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Back Azimuth

αb=α±180∘\alpha_b = \alpha \pm 180^{\circ}

Worked example: Azimuth 45° → back azimuth 225° — press Try an example to run it live, then adjust anything.

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Bearings and the needle →

UniversityApplied Field Engineering

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Back Azimuth explained

ααb

An azimuth is a direction measured clockwise from north, running 0° to 360°, and the back azimuth is the same line looked at from the other end. The rule is add 180° if the azimuth is under 180°, subtract 180° if it is over — which is one rule, not two, once you take the result modulo 360°. Surveyors need it constantly because a traverse leg measured from A to B has to be carried forward from B, and because the check on a closed traverse is that the back azimuth of the last leg reproduces the first bearing you started from.

Bearings are the older notation and behave differently: a bearing of N 30° E has a back bearing of S 30° W, the same numeric angle with both letters flipped. Azimuths avoid all that quadrant bookkeeping, which is why modern instruments and coordinate geometry work in them. A worked example: a property line runs at azimuth 45°, so its back azimuth is 225°; a line at azimuth 300° reverses to 120°. Note that a magnetic back azimuth taken in the field will not agree with a computed one to better than the local declination and the compass's own reversal error, which is why the check is done on the numbers, not the needle.

Back Azimuth formula

αb=α±180∘\alpha_b = \alpha \pm 180^{\circ}
Where
  • α\alpha= Forward azimuth (°)
  • αb\alpha_b= Back azimuth (°)

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Part of this formula set

Survey traverse closure

6 formulasClosing a traverse: latitudes and departures per leg, the misclosure they expose, and the precision ratio that decides whether it passes.