Free Surveying Tool
Traverse Closure Calculator
Enter your field bearings and distances. Get latitudes, departures, closure error, and precision ratio — then balance the traverse with Bowditch's (Compass) Rule, the Transit Rule, or the Crandall Method.
Defaults to 0, 0 — used to compute the coordinate table below.
Course 1 — Bearing
Distance
ftCourse 2 — Bearing
Distance
ftCourse 3 — Bearing
Distance
ftTraverse Closure Reference
Latitude
The N/S component of a course. Lat = Distance × cos(azimuth). Positive northward, negative southward.
Departure
The E/W component of a course. Dep = Distance × sin(azimuth). Positive eastward, negative westward.
Closure Error
The linear distance between the start and end of the traverse: √(ΣLat² + ΣDep²). A perfectly closed traverse has 0.
Precision Ratio
Perimeter ÷ Closure Error, expressed as 1:X. Higher is better. ALTA surveys require 1:10,000 or better.
Closure Bearing
The direction from the computed end point back to the true start. Reported as a quadrant bearing.
ALTA Standard
1:10,000 or better. Most boundary surveys require 1:7,500+. Rough work may accept 1:5,000.
Key Formulas
Latitude = Distance × cos(azimuth)
Departure = Distance × sin(azimuth)
Closure = √(ΣLat² + ΣDep²)
Precision = Perimeter ÷ Closure → 1 : X
Closure Adjustment Methods
Bowditch's (Compass) Rule
Distributes the closure error to each course in proportion to its length relative to the perimeter. Assumes distance and angle measurements are equally precise. The most commonly used method for typical boundary and land surveys.
Transit Rule
Distributes the closure error to each course in proportion to the magnitude of its own latitude and departure, rather than its length. Historically used when angles were considered more reliable than distances (e.g. transit-and-tape work) — rarely the preferred method with modern EDM equipment, but still taught and occasionally specified.
Crandall Method
A least-squares adjustment that holds the given bearings fixed and distributes the closure error by adjusting each course’s length. Traditionally starts from raw angle observations with a separate angular closure step; since this tool works from finished bearings, the implementation here performs the least-squares distance adjustment holding those bearings fixed — the mathematical core of the method.
Not sure which one fits your job? See our full breakdown: Bowditch vs. Transit vs. Crandall.
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