RHCES Closed Traverse & Area Calculator

Inputs

Bearing Format

Length Unit

Lines (one per line: bearing, distance) Format examples: N 45 30 E, 100 · S 60 0 W, 80 · or with azimuth: 135.5, 80

Starting N (Northing)

Starting E (Easting)

Notes & conventions

Quadrant bearings: angle from N/S toward E/W. Accepts N 45 30 E, N 45-30 E, N 45.5 E.
Azimuth: clockwise from north, 0 ≤ A < 360°.
Closure error e = √(ΣΔE² + ΣΔN²); precision = perimeter / e.
Balancing uses the Compass (Bowditch) rule.
Area by Coordinate method (a.k.a. shoelace) on balanced coordinates.

Results

Perimeter—

Closure Error e—

Precision (1:?)—

Area (balanced)—

StatusOK

Pt	Bearing	Dist	ΔN	ΔE	N	E

About this calculator

This tool reduces a closed traverse — a loop of bearings and distances typically run with a total station, theodolite or compass — into coordinates, linear closure error and enclosed area. Enter each leg's bearing (quadrant or azimuth) and distance; the tool computes latitudes/departures, balances the traverse by the Compass (Bowditch) rule, and reports the balanced area by the coordinate (shoelace) method. It's built for land surveyors, civil engineers and students checking field traverse data.

Method & Formulas

For each leg with azimuth Az (clockwise from north) and horizontal distance L: latitude ΔN = L·cosAz, departure ΔE = L·sinAz. Quadrant bearings (e.g., N45°30'E) are converted to azimuth first.

Linear closure error: e = √[(ΣΔN)² + (ΣΔE)²]; precision ratio = perimeter / e, reported as 1:x.

Compass (Bowditch) rule: each leg's correction is proportional to its share of the perimeter: correction_N,i = −(ΣΔN)·(L_i/perimeter), correction_E,i = −(ΣΔE)·(L_i/perimeter); adding these to the raw ΔN, ΔE of every leg produces balanced coordinates that close exactly.

Area by coordinates (shoelace method) on the balanced coordinates (N_i, E_i) for n vertices: Area = ½|Σ(E_i·N_i+1 − E_i+1·N_i)|.

Worked Example

Three-leg traverse starting at N = 1000, E = 1000: Leg 1 — azimuth 90° (due east), 100.00 m; Leg 2 — azimuth 0° (due north), 75.00 m; Leg 3 — azimuth 233°08', 125.10 m (back toward the start).

ΔN/ΔE per leg: Leg1 (0, +100.00); Leg2 (+75.00, 0); Leg3 (125.10×cos233.13° ≈ −75.06, 125.10×sin233.13° ≈ −100.08).

Sums: ΣΔN = 0+75.00−75.06 = −0.06 m; ΣΔE = 100.00+0−100.08 = −0.08 m.

Closure error e = √(0.06²+0.08²) = 0.10 m. Perimeter = 100+75+125.10 = 300.10 m → precision ≈ 1:3,000.

Balanced area (a 100 m × 75 m right triangle) ≈ ½×100×75 = 3,750 m² (0.375 ha).

Assumptions & Limitations

Assumes a properly closed loop traverse (the last leg returns approximately to the start point); open or branching traverses are not supported.

Distances are treated as horizontal — apply slope-distance, curvature and refraction corrections to raw field readings before entry.

The Compass (Bowditch) rule distributes closure error by distance only; it does not weight by instrument precision or apply the alternative Transit rule.

Very poor closure (parse errors or a low precision ratio) signals a field-data or entry problem — re-survey or re-check the data rather than trusting the balanced output.

Verify results against the governing code/standard for cadastral or engineering surveys and a licensed geodetic engineer's or surveyor's judgment.

FAQ

Quadrant or azimuth — which should I use?

Either — switch the Bearing Format toggle, or just type azimuths (0–360°) directly even in quadrant mode; the tool detects a leading N/S letter and parses accordingly.

What precision ratio is acceptable?

It depends on the class of survey (cadastral, control, topographic). The tool flags a warning below roughly 1:5,000 as a rule of thumb — check your project's specification for the required precision.

Does the reported area account for the Bowditch adjustment?

Yes — the area is computed from the balanced (adjusted) coordinates, not the raw unadjusted ones, so it reflects the traverse after closure error has been distributed across all legs.

InputsReset