Azimuth and Bearing

Az (N θ E) = θ, Az (S θ E) = 18 0^{\circ} - θ, Az (S θ W) = 18 0^{\circ} + θ, Az (N θ W) = 36 0^{\circ} - θ

Azimuth is clockwise from north (0–360°). Bearing is acute from N or S toward E or W. Interior-angle traverses convert to azimuths by Az_next = Az_prev + 180° ± interior (keep 0–360°). Grid, geodetic, and magnetic azimuths differ by convergence and declination.

$Az$: Azimuth from north
$θ$: Acute bearing angle
$N / S, E / W$: Bearing quadrant letters

Step-by-step solved example

Convert bearing S 42°30' E to azimuth.

Bearings measured from N/S; azimuths clockwise from north.

1. Quadrant
South toward east is the SE quadrant: azimuth = 180° − θ.
2. Subtract
180°00' − 42°30' = 137°30'.
$Az = 13 7^{\circ} 3 0^{'}$

Answer: Azimuth = 137°30'

10 practice questions

0/10 correct

1.Bearing N 32° E as azimuth is

2.Azimuth 220° as a bearing is

3.Bearing N 15° W equals azimuth

4.Back azimuth of 70° is

5.Bearing S 90° E is the same as

6.Magnetic azimuth 20°, declination 8° E. True azimuth is

7.A bearing angle is always

8.Azimuth 180° is bearing

9.Next azimuth = previous azimuth + 180° + right interior angle, then

10.Bearing S 42°30' W as azimuth is