Traverse Closure Calculator (Latitudes, Departures & Compass Rule)

How it works

Latitude = distance × cos(azimuth) · departure = distance × sin(azimuth) · linear misclosure = √(ΣLat² + ΣDep²) · relative precision = 1 : (perimeter ÷ misclosure) · compass (Bowditch) rule: correction to each latitude = −ΣLat × course length ÷ perimeter (same for departures) · area = ½ |Σ (Eᵢ·Nᵢ₊₁ − Eᵢ₊₁·Nᵢ)|.

In a closed traverse the surveyor returns to the starting point, so the north–south components (latitudes) and east–west components (departures) of all courses should add up to zero. Small errors in measured angles and distances leave a gap — the linear misclosure — and dividing the perimeter by it gives the relative precision, which is compared with the survey’s accuracy standard (often 1 : 5,000 to 1 : 10,000 for boundary work, 1 : 20,000 or better for control). The compass rule distributes the misclosure in proportion to course length, after which coordinates and the enclosed area follow from the coordinate (shoelace) method. Balance the angles before computing azimuths.

Worked example

A four-sided traverse: 30° for 200.00 m, 120° for 150.00 m, 215° for 180.00 m and 291.25° for 135.92 m (perimeter 665.92 m). The latitudes add up to 0.020 m and the departures to −0.018 m, a linear misclosure of 0.027 m, so the relative precision is 1 : 24,277 — well inside a 1 : 5,000 boundary standard. After the compass-rule adjustment the enclosed area is 26,882.37 m² (2.6882 ha).

Sources: Traverse (surveying) — latitudes, departures and closure · NOAA NGS — Standards and Specifications for Geodetic Control Networks (FGCC 1984)

Frequently asked questions