Traverse closure calculator: angular and linear misclosure, Bowditch adjustment
Enter the angles and distances of a closed traverse: the calculator shows the angular and linear misclosure, the precision 1:X, compares it with the tolerance and returns the adjusted coordinates (Bowditch) of every station.
The angles are the horizontal angles turned at each station, from backsight to foresight. The distance of each line is the horizontal distance to the next station (the last one closes back to station 1). Without E and N, we use 1000 / 1000 (local coordinates).
| Station | Angle (° ' ") | Distance to the next one (m) |
|---|
Paste from field book / Excel
One station per line: name, angle, distance (tab, semicolon or space). E.g. T2 91 12 30 152.374
Result
Fill in at least 3 stations with angle and distance.
How the closure is computed
1. Angular misclosure. The interior angles of an n-sided polygon add up to (n − 2)·180°; the exterior angles, to (n + 2)·180°. The difference between the measured and the theoretical sum is the angular misclosure, compared with the tolerance (e.g. 20"·√n). If it is within tolerance, it is distributed equally among the angles.
2. Azimuths. From the starting azimuth, each next azimuth = previous azimuth + angle right (clockwise) − 180°.
3. Linear misclosure. Adding up the departures ΔE = d·sin(Az) and the latitudes ΔN = d·cos(Az), a perfect closed traverse would give zero. What is left is the linear misclosure e = √(ΣΔE² + ΣΔN²), and the relative precision is 1 : (perimeter ÷ e).
4. Adjustment (Bowditch / compass rule). Each departure and latitude gets a correction proportional to the length of the line: c = −misclosure × d ÷ perimeter. The adjusted coordinates then close exactly on station 1.
FAQ
What is the angular closure tolerance?
It depends on the survey class and the instrument. A common reference is k·√n, with n = number of stations and k between 6" and 1' depending on the required accuracy. National standards and the project specifications set the tolerance for each traverse class (in Brazil, for example, NBR 13133). Here you choose k and the calculator tells you if the misclosure exceeds it.
What linear precision is acceptable?
As a rough guide: 1:5,000 for reconnaissance surveys, 1:10,000 or better for cadastral and construction work, 1:20,000 or more for control traverses with a good total station. Check the requirement of your contract or of the applicable standard.
Are the angles interior or exterior?
If you walk with the polygon on your left (counterclockwise) and turn the angle clockwise from backsight to foresight (angle right), you measure the interior angles. Walking clockwise, the same procedure gives the exterior angles. Set both options to match your traverse: the calculator checks the theoretical sum and warns you if they look swapped.
What about a link traverse (between known points)?
This calculator handles closed loop traverses (returning to the starting point). A link traverse between two pairs of known points follows the same logic, but the closure is checked against the closing azimuth and the coordinates of the end point. It is on our roadmap.
Slope distance or horizontal distance?
Use the horizontal (reduced) distance. Most total stations already display it (HD). If you have the slope distance and the zenith angle, the horizontal distance is d·sin(Z).