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Whole circle and reduced bearing

Short answer

Whole circle bearing (WCB) is measured clockwise from north 0°–360°. Quadrantal bearing (reduced bearing) is the acute angle from north or south towards east or west, e.g. N 30° E. Conversion: 1st quadrant N θ E, 2nd S (180°–θ) E, 3rd S (θ–180°) W, 4th N (360°–θ) W.

Explain whole circle bearing and reduced bearing of compass survey with neat sketch.

Whole circle bearing (WCB)

The bearing of a line measured clockwise from the north end of the meridian, from 0∘0^\circ to 360∘360^\circ. It is read directly on the prismatic compass. The bearing is stated as a single angle, e.g. 135∘30′135^\circ 30'.

Reduced bearing (quadrantal bearing, R.B.)

The acute angle which the line makes with the nearer end (north or south) of the meridian, measured towards the east or west. It is written with the quadrant letters, e.g. N 40∘40^\circ E.

            N (0°)
      NW    |    NE
  (IV)      |      (I)
 W (270°)---+---E (90°)
  (III)     |      (II)
      SW    |    SE
            S (180°)

Conversion

WCB (θ\theta)QuadrantReduced bearing
0∘0^\circ to 90∘90^\circNEN θ\theta E
90∘90^\circ to 180∘180^\circSES (180∘−θ)(180^\circ - \theta) E
180∘180^\circ to 270∘270^\circSWS (θ−180∘)(\theta - 180^\circ) W
270∘270^\circ to 360∘360^\circNWN (360∘−θ)(360^\circ - \theta) W

Example: WCB 215∘30′215^\circ 30' lies in the third quadrant, so the reduced bearing is S (215∘30′−180∘)(215^\circ 30' - 180^\circ) W = S 35∘30′35^\circ 30' W. Conversely, S 62∘62^\circ E has WCB =180∘−62∘=118∘= 180^\circ - 62^\circ = 118^\circ.

✓ Answer checked by Claude Opus 5.5 (high effort)

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