CADGISHow to use the calculator
- Enter the X (Easting) and Y (Northing) of each corner in meters, in order around the boundary. You can go clockwise or counter-clockwise.
- Use + Add point for more corners and × to remove a point. Point names are optional.
- Press Calculate. After that, results update as you edit.
- Choose the decimal places, then use Copy results to paste them into a report.
How coordinate area calculation works
If you know the coordinates of every corner of a parcel, you can calculate its area exactly, without measuring angles or splitting it into triangles by hand. Surveyors call this the coordinate method (or "area by coordinates"). CAD and GIS software use the same approach to report polygon areas.
Coordinates must be in a projected, flat grid measured in meters, such as UTM or a local site grid. Latitude and longitude in degrees won't give a correct area. Convert them to a projected system first.
The Shoelace formula in simple terms
List the points in order and repeat the first point at the end. Multiply each X by the next Y, and each Y by the next X. Written out in two columns, these multiplications criss-cross like shoelaces. Add up the first set, subtract the second, and halve the result:
Area = ½ × | Σ (Xi × Yi+1 − Xi+1 × Yi) |
The sign of the sum tells you the point order. A positive sum means counter-clockwise and a negative sum means clockwise. Taking the absolute value gives the same area either way. The perimeter is the sum of the straight-line distances between consecutive points, including the closing line from the last point back to the first:
Distance = √((X2 − X1)² + (Y2 − Y1)²)
Worked example
A four-sided parcel has these corner coordinates in meters:
| Point | X (m) | Y (m) | Xi·Yi+1 − Xi+1·Yi | Side length (m) |
|---|---|---|---|---|
| 1 | 100 | 100 | 100·110 − 160·100 = −5,000 | 1→2: 60.828 |
| 2 | 160 | 110 | 160·170 − 150·110 = 10,700 | 2→3: 60.828 |
| 3 | 150 | 170 | 150·150 − 90·170 = 7,200 | 3→4: 63.246 |
| 4 | 90 | 150 | 90·100 − 100·150 = −6,000 | 4→1: 50.990 |
| Total | 6,900 | 235.891 | ||
Area = ½ × |6,900| = 3,450.000 m² = 0.3450 ha = 0.8525 ac. Perimeter = 235.891 m. The sum is positive, so the points run counter-clockwise.
Unit conversions
- 1 hectare (ha) = 10,000 m²
- 1 acre (ac) = 4,046.8564224 m² (international acre)
Frequently asked questions
Do I need to enter the first point again at the end?
No. The polygon closes automatically. If you do repeat the first point, the calculator ignores the duplicate.
Does the order of points matter?
Yes. Points must follow the boundary in sequence, clockwise or counter-clockwise. If the order jumps across the shape, the edges cross and the area would be wrong, so the calculator shows an error.
Can I use UTM or large grid coordinates?
Yes. Large values such as 500000 / 6200000 work fine. Internally the calculator shifts coordinates relative to the first point to keep full precision.
Is this the same area my CAD or GIS software shows?
For the same projected coordinates, yes. This is planar (grid) area. Ground area can differ slightly because of map projection scale factor and elevation.