How is the angular misclosure computed and distributed?

For a closed loop of n interior angles the theoretical sum is (n − 2) × 180°. The difference between the observed angle sum and this value is the angular misclosure, usually distributed equally across all angles (or weighted by observation quality) before the azimuths are derived. This tool works directly on azimuths and distances and measures the resulting linear misclosure (ΔE, ΔN); the angular part is handled at the angle-observation stage.

What is the Bowditch (compass) rule?

The Bowditch rule assumes each leg’s error is proportional to its length, so it distributes the linear misclosure over the legs in proportion to leg length ÷ total perimeter: leg correction = − (misclosure × legLength ÷ perimeter), applied cumulatively to easting and northing so the adjusted coordinates land exactly back on the start. The area is taken from the adjusted coordinates.

What relative precision 1:x is acceptable?

Relative precision = perimeter ÷ linear misclosure, written “1 : x”. Limits depend on the class of work and the governing specification: ordinary topographic work may accept around 1:5,000, urban/cadastral work 1:10,000 or tighter, and geodetic control much higher. Always check your project’s adopted specification rather than a generic figure.

How do I get the adjusted coordinates into CAD?

The “Export CSV” button downloads the adjusted coordinates as a station,E,N file with Western digits at three decimals. Import it straight into AutoCAD/Civil 3D (points) or any survey package, or paste it into a spreadsheet. Points are in station order starting from the start point.

Free tool

Traverse calculator (Bowditch)

Misclosure and relative precision, Bowditch-adjusted coordinates, and the enclosed area of a closed loop in m², hectare, dunam, and feddan/qirat/sahm — computed instantly in your browser.

Start point

Closed loop (returns to start)

#	Azimuth (°)	Distance (m)	Actions
1
2
3
4

FAQ

A closed traverse starts and ends at the same point, so its misclosure can be measured, distributed, and the enclosed area computed. An open traverse ends at a different point and gives no internal check on closure, so we report no misclosure or area for it — only the sequential coordinates and the perimeter.

You may also need: Land area calculator · Curve calculator (horizontal/vertical) · Leveling calculator (rise & fall / HI) · Angle & bearing converter

From the free resource library

Files and examples to get started

All resources

Excel traverse observation sheet with a closed-square example

Record azimuths, horizontal distances and station order before entering observations in the Bowditch calculator.

Free file with a practical guide

Review the Egypt task reference

Official-source locators and review checklists; a calculation or template alone does not establish compliance.

Traverses in Egypt: horizontal control and closure review

Review the Saudi Arabia task reference

Official-source locators and review checklists; a calculation or template alone does not establish compliance.

Traverse in Saudi Arabia: ties and control-network adjustment

Surveying

Geomatics & CAD

Software DevelopmentNew

Quantity Surveying

Traverse calculator (Bowditch)

Need help with your survey project?

FAQ

Files and examples to get started

Excel traverse observation sheet with a closed-square example

Review the Egypt task reference

Review the Saudi Arabia task reference

Traverse calculator (Bowditch)