Calculate Bowditch compass rule corrections from course lengths, azimuths, and misclosure to adjust traverse latitudes, departures, and coordinates.

Compass Rule Adjustment Calculator

Single Course Correction Traverse (Bowditch)

Enter any 3 values to calculate the missing variable (Bowditch/Compass Rule proportional correction for one course component).

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Compass Rule Adjustment Formula

The Compass (Bowditch) Rule distributes traverse misclosure to each courseโ€™s latitude and departure components in proportion to the course length.

Course components (using azimuth measured clockwise from North):
Latitude (Lat) = L ยท cos(Az)
Departure (Dep) = L ยท sin(Az)

Bowditch (Compass Rule) corrections:
CLat,i = โˆ’(ฮฃLat) ยท (Li/ฮฃL)
CDep,i = โˆ’(ฮฃDep) ยท (Li/ฮฃL)

Adjusted components:
AdjLati = Lati + CLat,i
AdjDepi = Depi + CDep,i

  • Li is the length of course i (units of length)
  • ฮฃL is the sum of all course lengths in the traverse (total traverse length, units of length)
  • ฮฃLat is the latitude misclosure (sum of all unadjusted latitudes); ฮฃDep is the departure misclosure (sum of all unadjusted departures) (units of length)
  • CLat,i and CDep,i are the Compass Rule corrections applied to that courseโ€™s latitude and departure (units of length)

To apply the Compass Rule, compute each courseโ€™s latitude and departure, sum them to obtain ฮฃLat and ฮฃDep (the misclosures), then compute each courseโ€™s corrections in proportion to its length. After applying corrections, the adjusted latitudes and departures will sum to zero (closure), and adjusted coordinates can be computed by accumulating adjusted departures (Easting) and adjusted latitudes (Northing).

What is a Compass Rule Adjustment?

A Compass Rule Adjustment (also called the Bowditch method) is a surveying adjustment for a closed traverse. If the traverse begins and ends at the same point, the total latitude (northโ€“south component) and total departure (eastโ€“west component) should each sum to zero. When they do not, the resulting misclosures (ฮฃLat and ฮฃDep) are distributed to each traverse courseโ€™s latitude and departure in proportion to the course length. This produces adjusted components that close and typically yields a reasonable distribution of error when measurement precision is assumed to be roughly proportional to line length.

How to Calculate Compass Rule Adjustment?

The following steps outline how to calculate the Compass Rule (Bowditch) Adjustment.

  1. For each traverse course, record its length (L) and direction (bearing/azimuth).
  2. Compute each courseโ€™s latitude and departure components (Lat and Dep).
  3. Sum the unadjusted components to find the misclosures: ฮฃLat and ฮฃDep (these should be 0 for perfect closure).
  4. Compute the total traverse length ฮฃL (sum of all course lengths).
  5. Compute each courseโ€™s Bowditch corrections: CLat,i = โˆ’(ฮฃLat)(Li/ฮฃL) and CDep,i = โˆ’(ฮฃDep)(Li/ฮฃL).
  6. Add corrections to each courseโ€™s components to get adjusted latitudes and departures, then compute adjusted coordinates by accumulating adjusted departures (E) and adjusted latitudes (N).
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge (single-course correction for one component).

Course Length (Li) = 10 units

Total Misclosure in the Component (ฮฃLat or ฮฃDep) = 2 units

Total Traverse Length (ฮฃL) = 50 units

Course Correction (Ci) = โˆ’(2) ยท (10/50) = โˆ’0.4 units