Plan area, not surface area
A map shows the ground from directly above, so any area you measure on it is the plan area: the area projected onto a flat, horizontal surface. That's what lot sizes and most quantities use. On sloping ground the actual surface is bigger, which matters for anything laid on it, such as topsoil, turf, geofabric or erosion matting on a batter.
To convert, divide the plan area by the cosine of the slope angle:
Surface area = plan area ÷ cos(slope angle)
- 5° slope: 0.4% more than the plan area
- 10° slope: 1.5% more
- 20° slope: 6.4% more
- 30° slope: 15.5% more
Our guide to slope ratios covers converting a ratio like 1V:2H into an angle.
Method 1: trace it on a map
Online maps and apps let you place points around a boundary on aerial imagery and read off the area. It's fast, and good enough for planning and estimating. Zoom in when you place the corners, follow the real edge rather than shadows or tree canopy, and remember that imagery can sit a few metres away from its true position.
Method 2: coordinates and the shoelace formula
If you have coordinates for the corners, from a survey or a plan, you can calculate the area exactly with the shoelace formula. List the corners in order around the boundary. For each corner, multiply its x by the next corner's y, and subtract the next corner's x multiplied by its y. Add up the results and halve the total:
Area = ½ × | Σ (xi × yi+1 − xi+1 × yi) |
Here's an L-shaped yard with corners at (0, 0), (50, 0), (50, 20), (20, 20), (20, 40) and (0, 40), in metres:
| From | To | x × next y − next x × y |
|---|---|---|
| (0, 0) | (50, 0) | 0 × 0 − 50 × 0 = 0 |
| (50, 0) | (50, 20) | 50 × 20 − 50 × 0 = 1,000 |
| (50, 20) | (20, 20) | 50 × 20 − 20 × 20 = 600 |
| (20, 20) | (20, 40) | 20 × 40 − 20 × 20 = 400 |
| (20, 40) | (0, 40) | 20 × 40 − 0 × 40 = 800 |
| (0, 40) | (0, 0) | 0 × 0 − 0 × 40 = 0 |
The total is 2,800, so the area is 2,800 ÷ 2 = 1,400 m². As a check, the L is a 50 × 20 rectangle plus a 20 × 20 one: 1,000 + 400 = 1,400 m².
Method 3: the lot's official area
For a whole lot, the area is shown on its survey plan, which you can get from your state's land titles office, such as Landgate in Western Australia. That's the figure to use for anything legal.
Method 4: walk the boundary with GPS
A phone can record a boundary as you walk it, but phone GPS is typically only accurate to a few metres, so use it for rough areas only.
Units
- 1 hectare (ha) = 10,000 m²
- 1 acre ≈ 4,046.9 m²
- 1 ha ≈ 2.471 acres
The yard above is 1,400 m², which is 0.14 ha, or about 0.35 acres.
A note on accuracy
Map and app measurements are estimates for planning and quantities. Where the boundary or the exact area has legal or contractual weight, use a licensed surveyor.
Doing it on site
SiteArea measures plan area. You place points along the boundary on the map, and it gives the area as seen from above. It doesn't account for elevation, so on sloping ground, use the correction at the top of this article to get the surface area.