Area formulas
| Shape | Formula | Measure |
|---|---|---|
| Rectangle | A = length × width | Two adjacent sides |
| Square | A = side² | One side |
| Triangle | A = ½ × base × height | Base and the perpendicular height to it |
| Triangle (Heron) | s = (a + b + c) / 2; A = √(s(s−a)(s−b)(s−c)) | All three sides |
| Trapezoid | A = ½ × (a + b) × h | Both parallel sides and the distance between them |
| Circle | A = π × r² | Radius (half the diameter) |
| 4-sided plot | A = Heron(AB, BC, AC) + Heron(CD, DA, AC) | Four sides and one diagonal |
Square units come from multiplying two lengths: feet × feet gives square feet. To get acres, divide square feet by 43,560; to get hectares, divide square meters by 10,000. The calculator does those conversions for you with the exact definitions (1 ft = 0.3048 m).
Worked example: an irregular lot
A lot has sides AB = 210 ft, BC = 165 ft, CD = 281 ft and DA = 143 ft, and the diagonal AC measures 297 ft. The diagonal splits it into two triangles:
- Triangle ABC (210, 165, 297): s = 336, area = √(336 × 126 × 171 × 39) ≈ 16,803 ft²
- Triangle ACD (281, 143, 297): s = 360.5, area = √(360.5 × 79.5 × 217.5 × 63.5) ≈ 19,895 ft²
Total ≈ 36,698 ft², or about 0.84 acres (36,698 ÷ 43,560). Open this example. The longer guide how to calculate the acreage of an irregular lot walks through more methods.
Measuring tips
- Measure the height of a triangle or trapezoid at a right angle to the base, not along a sloping side.
- On sloping ground, hold the tape level. Land area is a horizontal (map) area; measuring along the slope makes the plot look bigger than it is.
- For more than four corners, or when you can’t measure a diagonal, record each corner with GPS and use the coordinate area calculator.