Free calculator

Traverse Closure — Misclosure, Compass Rule & Area

Enter each leg as an azimuth or a bearing with its distance, one leg per line. The calculator returns latitudes and departures, the linear misclosure and relative precision, compass-rule adjusted coordinates, and the enclosed area by the coordinate method. Distances in feet.

Lat = D cos(Az) Dep = D sin(Az) e = √[(ΣLat)² + (ΣDep)²] Corr_i = −Σ × D_i/perimeter

Az	azimuth from north, clockwise, degrees
e	linear misclosure, ft; precision reported as 1 : (perimeter/e)
Corr_i	compass-rule correction for leg i (opposite sign of the error sum)

Direction format Start northing (ft) Start easting (ft)

Legs — one per line, direction then distance in feet

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.

Worked example: traverse closure and the compass rule

Four-leg traverse (azimuth, distance): (90°, 200 ft), (180°, 150 ft), (270°, 200.5 ft), (0°, 149.5 ft). Start at N 1,000.00, E 1,000.00.

Latitudes: 0, −150, 0, +149.5 → ΣLat = −0.50 ft; departures: +200, 0, −200.5, 0 → ΣDep = −0.50 ft
Misclosure e = √(0.50² + 0.50²) = 0.707 ft; perimeter 700 ft → precision 700/0.707 ≈ 1:990
Compass rule on leg 1: Corr_Lat = +0.50 × 200/700 = +0.143 ft (same for departure) — corrections carry the opposite sign of the error sums
Adjusted coordinates close on the start point; area by the coordinate method ≈ 29,987 ft² = 0.69 acre

Exam tip: the compass rule spreads the error in proportion to leg length — don’t spread it evenly unless the legs are equal.

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Preparing for exam day? The 110-question FE Civil practice exam is a full 5-hour-20-minute rehearsal with detailed solutions.