Area from coordinates calculator with metes and bounds description and DXF plat
Calculate the area and perimeter of a lot from its coordinates or from measured sides. Get the table of courses with bearings, a metes and bounds legal description in Word, and a DXF plat for AutoCAD and Civil 3D.
- Free, no sign-up
- Bearings and distances
- Metes and bounds in Word
- DXF plat
Lot area and perimeter calculator
Lot already drawn in AutoCAD? Save it as DXF and import it: we read its polylines.
Result
- Area
- 17,480.59 ft²
- 0.401 ac · 1,624.00 m²
- Perimeter
- 507.84 ft
- Points
- 5
- Clockwise
At ground level (elevation 10 m): 17,491.60 ft² · combined scale factor 0.99968511.
✓ Sum of interior angles: 540°00'00". The polygon closes.
TABLE OF COURSES
| Point | Course | Bearing | Distance (ft) | Interior angle | Easting (m) | Northing (m) |
|---|---|---|---|---|---|---|
| 1 | 1–2 | N 80°16'21" E | 116.50 | 107°51'28" | 583900.000 | 4507300.000 |
| 2 | 2–3 | S 9°27'44" E | 119.74 | 89°44'05" | 583935.000 | 4507306.000 |
| 3 | 3–4 | S 62°35'33" W | 99.78 | 107°56'43" | 583941.000 | 4507270.000 |
| 4 | 4–5 | N 48°21'59" W | 79.01 | 110°57'32" | 583914.000 | 4507256.000 |
| 5 | 5–1 | N 8°07'48" E | 92.80 | 123°30'12" | 583896.000 | 4507272.000 |
Adjoiners: who borders each side?
Optional. What you type appears in the legal description.
Legal description
LEGAL DESCRIPTION
Lot 5, Block 12, Maple Street subdivision
Beginning at point 1, having grid coordinates of Northing 4,507,300.000 and Easting 583,900.000;
thence N 80°16'21" E, a distance of 116.50 feet, along the lands of Maple Street, to point 2;
thence S 9°27'44" E, a distance of 119.74 feet, along the lands of Lot 6, to point 3;
thence S 62°35'33" W, a distance of 99.78 feet, along the lands of Lot 12, to point 4;
thence N 48°21'59" W, a distance of 79.01 feet, along the lands of Lot 12, to point 5;
thence N 8°07'48" E, a distance of 92.80 feet, along the lands of Lot 4, to the point of beginning,
containing 17,480.59 square feet (0.401 acres), more or less.
Bearings, distances and area are grid values referenced to UTM Zone 18 North, WGS 84.
Check the lot on the map
If the polygon lands somewhere else, check the zone, the hemisphere or the column order.
In short
To calculate area from coordinates, use the shoelace formula: cross-multiply the easting and northing of consecutive points, add the results and take half the absolute value. A 5-point lot in this tool's example covers 17,480.59 square feet (0.401 acres). If you only have measured sides, a 4-sided lot also needs a diagonal: it splits the lot into two triangles solved with Heron's formula. With the four sides alone, the area is not determined.
How to calculate area from coordinates
It's the method every surveying program uses: the shoelace formula (also called Gauss's area formula). Walk the points in order and cross-multiply the coordinates of each consecutive pair:
Area = ½ · | Σ (Eᵢ · Nᵢ₊₁ − Eᵢ₊₁ · Nᵢ) |
E = easting, N = northing. The last point connects back to the first.
This is the lot preloaded in the calculator, in UTM coordinates (WGS 84, Zone 18 North, meters):
| Point | Easting | Northing | Course | Bearing | Distance (ft) |
|---|---|---|---|---|---|
| 1 | 583900.000 | 4507300.000 | 1–2 | N 80°16'21" E | 116.50 |
| 2 | 583935.000 | 4507306.000 | 2–3 | S 9°27'44" E | 119.74 |
| 3 | 583941.000 | 4507270.000 | 3–4 | S 62°35'33" W | 99.78 |
| 4 | 583914.000 | 4507256.000 | 4–5 | N 48°21'59" W | 79.01 |
| 5 | 583896.000 | 4507272.000 | 5–1 | N 8°07'48" E | 92.80 |
Result: 17,480.59 square feet (0.401 acres), or 1,624.00 m², with a perimeter of 507.84 feet. Points must be in order around the lot; if two sides cross, the tool flags it instead of returning a false area.
