Calculate the area of any common shape and convert land measurements between 18 units, including marla, kanal and bigha.
Area measures how much flat surface a shape covers, in square units: square metres, square feet, square inches. Here is every formula you’re likely to need, why it works and a quick example for each.
Quick reference
| Shape | Formula | Variables |
|---|---|---|
| Square | A = s² | s = side |
| Rectangle | A = l × w | length, width |
| Triangle | A = ½ × b × h | base, perpendicular height |
| Triangle (3 sides) | A = √(s(s−a)(s−b)(s−c)) | s = half the perimeter |
| Circle | A = πr² | r = radius |
| Ellipse | A = πab | a, b = semi-axes |
| Trapezoid | A = ½(a + b)h | parallel sides a, b; height h |
| Parallelogram | A = b × h | base, perpendicular height |
| Rhombus | A = (d₁ × d₂) ÷ 2 | diagonals |
| Kite | A = (d₁ × d₂) ÷ 2 | diagonals |
Squares and rectangles
A rectangle is rows of unit squares: length × width. A 12 ft × 15 ft room is 180 sq ft. A square is a rectangle with equal sides, so A = s². A 9 m square is 81 m².
Triangles
Base × height
A triangle is half of a parallelogram with the same base and height: A = ½bh. The height must be perpendicular to the base, not a slanted side. Base 10 cm, height 6 cm → 30 cm².
Three sides (Heron’s formula)
When you know the sides but not the height, which is common in land measurement, use s = (a + b + c) ÷ 2 and A = √(s(s−a)(s−b)(s−c)). Sides 13, 14, 15 → s = 21 → A = √(21 × 8 × 7 × 6) = 84. This is the basis of plot triangulation; see How to Calculate the Area of an Irregular Plot of Land.
Circles
A = πr², where r is the radius (half the diameter). A pizza with a 30 cm diameter has r = 15 → A ≈ 706.9 cm².
Doubling a circle’s diameter quadruples its area. One 16-inch pizza (201 in²) has more than two 10-inch pizzas (2 × 78.5 = 157 in²).
Ellipses
A = πab, where a and b are half the longest and shortest widths. An oval table 2 m long and 1.2 m wide: a = 1, b = 0.6 → 1.885 m². A circle is just an ellipse with a = b = r.
Trapezoids
Average the two parallel sides, then multiply by the height: A = ½(a + b)h. Parallel sides 8 m and 12 m, height 5 m → 50 m². Useful for sloped plots and offset survey strips.
Parallelograms
Slide a triangle from one end to the other and a parallelogram becomes a rectangle: A = base × perpendicular height. Base 10, height 4 → 40. Using the slanted side instead of the height is the most common mistake.
Rhombuses and kites
Both have perpendicular diagonals, so the area is half their product: A = (d₁ × d₂) ÷ 2. Diagonals 10 and 6 → 30.
Unit conversions
Area units convert by the square of the length factor:
- 1 m = 3.2808 ft → 1 m² = 10.764 sq ft
- 1 ft = 12 in → 1 sq ft = 144 sq in
- 1 yd = 3 ft → 1 sq yd = 9 sq ft
So you can’t convert 100 m² to square feet by multiplying by 3.28; it’s 100 × 10.764 = 1,076 sq ft. The area calculator handles all of this, including land units like marla and kanal (see the conversion guide).
Composite shapes
Break complex shapes into the basic shapes above, calculate each, and add the parts, or subtract cut-outs. A rectangular garden of 20 × 10 m with a circular pond of radius 2 m has a lawn area of 200 − 12.57 = 187.4 m².
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Calculate the area of any common shape and convert land measurements between 18 units, including marla, kanal and bigha.