Traverse Closure Calculator
The traverse closure calculator checks the accuracy of a closed survey traverse by computing the linear error of closure and the precision ratio. Enter the latitudes (north-south components, positive north) and departures (east-west components, positive east) for each course of the traverse, one per line as "latitude,departure". The calculator sums all latitudes and departures, computes the linear misclosure, and reports the precision ratio in the form 1:N. This is the standard field check used in US land surveying after every closed traverse.
Traverse closure formulas
Sum of latitudes = sum(distance * cos(bearing))
Sum of departures = sum(distance * sin(bearing))
Linear error = sqrt((sum lat)^2 + (sum dep)^2)
Precision = Perimeter / Linear error (expressed as 1:N)
For a perfect closed traverse, sum of latitudes = 0 and sum of departures = 0. Any deviation is the misclosure. The Compass Rule (Bowditch Method) then distributes this error proportionally to each course length.
Traverse precision standards (ACSM)
- 1:5,000 minimum for general land surveys (many US jurisdictions).
- 1:10,000 for standard property boundary surveys.
- 1:20,000 for urban property surveys and higher-order control.
- 1:50,000 or better for geodetic control traverses.
- GPS-based surveys often achieve 1:100,000 or better with post-processing.
Traverse closure calculator: frequently asked questions
What is traverse closure in surveying?
A closed traverse is a series of survey lines that form a closed polygon returning to the starting point. Traverse closure is the process of checking how closely the computed end point matches the known start point. Any discrepancy is the closure error, caused by small measurement errors.
What are latitudes and departures?
In a traverse, each course (line segment) has a latitude (north-south component) and a departure (east-west component). Latitude = distance * cos(bearing); Departure = distance * sin(bearing). In a closed traverse, the sum of all latitudes and all departures should each equal zero.
What is linear error of closure?
The linear error of closure is the straight-line distance between the starting point and the computed endpoint of a closed traverse: linear error = sqrt((sum of latitudes)^2 + (sum of departures)^2). It represents the total misclosure in the traverse.
What is traverse precision ratio?
Precision ratio = total perimeter length / linear error of closure, expressed as 1 in N. For example, 1:5,000 means the error is 1 unit per 5,000 units of total traverse length. ACSM standards require 1:10,000 for most property surveys and 1:20,000 for higher-order control.
What is the Compass Rule (Bowditch Rule) adjustment?
The Compass Rule distributes closure error proportionally to the length of each course. Correction to latitude of any course = -(sum of latitudes) * (course length / total perimeter). The Bowditch Rule is the most common traverse adjustment method in US land surveying.
Official sources
- NOAA National Geodetic Survey: NGS surveying standards.
- BLM General Land Office Records: BLM GLO surveying methods.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.