Land Area Calculator

How to calculate land area with 4 different sides

Measure the four sides and one diagonal, from corner A to corner C. The diagonal splits the plot into two triangles, each worked out from its three sides alone (Heron's formula), and the two added up are the area. Choose "4 sides" above. Any plot can be split into triangles this way, so a measuring tape is all you need:

area = √(s(s − a)(s − b)(s − c)),  s = (a + b + c) ÷ 2

Example: a plot with sides AB 40 ft, BC 62 ft, CD 45 ft, DA 60 ft and the diagonal AC 75 ft. Triangle ABC (40, 62, 75) is 1,239.17 sq ft and triangle ACD (75, 45, 60) is 1,350 sq ft: together 2,589.17 sq ft, which is 287.69 gajam or 5.94 cents.

Plot area in gaj (square yards)

Divide the square feet by 9: a gaj (gajam, square yard) is 3 ft × 3 ft. The calculator shows every plot in gajam and cents, or acres and guntas for a field; for other units, use the land area converter.

How to measure a plot

• Name the corners A, B, C, D… going round the boundary, and measure each side from corner to corner with the tape pulled tight and level.
• For four or more sides, measure the diagonal from A to C too (and A to D… for more sides). Four sides alone do not fix the shape: like a door frame, the plot can lean and hold less.
• The diagonals must run inside the plot: the area is the triangles they cut it into, added up. If a corner points inwards (an L-shaped or arrow-shaped plot), name it A, so every diagonal starts there and stays inside; a diagonal across the outside would add land that is not in the plot.
• For a rectangle the diagonal checks the corners: with square corners it equals √(length² + width²), 50 ft for a 40 × 30 ft plot. A shorter or longer diagonal means the plot leans and holds less than length × width.
• For an L-shaped or odd plot, choose as A a corner from which every other corner can be seen, or split the plot into simple parts and add their areas.

From coordinates

Choose "Coordinates" and give each corner's latitude and longitude, going round the plot: from a surveyor's sketch or a land record that lists them, or from Google Maps (press and hold the spot). The corners are placed on a flat map around the plot and the area worked out from them, so the answer is only as good as the coordinates. Their last digit says how far rounding can move a corner:

Degrees, minutes and seconds work too, each number read by its mark (17°30″ is 17° 0′ 30″): whole seconds (17°23'06"N) round a corner by up to about 15 m, tenths of a second by about 1.5 m.

The digits are not the whole story. A spot picked on Google Maps or read from a phone's GPS has six decimals and is still usually about 5 m from the true corner: enough to put a field of an acre off by about ±11% and a 30 × 40 ft house plot by about ±68%. For a house plot, measure the sides with a tape (the other shapes) or use a survey's coordinates. Each corner says how precise its digits are, and the result how far rounding and a phone's or a map's usual error can move the area. A link you share carries the coordinates.

Why not average the opposite sides?

The old shortcut, (40 + 45) ÷ 2 × (62 + 60) ÷ 2 = 2,592.5 sq ft for the example, is exact only for a rectangle; for every other shape it gives more than the true area. Without a diagonal, the most four sides can enclose is Brahmagupta's √((s − a)(s − b)(s − c)(s − d)), 2,589.6 sq ft here: the calculator shows it as an upper limit until you add the diagonal.

Links, chains and cents

Survey sketches such as the FMB often give lengths in links of Gunter's chain: 1 link = 7.92 inches (0.66 ft), 100 links = 1 chain = 66 ft. That makes 1,000 square links exactly 1 cent and 1,00,000 square links 1 acre. Check the sketch's legend first: newer surveys use metres, and a metric chain's link is 20 cm.

భూమి విస్తీర్ణం ఎలా లెక్కించాలి?

స్థలం నాలుగు భుజాలు వేర్వేరుగా ఉంటే, నాలుగు భుజాలతో పాటు A నుంచి C వరకు ఒక కర్ణం కొలవండి. కర్ణం స్థలాన్ని రెండు త్రిభుజాలుగా విభజిస్తుంది: రెండింటి వైశాల్యం కలిపితే స్థలం విస్తీర్ణం. చదరపు అడుగులను 9తో భాగిస్తే గజాలు: 30 × 40 అడుగుల స్థలం 133.33 గజాలు, 2.75 సెంట్లు.

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