How this calculation works
Treat offsets as perpendicular widths from one straight horizontal baseline. Join adjacent measured boundary points with straight segments, integrate each strip using its actual station spacing, and add the two nonnegative side areas. End caps connect left/right offsets at the first and last stations.
Area = Σ interval × (first width + next width) / 2, separately for each sideA worked example
At stations 0, 10 and 25 m, left offsets 2, 4 and 0 m give 60 m². Right offsets 1, 3 and 2 m give 57.5 m². Together the piecewise-straight outline encloses 117.5 m².
Good to know
Horizontal perpendicular offsets to one straight baseline, not slope lengths or latitude/longitude coordinates. Between observations the boundary is straight. No unseen curved boundary, multiple-valued offset, cadastral accuracy or legal area is reconstructed. Unequal station intervals are supported explicitly.
Reference: FAO: perpendicular offsets and trapezoidal area estimation (opens in a new tab) ↗
Check the land-unit definitions and sources
The standard factors use the international foot and an acre of 43,560 sq ft. Cent means 1/100 acre; gunta means 1/40 acre; the selected Chennai ground means 2,400 sq ft.
The Assam report defines bigha as 14,400 sq ft, katha as 2,880 sq ft and lecha as 144 sq ft. The cited West Bengal court order mentions a 720-sq-ft katha convention. These are explicit presets, not an automatic definition for every record or every place using the same name. Match your record to the stated convention, or use its verified custom factor.
- NIST: exact international-foot and acre factors (opens in a new tab) ↗
- API Setu MDDS: acre/cent and acre/gunta relationships (opens in a new tab) ↗
- Greater Chennai Corporation: one ground is 2,400 sq ft (opens in a new tab) ↗
- Government of Assam AIRBMP framework: section 7.2, page 28 (bigha, katha and lecha) (opens in a new tab) ↗
- Supreme Court order, 7 May 2025: paragraph 2, page 2 (West Bengal katha) (opens in a new tab) ↗
The acre relationships are converted using exact base factors. Rounded or unrelated regional values in a reference table are not substituted for these definitions.
Widths need a measured baseline and station spacing
Each row supplies a position along one straight baseline and two perpendicular distances to the boundary. Left and right are nonnegative widths on opposite sides; they are not signed coordinates that should cancel. Use zero on a side when you only want the strip between the baseline and one boundary.
For stations 0, 10 and 25 m, left widths 2, 4 and 0 m give strips of (2 + 4) × 10 / 2 = 30 m² and (4 + 0) × 15 / 2 = 30 m². The unequal station intervals matter. Replacing them with an assumed uniform ten-metre spacing changes the model.
Right widths 1, 3 and 2 m give 20 m² and 37.5 m² for the same intervals. The combined area is 117.5 m². The outline joins adjacent offsets with straight segments and closes between the two sides at the first and last measured stations.
The polygon coordinate calculator starts from ordered Cartesian corners, while baseline offset area starts from stations and perpendicular widths. Both require an explicit horizontal geometry model.
The outline describes interpolation between observations
The SVG uses equal scales horizontally and vertically. Positive offsets appear on the left-side boundary above the baseline in the local drawing, while right-side offsets appear below it. This display convention establishes neither compass orientation nor which direction a physical parcel faces. Save SVG sketch exports the current mathematical outline with its axis description; it does not turn the drawing into an approved survey.
The trapezoidal calculation is exact for the supplied piecewise-straight outline, subject to numerical display rounding. It is an estimate of an actual curved boundary. Extra measured offsets may reveal bends that the earlier straight interpolation could not include; the tool does not invent those measurements.
If your data are already ordered Cartesian corners, the polygon coordinate calculator handles a different input workflow. If you have modern side lengths, measured plot area needs an internal diagonal for a general quadrilateral. Do not substitute latitude/longitude degrees or slope distances for these horizontal baseline offsets.
A few questions, answered
Must the stations be equally spaced?
No. Each actual interval is used separately. Stations must increase strictly and are not silently sorted.
Must the first and last offsets be zero?
No. End caps connect the two sides at those stations. Zero offsets are appropriate only where the boundary actually meets the baseline.
Does it find bends between the measured rows?
No. It joins each side’s adjacent measured points with straight segments. A curve or an overhanging boundary can require additional measurements or a different representation.