Coordinate Area Calculator
Calculate land area from a table of survey (Northing, Easting) coordinates using the surveyor's coordinate-method formula — enter the traverse points in order and get the enclosed area in m², hectares, acres and ft², the boundary perimeter, plus a per-leg bearing and distance table.
Input
Enter at least 3 points, one per line, in order around the closed traverse (the last point connects back to the first automatically). An optional leading label names the point (e.g. "P1, 1000.000, 2000.000").
The linear unit your Northing/Easting values are already in.
Output
| Point | Northing | Easting | Leg to | Bearing | Distance |
|---|---|---|---|---|---|
| No data yet | |||||
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/coordinate-area-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"vertices": "P1, 0, 0\nP2, 0, 100\nP3, 100, 100\nP4, 100, 0",
"units": "meters"
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `coordinate-area-calculator` tool (Coordinate Area Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/coordinate-area-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Coordinate Area Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
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Guides
Land surveyors measure boundaries as a closed traverse — a series of points, each recorded in local plane coordinates as a Northing (N) and an Easting (E), usually from a total station or GPS-RTK survey. The coordinate method (also called the Shoelace formula) turns that coordinate table directly into an enclosed area, with no need to draw the boundary or measure it on a plan.
How it works
- Traverse coordinates are entered one point per line, in order around the boundary, as
Northing, Easting(an optional leading label names the point, e.g.P1, 1000.000, 2000.000). The traverse closes automatically — the last point connects back to the first. - Coordinate units tells the tool whether your Northing/Easting values are in meters or feet, which drives the acre/hectare/ft²/m² conversions.
- Area is computed with the coordinate-method formula:
Area = ½ · |Σ (E_i · N_{i+1} − E_{i+1} · N_i)|, summed around the closed traverse. - Perimeter is the sum of the straight-line distance between each consecutive pair of points, including the closing leg back to the first point.
- Each row of the results table also reports the bearing (0–360°, clockwise from north) and distance of that leg — the same two figures a field book or a legal property description records for each boundary line.
Reading the result
The table lists every leg of the traverse: the point, its coordinates, the next point it connects to, and that leg's bearing and distance. The summary line gives the total enclosed area in your input units plus the other three common land units, and the total perimeter in both linear units.
Does the order of the points matter?
Yes — enter them in order around the boundary (either clockwise or counter-clockwise, both give the same area). Points out of order will still produce a number, but it describes a different, self-intersecting shape rather than your actual parcel.
Why report the area in four units at once?
A raw land survey is usually recorded in meters or feet, but the area is described to a client, on a title, or in a permit application in acres or hectares. Converting all four at once means you don't need a separate calculator to hand off the number in whichever unit the recipient expects.
What if my traverse doesn't quite close (Northing/Easting misclosure)?
This tool assumes the last point already connects correctly back to the first — it doesn't do the separate leg-by-leg closure/adjustment check surveyors run against measured bearings and distances. If your raw field measurements don't close, adjust them first (e.g. with a Bowditch/compass rule) before entering the corrected coordinates here.