Calculate the area of any common shape and convert land measurements between 18 units, including marla, kanal and bigha.
Real plots are rarely perfect rectangles. Boundaries follow roads, streams and old fences, and you end up with four, five or six sides of different lengths. You can still find the area accurately with a tape measure and some geometry. Here are three methods, from simplest to most precise.
Before you measure
- Use a 30 m / 100 ft tape, or a laser distance meter for long sides.
- Measure horizontal distances. On sloping ground, keep the tape level, as surveyors do.
- Sketch the plot first and label each corner (A, B, C, D…).
- Measure everything twice. Small errors on long sides add up.
Method 1: Split into rectangles and triangles
Most irregular plots can be divided into simple shapes.
Example: an L-shaped plot. Split it into two rectangles:
- Rectangle 1: 40 ft × 30 ft = 1,200 sq ft
- Rectangle 2: 20 ft × 25 ft = 500 sq ft
- Total = 1,700 sq ft
Calculate each piece with the area calculator (rectangle, triangle and trapezoid modes), then add them up.
Method 2: Triangulation (Heron’s formula)
Any polygon can be divided into triangles by drawing diagonals from one corner. If you can measure all three sides of each triangle, you don’t need any angles or heights.
Heron’s formula:
s = (a + b + c) ÷ 2
Area = √(s(s − a)(s − b)(s − c))
Worked example: a four-sided plot
Sides: AB = 60 ft, BC = 45 ft, CD = 55 ft, DA = 40 ft. Diagonal AC = 70 ft.
Triangle ABC (60, 45, 70): s = 87.5 → Area = √(87.5 × 27.5 × 42.5 × 17.5) ≈ 1,338 sq ft
Triangle ACD (70, 55, 40): s = 82.5 → Area = √(82.5 × 12.5 × 27.5 × 42.5) ≈ 1,098 sq ft
Total ≈ 2,436 sq ft, about 10.8 marla at 225 sq ft or 8.9 marla at 272.25 sq ft (see Marla, Kanal and Acre Conversion: The Complete Guide (Pakistan & India)).
Use the Triangle (3 sides) shape in the calculator for each triangle. For five or six sides, add more diagonals from the same corner.
Why the diagonal matters: a four-sided plot’s area is not fixed by its four sides alone. The shape can “flex”. You need at least one diagonal to pin it down.
Method 3: The shoelace formula (coordinates)
If you have corner coordinates, from a site plan, GPS or by measuring from a fixed baseline, the shoelace formula gives the exact area of any simple polygon:
Area = ½ |Σ (xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)|
Example: corners at (0, 0), (60, 0), (70, 40), (10, 50):
| Step | xᵢ·yᵢ₊₁ | xᵢ₊₁·yᵢ |
|---|---|---|
| (0,0)→(60,0) | 0 | 0 |
| (60,0)→(70,40) | 2,400 | 0 |
| (70,40)→(10,50) | 3,500 | 400 |
| (10,50)→(0,0) | 0 | 0 |
| Sum | 5,900 | 400 |
Area = ½ × |5,900 − 400| = 2,750 sq ft
This is what surveying and GIS software does internally.
Curved boundaries
For a curved edge, such as a stream, take offsets: measure perpendicular distances from a straight baseline at regular intervals, then treat each strip as a trapezoid. Narrower intervals give more accuracy.
Accuracy tips
- A 1% error in each of two sides is about a 2% error in area.
- Close the loop: add up your triangles two different ways (using different diagonals) and compare. If the results differ by more than 1–2%, re-measure.
- For legal transfers or disputes, hire a licensed surveyor. Tape measurements are fine for planning but not for title documents.
For the formulas behind each shape, see Area Formulas for Common Shapes (With Diagrams in Words and Examples).
Calculate the area of any common shape and convert land measurements between 18 units, including marla, kanal and bigha.