Use the Single Course Correction tab to compute a Bowditch (Compass Rule) proportional correction for one course’s latitude or departure component (run it separately for latitude and for departure). Use the Traverse (Bowditch) tab to adjust an entire traverse from distances and azimuths.

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).

Related Calculators

Compass Rule Adjustment Formula

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

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

Bowditch (Compass Rule) corrections:
CLat,i = −(ΣLat) · (Li/ΣL)
CDep,i = −(ΣDep) · (Li/ΣL)

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

  • Li is the length of course i (units of length)
  • ΣL is the sum of all course lengths in the traverse (total traverse length, units of length)
  • ΣLat is the latitude misclosure (sum of all unadjusted latitudes); ΣDep 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 course’s latitude and departure (units of length)

To apply the Compass Rule, compute each course’s latitude and departure, sum them to obtain ΣLat and ΣDep (the misclosures), then compute each course’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 (north–south component) and total departure (east–west component) should each sum to zero. When they do not, the resulting misclosures (ΣLat and ΣDep) are distributed to each traverse course’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 course’s latitude and departure components (Lat and Dep).
  3. Sum the unadjusted components to find the misclosures: ΣLat and ΣDep (these should be 0 for perfect closure).
  4. Compute the total traverse length ΣL (sum of all course lengths).
  5. Compute each course’s Bowditch corrections: CLat,i = −(ΣLat)(Li/ΣL) and CDep,i = −(ΣDep)(Li/ΣL).
  6. Add corrections to each course’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 (ΣLat or ΣDep) = 2 units

Total Traverse Length (ΣL) = 50 units

Course Correction (Ci) = −(2) · (10/50) = −0.4 units