Irregular Land Area Calculator

How it works

Heron: area = √(s(s − x)(s − y)(s − z)), s = (x + y + z) ÷ 2 · plot area = triangle(AB, BC, AC) + triangle(CD, DA, AC) · 1 ha = 10,000 m² · 1 acre = 4,046.86 m² · 1 vara² = 0.6987 m²

Four sides alone do not fix the shape of a quadrilateral — the same sides can enclose different areas as the corners lean — so surveyors also measure one diagonal. The diagonal splits the plot into two triangles whose areas follow from their three sides by Heron’s formula, and the plot area is their sum. This is the classic tape-and-diagonal method for small irregular lots. For plots with five or more corners, divide them into more triangles from one corner, or use surveyed coordinates and the shoelace formula. Square varas use the Central American vara of 0.8359 m; Mexican and Spanish varas differ slightly.

Worked example

A plot with sides 30, 20, 28 and 22 m and a 36 m diagonal: triangle ABC has s = 43 and area √(43 × 13 × 23 × 7) = 300.00 m²; triangle ACD has s = 43 and area √(43 × 15 × 21 × 7) = 307.92 m². The plot covers 607.92 m², which is 0.0608 ha, 6,544 ft² or 0.150 acres.

Sources: Heron’s formula (Wolfram MathWorld) · NIST Handbook 44 Appendix C — General tables of units of measurement

Frequently asked questions