Area of an irregular 4-sided lot: why you need a diagonal
Four sides alone don't fix the shape of a lot: like a frame without a square, it can lean into many shapes, each with a different area. You need one more measurement, a diagonal. It splits the lot into two triangles, each solved with Heron's formula:
Area = √( s · (s − a) · (s − b) · (s − c) ), s = (a + b + c) / 2
a, b, c = triangle sides; s = semi-perimeter.
Example, the one in “By measurements” mode: sides of 30.00, 21.50, 27.80 and 19.60 feet and a diagonal 1–3 of 37.40 feet give 588.02 square feet.
What a metes and bounds description contains
- Point of beginning (POB): a defined starting point, here with its grid coordinates.
- Courses: from point to point, each with a bearing and a distance (“thence N 80°16'21" E, a distance of 116.50 feet”), optionally along the adjoining owner.
- Closure: the last course returns “to the point of beginning”.
- Area: “containing … square feet (… acres), more or less”.
- Basis of bearings: the grid or system the bearings refer to.
Bearings, azimuths and interior angles
- Quadrant bearing: the angle from north or south toward east or west, up to 90° (S 62°35'33" W).
- Azimuth: the angle from north, clockwise, from 0° to 360°. S 62°35'33" W is an azimuth of 242°35'33".
- Interior angle: the angle of the lot at each point. The interior angles of an n-sided polygon always add up to (n − 2) × 180°: 540°00'00" for this 5-point lot.
Grid area vs. ground area
Projected coordinates (UTM or State Plane) live on a grid. A grid distance is not exactly the distance measured on the ground: the combined scale factor accounts for the projection and the elevation.
For the example lot near New York City, 10 m above the ellipsoid, the combined factor is 0.99968511: the grid area is 1,624.00 m² and the ground area 1,625.02 m², about 11 square feet more. The calculator shows both. To convert points or check each point's factor, use the UTM to lat long converter.
From an AutoCAD polyline to a description, and back to the plat
Already drawn the lot? Save the drawing as DXF (SAVEAS, DXF type) and upload it with Import DXF: the calculator reads the polylines and extracts their vertex coordinates, no LISP routine needed.
The other way around, the DXF the tool creates contains the boundary, point names, the distance on each side and the table of courses already drawn, on separate layers and at real coordinates. It opens in AutoCAD, Civil 3D or any CAD program. To automate this in your office, see how to automate Civil 3D.
Drafting plats and legal descriptions every week? We automate them in Civil 3D.
We build plugins that generate the plat, the table of courses and the legal description from the drawing, in your office's format. What takes an afternoon today, in one click.
Free initial diagnosis · No commitment · We reply the same day
Frequently asked questions
How do I calculate area from coordinates?
Use the shoelace formula: list the points in order, cross-multiply the easting and northing of each consecutive pair, add them and take half the absolute value. This calculator does it when you paste the coordinates from Excel.
How do I find the area of an irregular 4-sided lot?
Measure one diagonal as well: it splits the lot into two triangles whose areas come from Heron's formula. With the four sides alone the area is not determined, and averaging opposite sides overestimates it.
What is a metes and bounds legal description?
A description of a parcel's boundary as a sequence of courses — bearing and distance — from a point of beginning back to it, with the adjoining owners, the area and the basis of bearings.
How do I convert a bearing to an azimuth?
For N θ E the azimuth is θ; for S θ E it is 180° − θ; for S θ W it is 180° + θ; and for N θ W it is 360° − θ. S 62°35'33" W equals an azimuth of 242°35'33".
How do I get coordinates from an AutoCAD polyline?
Save the drawing as DXF, upload it with “Import DXF” and pick the polyline: the calculator extracts its vertices. Then download the Excel table or the legal description.
Is the area from grid coordinates the true area?
It's the grid area. On the ground it differs by the combined scale factor, typically by a few hundredths of a percent; about 11 square feet for the example lot. The calculator shows both.
Are my coordinates sent to a server?
No. The calculation and the files are generated in your browser. The map downloads OpenStreetMap tiles for the area it shows.
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