Plot Area Calculator from Sides and Diagonals
Calculate irregular land area from side lengths and internal diagonals using Heron's formula. See a to-scale plot, check an extra diagonal, and convert to metric, US and local units.
This plot area calculator estimates the horizontal area of a straight-sided plot with three to six corners. It is useful for engineers checking site dimensions, students learning surveying geometry, and landowners comparing measurements. An irregular plot area cannot normally be determined from its boundary sides alone: the shape can change while those side lengths remain unchanged. Measured diagonals supply the missing information.
Enter the measurements
Label the corners A, B, C and so on as you walk around the boundary. Choose the number of corners, enter the boundary sides, and enter the closing side from the last corner back to A. For a quadrilateral, measure diagonal AC. For five corners, also measure AD; for six, add AE. A triangle needs no diagonal. Use horizontal distances throughout. The unit controls let you enter metric or US lengths without changing the underlying geometry.
Every diagonal from A must stay inside the plot, dividing it into non-overlapping triangles ABC, ACD, ADE and AEF as applicable. This includes convex plots and concave plots that admit this arrangement. Choose another starting corner or divide the land into separate parcels if the required diagonals cross outside the boundary. The drawing uses the same scale in both directions, with AB horizontal; it is not a north-oriented cadastral map.
Read the result and check the shape
The land area calculator from sides applies Heron's formula to each triangle and adds their areas. The triangle table shows the sides, semiperimeter and individual area. Impossible or nearly collapsed triangles stop the result. The reconstructed outline must also fit into one turn around A, preventing an overlapping fan.
For an independent measurement check, enable the extra diagonal and enter BD, BE or BF for four, five or six corners. Compare the predicted length with the measured length using a tolerance appropriate to your measurements. A mismatch asks you to remeasure; no automatic adjustment is made. Passing one diagonal check does not establish a full survey traverse closure or guarantee an accurate area.
Area units and limits
Results include m², square feet, international acres and hectares. The local-unit table also gives gaj interpreted as square yards, guntha at 1089 ft², and cent at 435.6 ft². Enter your local marla size; a kanal is taken as 20 such marlas. Bigha conversion stays off until you enable it and enter a confirmed local size. There is no universal bigha.
This is a geometric estimate, without an uncertainty interval. Curved boundaries, holes, slope surface area, map projections and large geodetic parcels need other methods. Rounded or inaccurate lengths can strongly affect thin triangles. Legal area comes from the land record or a qualified survey, which also determines boundaries and the applicable local unit conventions.
How it is calculated
Divide the polygon into a fan of triangles from A. For each triangle with sides a, b, c, calculate and , then . See Brilliant's Heron examples and Suparn Patra Math Lab's quadrilateral walk-through (links below). Negative products are clamped only to keep rejected, impossible inputs numerically safe; the triangle conditions still withhold their results.
Reconstruct each triangle's included angle with . Accumulate those angles from AB to locate each corner. The total must be less than 360°. A separate shoelace sum checks the area from these coordinates. Optional BD, BE or BF is predicted from the coordinates and compared with an independently measured length; exceeding the user's absolute tolerance blocks results, without adjusting any lengths.
Lengths use international feet and yards. One acre is 43560 ft² and one hectare is 10000 m². The local table uses gaj = square yard, guntha = 1089 ft², cent = 435.6 ft², the entered marla size, kanal = 20 marlas, and an optional user-defined bigha.
Assumptions
All lengths are horizontal distances between straight boundary corners on a locally flat plane. Corners follow boundary order. A sees every other corner through the plot interior, and consecutive rays from A follow one direction without overlapping. Mirroring or rotating the outline leaves area unchanged. The diagram fixes AB horizontal and uses a common x/y scale.
The default marla is the 272.25 ft² convention, not a universal definition. Kanal means 20 entered marlas here. Guntha and cent use the explicitly stated conventions. Bigha conversion is off initially; its example size of 2500 m² has no assigned jurisdiction and must be replaced with the local record's definition.
Where it applies
For 3–6 corner, simple, straight-sided polygons that admit the specified internal fan from A. Convex plots and suitable concave plots are supported. Rejects failed triangle inequalities, numerically collapsed triangles and a fan reaching a full turn; warns about thin triangles. Confirm that every diagonal is internal on your real plot: lengths cannot establish which side of a diagonal the actual boundary occupies.
The optional extra diagonal is one redundant distance check, not a traverse adjustment, full survey closure or accuracy guarantee. Its tolerance is user-selected and has no regulatory status. No slope correction, holes, curved boundaries, coordinate projection, earth curvature or uncertainty propagation is included. Legal area comes from the land record or a qualified survey. Local-unit definitions must agree with that record.
