Plot Area Calculator (Irregular Land)
Measure the sides and a diagonal — get the area, a sketch and land units.
Measurements
Name the corners A, B, C … in order round the plot. Measure every side, and the diagonals from corner A. You can type a unit with any length, such as 30 ft or 32' 6".
Land units and price optional
Triangles
| Triangle | Sides | Area |
|---|
Area in land units
| Unit | Area |
|---|
For general information only, not legal advice. Templates are generic starting points — have a qualified lawyer review anything you rely on.
About the Plot Area Calculator (Irregular Land)
Work out the area of a plot of land that is not a neat rectangle, from the measurements you can take with a tape. Name the corners A, B, C … in order round the plot, measure every side and the diagonals from corner A, and the calculator splits the plot into triangles and adds their areas with Heron’s formula — three corners make a triangle, four corners need one diagonal, five need two. It draws the plot to scale, so you can see at once whether the lengths make sense, and a second diagonal can be checked against the drawing.
With a site plan or survey sketch, enter the corner coordinates instead (shoelace formula). For a boundary that curves, such as a stream or a road, use a baseline with offsets measured at regular intervals (Simpson’s and the trapezoidal rule). Lengths can be in metres, feet, yards (gaj), Gunter’s chains and links, or the Haryana karam, and the area is given in square metres, square feet, gaj, acres, hectares, cents and gunthas — plus kanal–marla or bigha–katha where those state units are chosen.
How to use it
- Choose Measured sides, the number of corners and the unit of your tape. Walk round the plot and call the corners A, B, C … in order.
- Enter every side (AB, BC, … back to A) and the diagonals from corner A (AC, AD, …). For four corners you can also enter the other diagonal BD as a check.
- Or choose Corner coordinates and paste one “x, y” pair per line from a plan, or Baseline and offsets for a curved edge: one “distance along the baseline, offset” pair per line.
- Check the sketch, read the area in the unit you need, choose a state for kanal–marla or bigha–katha, and copy or download the result.
Examples
600 m² = 6,458.35 sq ft = 717.59 gaj = 14.83 cents
Triangles 509.82 + 613.35 = 1,123.17 m² = 12,089.75 sq ft = 1,343.31 gaj = 11.10 guntha; the other diagonal BD should measure about 48.32 m
174.54 + 208.22 + 175.66 = 558.42 m² = 6,010.78 sq ft
Shoelace formula: 400 m² = 4,305.56 sq ft
Simpson’s rule 213.33 m² (trapezoidal rule 210 m²)
Common uses
- Checking the area of a plot before buying it, from your own tape measurements.
- Working out the land under a farm field or garden with an irregular shape.
- Turning the corner coordinates of a site plan into an area.
- Measuring land along a river bank or a curved road with a baseline and offsets.
Formulas
- Triangle from three sides (Heron): area = √(s(s − a)(s − b)(s − c)), with s = (a + b + c) ÷ 2. Three sides fix a triangle, so a plot cut into triangles by diagonals is fixed too.
- Plot from sides and diagonals: the diagonals from corner A cut an n-sided plot into n − 2 triangles (A-B-C, A-C-D, …); the plot’s area is their sum.
- Corner coordinates (surveyor’s or shoelace formula): area = ½ |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)| with the corners in order.
- Offsets, trapezoidal rule: area = Σ (distance between offsets) × (sum of the two offsets) ÷ 2.
- Offsets, Simpson’s rule: for equal intervals d and an odd number of offsets, area = d ÷ 3 × (first + last + 4 × the even-numbered + 2 × the other odd-numbered offsets). With an even number of offsets the last strip is added as a trapezoid.
Measuring a plot in the field
- Four sides alone do not fix a four-sided plot — it can lean like a parallelogram. Always measure at least one diagonal; for five corners, two; and so on.
- Choose corner A so that every diagonal from it runs inside the plot. For a plot without inward corners any corner works.
- Measure an extra diagonal (BD for a four-sided plot) as a check. If it differs from the drawing by more than a few tenths of a per cent, one of the lengths was misread.
- Keep the tape straight and level, and measure along the ground only where it is flat — this calculator works on a flat plane.
- Lengths can be typed with their own unit, such as
30 ftor32' 6", whatever unit is chosen.
Units
1 ft = 0.3048 m and 1 yd = 0.9144 m exactly. A Gunter’s chain is 66 ft (20.1168 m) and has 100 links of 7.92 in; 10 square chains make an acre. The Haryana karam is 66 inches (Haryana Revenue Department, jamabandi.nic.in). Areas: an acre is 43,560 sq ft, a gaj (square yard) 9 sq ft, a cent 435.6 sq ft and a guntha 1,089 sq ft. For other land units, use the Land Area Converter.
Limitations
- The plot is treated as flat. On sloping land the area along the ground is larger than the plan area surveyors and land records use.
- Curved edges other than baseline offsets must be split into short straight sides.
- Measured sides only work when every diagonal from corner A runs inside the plot; otherwise start from another corner or use coordinates.
- An estimate from your measurements, not a survey. For a sale, mutation or boundary dispute, rely on a licensed surveyor and the official land record.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How do I calculate the area of a plot with four unequal sides?
Measure the four sides and one diagonal. The diagonal splits the plot into two triangles whose areas come from their three sides by Heron’s formula; add them. For sides 38, 27, 41 and 30 m with a 49 m diagonal, that is 509.82 + 613.35 = 1,123.17 m².
Why do I need a diagonal — are four sides not enough?
No. A frame with four fixed sides can still lean, like a parallelogram, and its area changes as it leans. A diagonal locks the shape, just as three sides lock a triangle.
What is Heron’s formula?
The area of a triangle from its three sides a, b and c: √(s(s − a)(s − b)(s − c)), where s is half the perimeter. A 30-40-50 m triangle has s = 60 and area √(60 × 30 × 20 × 10) = 600 m².
How do I find the area of land from corner coordinates?
Use the shoelace formula: list the corners in order, multiply each x by the next y and each y by the next x, subtract the two totals and halve the result. Choose Corner coordinates and paste the points; the calculator also checks that the outline does not cross itself.
How do I measure a plot with a curved side?
Stretch a straight baseline along the curve and measure offsets at right angles to it at regular intervals, say every 5 m. Enter each distance and offset; with equal intervals Simpson’s rule gives a closer answer than the trapezoidal rule.
How many gaj is my plot?
Divide the area in square feet by 9 — a gaj is a square yard. A 600 m² plot is 6,458.35 sq ft or 717.59 gaj; the calculator shows gaj, cents, gunthas and acres together.