Land Area Calculator

Few plots are perfect rectangles, and that is what makes land awkward to measure. A fence line drifts, a road cuts a corner, a field narrows toward the back. This calculator handles the common cases with lengths alone, so you need no angle-measuring tools, only a long tape or a measuring wheel. Each input has its own unit menu, and the plot's size comes back in the units buyers, farmers and councils tend to ask for.

Formula

A = l × w

A

the area of a rectangular plot

l

the length of the plot

w

the width of the plot

Other plot shapes are cut into triangles and solved with Heron's formula.

Rectangular plots

If the corners are square, multiply the length by the width. A field of 660 ft by 330 ft covers 217,800 ft², which is exactly 5 acres or about 2.02 hectares. In metric, a plot of 250 m by 120 m covers 30,000 m², which is 3 hectares or about 7.41 acres.

To check that the corners really are square, compare the opposite sides and then the two diagonals. If both pairs of sides match and the diagonals match too, the plot is a true rectangle. If not, use the 4 sides method instead.

Triangular plots

Three boundary lengths fix a triangle completely, so no height or angle is needed. Heron's formula takes them directly. A corner plot with sides of 120 ft, 150 ft and 200 ft has an area of about 8,966.6 ft², or about 0.21 acres. Triangles are also the reason surveyors like cutting land up: unlike a four-sided plot, a triangle cannot change shape once its sides are known.

4-sided plots with a diagonal

Four boundary lengths are not enough on their own, because the same four sides can lean into many different shapes with different areas. One diagonal, measured corner to corner across the plot, locks the shape into two triangles. Label the sides in order around the plot, so that a and b form one triangle with the diagonal and c and d form the other.

For sides of 80, 60, 70 and 50 ft with a 90 ft diagonal, the two triangles come to about 2,352.5 ft² and 1,741.2 ft², for a total of about 4,093.7 ft². Use a diagonal that runs inside the plot. If the plot has a corner that points inward, a diagonal that crosses outside the boundary will give the wrong answer.

The average sides estimate

A traditional surveyors' shortcut averages each pair of opposite sides and multiplies the two averages. It needs no diagonal, which is why it is still used for rough field work. It is an estimate only, and this calculator labels it as one. Except on a rectangle, it always comes out above the true area.

With the same four sides as above, the shortcut gives 75 × 55 = 4,125 ft², less than 1% above the 4,093.7 ft² found with the 90 ft diagonal. But if the true diagonal is 60 ft, the plot really covers about 3,258.5 ft² and the shortcut is about 27% too high. The more a plot leans, the worse it gets. It is fine for a first guess at seed or fertilizer, not for a sale price.

• A ≈ ½(a + c) × ½(b + d)

Land units compared

Acres and hectares are the usual units for farmland, while house lots are more often quoted in square feet or square meters. The conversions below are exact definitions or rounded from them. Regional units such as the bigha vary from place to place, so check the local value before converting to them.

Measuring on the ground

Measure along the ground in straight lines from corner to corner, and hold the tape level on sloping land. A tape laid along a slope reads longer than the flat distance, which inflates the result. For a boundary with bends, add a corner at each bend and use the irregular shape calculator with coordinates. These figures are good for planning, but a sale, a boundary dispute or a planning application calls for a licensed surveyor.

Frequently asked questions