When to use this calculator
Use it when a lot has five or more sides, or when you already have corner coordinates from a plat, a survey or a GPS. For a four-sided lot where you only know the length of each side, the irregular land area calculator is quicker.
Unlike the side-averaging shortcut, the result here is exact for any shape with straight sides, including L-shaped lots and lots with notches.
How to use it
- Pick the unit of your coordinates (feet, meters or yards).
- Enter the corners in order, walking around the boundary in one direction. You can start at any corner and go clockwise or counterclockwise.
- Add as many corners as the lot has with Add vertex.
- Area, hectares, perimeter and a drawing update as you type. If the drawing looks like a figure eight, some corners are out of order.
Getting the coordinates
- Plat or survey: many surveys include a table of corner coordinates. Copy them as they are.
- GPS or mapping app: use projected coordinates in feet or meters, such as UTM or State Plane. Latitude and longitude in degrees can't be used directly.
- With a tape: call one corner (0, 0) and use one straight side as the X axis. For each corner, measure how far along that line it is (X) and how far it sits from it at a right angle (Y).
The formula
The calculator uses the shoelace formula, also known as Gauss's area formula:
Each term is twice the area of a triangle formed by the origin and one side. Added together, the parts outside the lot cancel out and only the area inside remains.
A five-sided lot (the “Load example” button)
Corners: (0, 0), (40, 0), (45, 25), (20, 38) and (−5, 22).
| Side | xᵢ · yᵢ₊₁ − xᵢ₊₁ · yᵢ |
|---|---|
| 1 → 2 | 0 · 0 − 40 · 0 = 0 |
| 2 → 3 | 40 · 25 − 45 · 0 = 1,000 |
| 3 → 4 | 45 · 38 − 20 · 25 = 1,210 |
| 4 → 5 | 20 · 22 − (−5) · 38 = 630 |
| 5 → 1 | −5 · 0 − 0 · 22 = 0 |
The sum is 2,840, so the area is 2,840 ÷ 2 = 1,420 square units. In meters that is 1,420 m² (0.142 ha); in feet, 1,420 ft² (0.0326 acres). The perimeter is 145.92 units.
Frequently asked questions
Can I use latitude and longitude?
Not directly. Convert them to a projected system in feet or meters first. Most GPS and survey apps can show UTM coordinates for each point.
Does it matter which corner I start with?
No. What matters is going around the boundary in order. Clockwise or counterclockwise gives the same area.
Does it work for curved boundaries?
Only approximately. Add several points along the curve: the more points, the closer you get to the real area.
Why does it say two sides cross?
In that order the boundary crosses itself, like a figure eight, so the computed area is not the lot's. Reorder the corners along the boundary.