Area by Coordinates Worksheet
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Boundary corners (in order)
| Point | Easting (m) | Northing (m) | |
|---|---|---|---|
Enter corners in order around the boundary. The polygon closes back to the first point automatically — do not repeat it. Runs in your browser.
Result
Area = ½ |Σ(Eᵢ·Nᵢ₊₁ − Eᵢ₊₁·Nᵢ)|. The sign shows the order direction; the magnitude is the area either way.
How to use this calculator
- Enter the easting and northing of each boundary corner, in order around the boundary.
- Add or remove points to match your figure — don't repeat the first point, the tool closes the polygon for you.
- Read the enclosed area in square metres and hectares, plus the perimeter.
How it works
The worksheet uses the surveyor's cross-multiplication (shoelace) rule: area = ½ |Σ(Eᵢ·Nᵢ₊₁ − Eᵢ₊₁·Nᵢ)| taken around the closed figure.
The signed result tells you the point order (positive anticlockwise, negative clockwise); the magnitude is the enclosed area either way. The perimeter is the sum of the straight sides.
Worked example
A 40 m × 30 m rectangle. Four corners 40 m apart east and 30 m apart north enclose 1,200 m² (0.12 ha) with a 140 m perimeter, regardless of which corner you start from.
Tips
- Works for any closed figure with straight sides; curved boundaries need to be broken into chords or handled separately.
Frequently asked questions
Does the order of the points matter?
The points must go in sequence around the boundary (all clockwise or all anticlockwise). Out-of-order points create a self-crossing figure and a wrong area. The starting corner doesn't matter.
Do I repeat the first point at the end?
No — enter each corner once. The tool automatically closes the polygon from the last point back to the first.
Is this official course material?
No. It is free study support mapped to surveying course levels — not official North Metropolitan TAFE content or advice. Always follow your lecturer and the official assessment brief, and check your own working.
Related tools
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.