat and longitude or lng for lon are accepted so GeoJSON-adjacent objects and typed forms can reuse the same contract without renaming columns. Aliases for the whole list include points, polygon, coords, and ring. After that normalization, fewer than three distinct vertices raises invalid_input with a message that names the requirement—this is the hard product rule for the capability. Optional radius (aliases R and earth_radius) sets the sphere radius in meters and defaults to the IUGG mean Earth radius 6371008.8 m; optional precision (aliases decimals and dp) chooses decimal places for the primary area fields, defaulting to three so large m² values stay readable while still stable for JSON goldens. Pair the free browser run on this page with the priced API when you need the same mathematical result inside an automated pipeline without re-implementing spherical ring area yourself.
Where geographic polygon area fits in mapping, survey, and software
Survey prep and environmental reporting often need a second opinion on a ring exported from a handheld GNSS unit: pasting vertices here and comparing area_m2 to the field logger catches unit mistakes early. Contest and interview problems sometimes ask for spherical area formulas; a deterministic endpoint gives reference values for grading scripts. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split—free interactive exploration and a priced, identical API—matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result.
Integration use cases
Deterministic CI fixtures
Generate reproducible area_m2 values for unit tests of mapping UIs, cadastral tools, and analytics jobs.