Closed Traverse Calculator — Plane Bowditch Adjustment
Compute a closed plane traverse’s coordinate misclosure and optionally apply length-weighted Bowditch corrections to horizontal distances and azimuths.
Compute coordinate closure for a horizontal traverse intended to return to its starting point. The raw easting and northing sums reveal how far the measured loop misses closure. An optional Bowditch adjustment distributes those coordinate errors across the legs in proportion to their lengths.
How to use this tool
- Enter one horizontal distance and clockwise-from-north azimuth per row, including the final leg back to the start.
- Enter start coordinates and a common metre or international-foot unit.
- Inspect raw closure before choosing an adjustment.
- If the assumptions are appropriate, select Bowditch and inspect every correction and endpoint.
Formula
fE = Σ(d sin A); fN = Σ(d cos A); correction Eᵢ = −fE dᵢ/Σd; correction Nᵢ = −fN dᵢ/Σd
Linear misclosure is √(fE² + fN²). Perimeter divided by raw misclosure gives the denominator in a descriptive 1:N closure ratio. Very small closure near floating-point resolution does not provide a reliable finite ratio or prove perfect measurements.
Example
Four cardinal legs of 101 m north, 100 m east, 100 m south and 100 m west total 401 m and leave 1 m northing misclosure. Bowditch applies −101/401 m northing correction to the first leg and −100/401 m to each other leg. Their corrections sum to −1 m.
Frequently asked questions
Are interior-angle observations adjusted?
No. Supply leg azimuths after any required angular adjustment. The calculator does not derive azimuths from interior angles or correct an angular closing error.
When is Bowditch appropriate?
It assumes angular and distance errors have comparable effects on position. It is a conventional distribution method, not a least-squares network solution. Large misclosure or suspected blunders should be investigated rather than hidden by adjustment.
Does the closure ratio meet a surveying standard?
No pass/fail rule is applied. Applicable tolerances depend on survey purpose and procedures. Exact arithmetic closure after adjustment does not establish observation accuracy or a legal boundary.
What input limits apply?
Use 3–100 legs and at most 20,000 text characters. Start coordinates are limited to ±1 billion selected units and each distance to one billion. The model remains a local plane loop, with no projection, atmospheric, slope or geodetic corrections.
Sources
Last updated: 2026-10-30