How this calculation works
Resolve each measured leg into local east/north components, then accumulate from the entered start. Treat the final point as intended to return to that start. Report the measured gap independently of the optional adjustment. Bowditch allocates the opposite component misclosure in proportion to each entered leg length; original inputs and raw coordinates stay visible beside the reported coordinates.
ΔE = L sin A; ΔN = L cos A; closure gap = √[(ΣΔE)² + (ΣΔN)²]A worked example
Legs north 100 m, east 100 m, south 100 m and west 99 m finish 1 m east of the start. Their total length is 399 m, so length divided by gap is 399. Bowditch assigns eastward-component corrections −100/399 m to each 100 m leg and −99/399 m to the final leg.
Good to know
A local plane loop, not geodesic navigation or a certified boundary survey. Use horizontal lengths and a common north reference; no slope reduction, magnetic declination, grid convergence, angle balancing or acceptance threshold is inferred. Bowditch changes coordinate increments, not original measurements, and cannot remove gross mistakes. The SVG shows only the reported path without an invented closing segment; no area is computed for potentially crossing paths.
Reference: Esri: compass/Bowditch rule and its precision assumption (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.
Follow each measured course before closing the loop
An azimuth is a whole-circle direction clockwise from north. North is 0°, east 90°, south 180° and west 270°. At azimuth 30°, a 100 m horizontal leg has eastward component 100 × sin 30° = 50 m and northward component approximately 86.602540 m. Reversing the sine and cosine would rotate the direction interpretation.
The calculator begins at your supplied local easting and northing and adds every measured component. It expects that the final observed leg was intended to return to the start. The resulting gap is the distance between those endpoints. It does not invent a return line when the entered courses stop early.
Consider north 100 m, east 100 m, south 100 m and west 99 m. The final point is 1 m east of the start, total measured length is 399 m, and length divided by the gap is 399. Changing the start from (0, 0) to (500, 800) changes all point coordinates but leaves that misclosure unchanged.
An adjustment is a model, not proof that the observations were right
Measured accumulation is the default. Choose Bowditch only when you want to inspect that adjustment model for an intended closed loop. It distributes each component misclosure by entered leg length: correction E for a leg is −total E misclosure × leg length / total length, and the northing component follows the same rule.
In the 399 m example, the first three legs receive east-component corrections of −100/399 m each and the final leg receives −99/399 m. Their sum is −1 m, returning the modeled endpoint to the start. North-component corrections are zero in this example. The table preserves the raw coordinates next to the reported adjusted ones.
Esri describes the compass/Bowditch rule with an assumption of comparable precision in direction and distance. This page does not establish that assumption for your measurements. A missing course, wrong unit or wrong direction can be spread around a loop by an adjustment; the resulting closure does not validate the observations.
The SVG draws the reported path at equal east/north scale. It leaves an unadjusted gap open and shows no inferred parcel area. A self-crossing path can still have an endpoint gap of zero. If you already have checked ordered Cartesian boundary points, the polygon coordinate calculator is the separate tool for simple-polygon area and centroid; measured plot area instead uses side lengths and, for a general quadrilateral, an internal diagonal.
Read more: Esri: compass/Bowditch adjustment assumption and distribution (opens in a new tab) ↗
A few questions, answered
Can I enter quadrant bearings such as N 30 E?
Convert them to a whole-circle azimuth first. This input accepts decimal degrees clockwise from north, followed by horizontal distance. It does not parse quadrant notation or degrees/minutes/seconds.
Does a zero gap mean the boundary is correct?
No. Common systematic errors and some mistakes can cancel. Zero is a computed endpoint condition, not an accuracy certificate or a legal boundary determination.
Are measured distances changed by the Bowditch option?
The original distance and azimuth columns remain unchanged. Corrections alter the reported coordinate increments, so their reconstructed lengths and directions can differ from the observations.
Can I compare different UTM zones or magnetic and grid bearings?
Not directly. Use one consistent local coordinate frame, length unit and north reference. The WGS84 UTM converter performs a separate projection, but this traverse tool applies no zone stitching, convergence, declination, geodesic or grid-to-ground correction.