References
- Ratna Sagar, Worksheet 12, Chapter 12 — Heron's Formula: questions on PDF pp. 1–2, answer key p. 3. Independent published checks include 306 m² for the quadrilateral, 196 m² for the trapezium, 60 cm² for the isosceles triangle and 48 m² per cow for the rhombus. https://rsadmin.rsgr.in/storage/app/SbsupportAsset/62970159db453_Math_9__-_Worksheet_-_Chp_12.pdf
- Brilliant, Heron's Formula: derivation and worked triangle examples. https://brilliant.org/wiki/herons-formula/
- Suparn Patra Math Lab, Area of a Quadrilateral by Triangulation: worked 9–40–28–15 quadrilateral with AC = 41, total area 306 square units. https://math.suparnpatra.com/classes/ix/ch10-herons-formula/04-area-of-quadrilateral
- NIST SP 811, Appendix B.9: square foot, square yard and hectare conversions. This tool uses the international acre, not the US survey-foot acre listed in the older NIST table. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9
- NRSP / Landesa, Pakistan House and Garden Plot Field Study (2011), definitions, PDF p. 10: acre, marla, kanal and ghunta conventions. https://nrsp.org.pk/publications/Evaluation-Assessment-Studies/House-cum-Garden-Plot-Study.pdf
- Adarsh Bhatt, Margdarshi Bhatt and Ashish Negi, Transforming Agriculture in Uttarakhand, Just Agriculture, March 2025, printed p. 18 (PDF p. 7), land-unit table: cent = 435.6 ft², guntha = 1089 ft², and gaj interpreted as square yard. These are stated conventions; the tool does not choose a state's bigha. https://justagriculture.in/wp-content/uploads/2025/04/002-Transforming-Agriculture-in-Uttarakhand.pdf
Inputs
| Input | Symbol | Unit | Default |
|---|---|---|---|
| Number of plot corners Walk around A–B–C–D–E–F in order, stopping at your last corner. All diagonals from A must lie inside the plot. | n | 4 | |
| Side AB Measure the straight boundary side as a horizontal distance. | AB | m | 30 |
| Side BC Measure the straight boundary side as a horizontal distance. | BC | m | 22 |
| Side CD Measure the straight boundary side as a horizontal distance. | CD | m | 28 |
| Side DE Measure the straight boundary side as a horizontal distance. | DE | m | 18 |
| Side EF Measure the straight boundary side as a horizontal distance. | EF | m | 18 |
| Closing side: last corner to A CA for a triangle; DA, EA or FA for 4, 5 or 6 corners. Use horizontal distances. | ZA | m | 25 |
| Diagonal AC Measure the straight internal diagonal from A. Check that it stays within the boundary. | AC | m | 38 |
| Diagonal AD Measure the straight internal diagonal from A. Check that it stays within the boundary. | AD | m | 34 |
| Diagonal AE Measure the straight internal diagonal from A. Check that it stays within the boundary. | AE | m | 28 |
| Check an extra measured diagonal For 4, 5 or 6 corners, measure BD, BE or BF independently. This check does not adjust the area. | check_extra | false | |
| Extra diagonal: B to last corner BD for four corners, BE for five, BF for six. Do not copy the predicted value; measure it. | BZ | m | 36 |
| Allowed extra-diagonal difference Your chosen consistency tolerance, not a legal surveying standard. | check_tol | m | 0.1 |
| Area of one local marla Default: 272.25 ft², as in the Punjab convention. Replace with your record's size. One kanal is taken as 20 of these marlas. | marla_size | ft^2 | 272.25 |
| Convert using my local bigha size Bigha varies by state and locality. Enable only after confirming the area of one bigha in your land record. | use_bigha | false | |
| Area of one local bigha 2500 m² is an example only. Enter the size confirmed for your locality; this calculator does not choose a state's bigha. | bigha_size | m^2 | 2500 |
Results
With the default inputs above, the calc gives:
| Result | Value |
|---|---|
| Plot area | 679.55 m² |
| Plot area (ft²) | 7,314.61 ft² |
| International acres | 0.16792 acre |
| Hectares | 0.06795 hectare |
| Boundary perimeter | 105 m |
| Measurement consistency | Not checked: extra diagonal off |
| Predicted B to last corner | 36.557 m |
Checked against sources
Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).
Published quadrilateral: 306 m²
Source: Ratna Sagar, Worksheet 12, question 3 (PDF p. 1), answer key p. 3: 306 m². The first two sides meet at a right angle, independently giving AC = 41 m. Also worked in Suparn Patra Math Lab: https://math.suparnpatra.com/classes/ix/ch10-herons-formula/04-area-of-quadrilateral . The attached PDF's source title says Raghav School; its actual publisher is Ratna Sagar.
