How to Calculate the Area of Irregular Land (4 Unequal Sides)

Published October 31, 2026

To calculate the area of an irregular piece of land, split it into triangles with a diagonal, work out each triangle from its three sides (Heron's formula), and add them up. Four side lengths alone are not enough: you need at least one diagonal, or the corner positions. The fastest route is to tap the corners on a satellite map and let an app do the math.

Below you'll find the triangle method step by step, a worked example with real numbers, why the popular "average the opposite sides" shortcut can be badly off, and how to convert the result to acres.

Why four sides aren't enough

Picture a 130 × 100 ft rectangle made of four hinged boards. Push one corner and it leans into a parallelogram: the four sides stay exactly the same length, but the area shrinks. At a 60° lean, 13,000 ft² becomes about 11,260 ft². Same tape measurements, 13% less land.

That's why there's no formula that turns four unequal side lengths into one area. Something has to pin the shape down:

• a diagonal (corner to opposite corner), which splits the plot into two rigid triangles, or
• the corner angles, which are hard to measure without survey gear, or
• the coordinates of each corner, which is what a map or GPS gives you.

The triangle method, step by step

1. Sketch the plot and label the corners A, B, C, D in order around the boundary.
2. Measure the four sides (AB, BC, CD, DA) with a tape or wheel, keeping the tape level and tight.
3. Measure one diagonal, for example A to C. Pick the shorter, clearer one if you can.
4. For each triangle, find the semi-perimeter: s = (a + b + c) ÷ 2.
5. Apply Heron's formula: area = √( s × (s − a) × (s − b) × (s − c) ).
6. Add the two triangle areas. For a five- or six-sided plot, add more diagonals from the same corner and repeat for each triangle.

Worked example

A lot with sides AB = 140 ft, BC = 100 ft, CD = 130 ft, DA = 85 ft, and diagonal AC = 160 ft.

Triangle ABC (140, 100, 160):

• s = (140 + 100 + 160) ÷ 2 = 200
• area = √(200 × 60 × 100 × 40) = √48,000,000 ≈ 6,928 ft²

Triangle ACD (130, 85, 160):

• s = (130 + 85 + 160) ÷ 2 = 187.5
• area = √(187.5 × 57.5 × 102.5 × 27.5) ≈ 5,513 ft²

Total: about 12,441 ft², which is 12,441 ÷ 43,560 ≈ 0.29 acre, or about 1,156 m². The perimeter is 140 + 100 + 130 + 85 = 455 ft.

The "average the sides" shortcut, and when it fails

A rule of thumb you'll hear a lot: average the two opposite sides, average the other two, multiply. For the example above: (140 + 130) ÷ 2 × (100 + 85) ÷ 2 = 135 × 92.5 = 12,487.5 ft². That's within 0.4%, because the lot is almost a rectangle.

It's a different story on a wedge-shaped plot. Take sides of 200, 125, 105 and 115 ft with a 190 ft diagonal. The triangle method gives about 16,768 ft²; averaging gives 18,300 ft², 9% too much. Averaging always assumes square corners, so the more the plot leans or tapers, the more it overestimates. Fine for a rough guess on a near-rectangle; not something to price a sale on.

Measuring by coordinates instead of a tape

When you know the position of every corner, you don't need diagonals at all. Surveyors use the "shoelace" (coordinate) formula, which works for any number of corners. For a property of any real size, the earth's curvature matters too, so good mapping software computes the area on the ellipsoid instead of a flat sheet.

That's what Field Maps with Area Measure does on iPhone and iPad (iOS 17 or later). You can:

1. Tap each corner on the satellite map, using the magnifier loupe to place points precisely, with extra points along curved edges.
2. Or walk the boundary with GPS, and the app records the path and closes the shape for you.

Area and perimeter appear as you go, calculated geodesically on the WGS-84 ellipsoid, in ft², yd², acres, m², hectares, km² or mi². For an irregular lot with five, eight or twenty corners, that's a lot faster than measuring diagonals and running Heron's formula for each triangle. If you'd like a deeper look at the two methods, see how to measure land area by satellite or GPS.

Converting the result to acres

• 1 acre = 43,560 ft² = 4,840 yd² ≈ 4,046.9 m²
• ft² to acres: divide by 43,560
• m² to acres: divide by 4,046.9
• 1 hectare = 10,000 m² ≈ 2.47 acres

So a 0.29-acre lot is about 12,600 ft²; a 2-acre field is 87,120 ft².

Tips for an accurate irregular-lot measurement

• Measure diagonals between real corners, not fence posts set back from the line.
• Break curved edges into short straight sections. A creek or curved road frontage needs several points, or the triangles will cut off land.
• Check your arithmetic two ways. Measure the other diagonal (B to D) too and redo the math. If the two totals differ by more than a percent or two, one of the tapes is off.
• On a map, zoom in fully before placing each corner, and don't snap to the shadow of a wall or tree.
• With GPS, walk slowly under open sky. A phone is typically accurate to about 3–5 m (10–16 ft); under trees or next to buildings it gets worse. On a small lot, tapping on the satellite image is usually more precise.
• Remember slope. Maps and deeds give the horizontal area. On a steep lot, the ground surface is larger than the number you calculate.

FAQ

Is there a formula for the area of a quadrilateral with four different sides?

Not from the sides alone. You also need a diagonal or the angles. With one diagonal, split it into two triangles and use Heron's formula on each.

Can I calculate irregular land area in acres on my phone?

Yes. Tap the corners on a satellite map or walk the boundary with GPS, and the app shows the area in acres, square feet or hectares. Measuring, saving and exporting to CSV are free.

How accurate is the averaging method?

On a near-rectangle it's usually within a percent. On a tapered or skewed plot it can overestimate by 10% or more, because it assumes square corners.

Can I use my own measurement for a sale or a boundary dispute?

No. A tape or phone measurement is an estimate, useful for planning and budgeting. For anything legal or official, rely on a licensed surveyor and the recorded plat.