How to use the Traverse Closing Error Calculator
- 1. Enter each lineName, length in m and bearing, going round the traverse in order.
- 2. Pick the ruleBowditch (compass) rule or transit rule.
- 3. Read the tableLatitudes, departures, corrections, adjusted coordinates and a plot.
Formulas
Latitude = l cos θ and departure = l sin θ, where θ is the whole circle bearing. In a closed traverse ΣL and ΣD should be zero. The closing error e = √(ΣL² + ΣD²), its direction is tan⁻¹(ΣD / ΣL), and the relative precision is 1 in (perimeter / e).
Bowditch rule: correction to a line's latitude = −ΣL × (line length / perimeter), and the same for departures. Transit rule: correction = −ΣL × |latitude| / Σ|latitude|. Bowditch suits compass traverses where angles and lengths are equally precise; transit suits theodolite traverses with more precise angles.
Worked example and lab tips
For the default five-sided traverse (perimeter 851.6 m), the tool finds ΣL = +0.509 m and ΣD = +0.224 m, so e = 0.556 m and the precision is about 1 in 1530. Bowditch corrections share this error in proportion to line lengths, after which the traverse closes exactly.
- Balance the angles first: interior angles of an n-sided traverse add up to (2n − 4) × 90°.
- Check the signs: N and E are positive, S and W negative.
- Report coordinates from a known starting station, for example 1000 m E, 1000 m N.
Frequently asked questions
Can I enter reduced (quadrant) bearings?
Yes. Write them like N45.5E or S 30 15 W. Whole circle bearings can be decimal degrees or D M S.
What precision is acceptable?
It depends on the survey type and your instructions; the tool reports the precision so you can compare it with the allowed value.
Does it adjust angles?
No. Adjust the angular error first, work out the bearings, then enter the lines here.
Is this calculator free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form. Everything is calculated in your browser.