Inputs: Side AB = 9 m; Side BC = 40 m; Closing side: last corner to A = 15 m; Diagonal AC = 41 m; the others as above.
| Result | Source | This calc |
|---|---|---|
| Plot area | 306 m² | 306 m² |
| Areas of ABC, ACD, ADE, AEF (active triangles) [1] | 180 m² | 180 m² |
| Areas of ABC, ACD, ADE, AEF (active triangles) [2] | 126 m² | 126 m² |
Published isosceles triangle: 60 cm²
Source: Ratna Sagar, Worksheet 12, question 2, PDF p. 1; answer key p. 3. Sides 13, 13 and 24 cm, published area 60 cm² = 0.006 m². This also follows independently from the 5–12–13 right triangle and base × height / 2.
Inputs: Number of plot corners = 3; Side AB = 0.13 m; Side BC = 0.24 m; Closing side: last corner to A = 0.13 m; the others as above.
| Result | Source | This calc |
|---|---|---|
| Plot area | 0.006 m² | 0.006 m² |
Published scalene triangle: 84 m²
Source: Brilliant, Heron's Formula, worked example: sides 13, 14, 15 yield area 84 square units; lengths instantiated in metres. https://brilliant.org/wiki/herons-formula/
Inputs: Number of plot corners = 3; Side AB = 13 m; Side BC = 14 m; Closing side: last corner to A = 15 m; the others as above.
| Result | Source | This calc |
|---|---|---|
| Plot area | 84 m² | 84 m² |
Published trapezium: 196 m²
Source: Ratna Sagar, Worksheet 12, question 4, PDF p. 1: parallel sides 25 and 10 m, legs 14 and 13 m; answer p. 3 is 196 m². Independent coordinate construction gives height 11.2 m and AC = sqrt(401) = 20.0249843945 m; 0.5(25+10)×11.2 = 196. No Heron formula is used to obtain the reference.
Inputs: Side AB = 25 m; Side BC = 14 m; Side CD = 10 m; Closing side: last corner to A = 13 m; Diagonal AC = 20.025 m; the others as above.
| Result | Source | This calc |
|---|---|---|
| Plot area | 196 m² | 196 m² |
Published rhombus: 18 × 48 = 864 m²
Source: Ratna Sagar, Worksheet 12, question 13, PDF p. 1: each side 30 m, longer diagonal 48 m, 18 cows; answer p. 3 is 48 m² per cow. Thus total reference area is 18 × 48 = 864 m². Independently, the half-diagonal right triangle gives the other diagonal 36 m and area 48 × 36 / 2.
Inputs: Side BC = 30 m; Side CD = 30 m; Closing side: last corner to A = 30 m; Diagonal AC = 48 m; Check an extra measured diagonal = yes; Allowed extra-diagonal difference = 0.001 m; the others as above.
| Result | Source | This calc |
|---|---|---|
| Plot area | 864 m² | 864 m² |
| Predicted B to last corner | 36 m | 36 m |
| Extra diagonal absolute mismatch | 0 m | 0 m |
Published small quadrilateral: rounding tolerance
Source: Ratna Sagar, Worksheet 12, question 6, PDF p. 1; p. 3 gives 15.16 cm² = 0.001516 m². That printed result is truncated: the exact area is 6 + 2√21 = 15.1651513899 cm² (nearest hundredth 15.17). The calculator retains the correct geometry; tolerance 0.01 cm² covers the printed truncation.
Inputs: Side AB = 0.03 m; Side BC = 0.04 m; Side CD = 0.04 m; Closing side: last corner to A = 0.05 m; Diagonal AC = 0.05 m; the others as above.
| Result | Source | This calc |
|---|---|---|
| Plot area | 0.001516 m² | 0.001517 m² |
Same published triangle entered in feet
Source: Brilliant's 13–14–15 triangle has published area 84 square units (https://brilliant.org/wiki/herons-formula/). The same 13, 14, 15 m lengths are entered in international feet, using NIST SP 811's exact 1 ft² = 0.09290304 m² (1 ft = 0.3048 m). This verifies dimensional input conversion without changing physical area.
Inputs: Number of plot corners = 3; Side AB = 42.6509186351706 ft; Side BC = 45.9317585301837 ft; Closing side: last corner to A = 49.2125984251969 ft; the others as above.
| Result | Source | This calc |
|---|---|---|
| Plot area | 84 m² | 84 m² |
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