---
title: "Whole circle and reduced bearing"
subject: "Surveying I"
chapter: 4
key: "semester_3/surveying_i:whole-circle-and-reduced-bearing"
source: https://www.bctengineer.com/q/semester_3/surveying_i/whole-circle-and-reduced-bearing
site: BCT Engineering
---

# Whole circle and reduced bearing

Surveying I · Chapter 4: The Compass

- Asked in: 2074 Asoj, 4 marks
- Video: [Bearing in Surveying/Geomatics, Whole Circle Bearing and Reduced Bearing System](https://www.youtube.com/watch?v=Ujs0b7jqtTM) — CIVIL Solved
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/whole-circle-and-reduced-bearing
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-4

## Question

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

## 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.

## Answer

#### Whole circle bearing (WCB)

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

#### 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 $40^\circ$ E.

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

#### Conversion

| WCB ($\theta$) | Quadrant | Reduced bearing |
|---|---|---|
| $0^\circ$ to $90^\circ$ | NE | N $\theta$ E |
| $90^\circ$ to $180^\circ$ | SE | S $(180^\circ - \theta)$ E |
| $180^\circ$ to $270^\circ$ | SW | S $(\theta - 180^\circ)$ W |
| $270^\circ$ to $360^\circ$ | NW | N $(360^\circ - \theta)$ W |

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

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The whole circle bearing is read directly on:
   A. The surveyor's compass
   B. A plane table
   C. The prismatic compass
   D. A level
   Answer: C. WCB 0°-360° is the prismatic compass system. (Key point: Whole circle bearing)

2. A reduced bearing is:
   A. Clockwise angle from north up to 360°
   B. FB minus BB
   C. Angle between two lines
   D. The acute angle from the nearer N or S end towards E or W
   Answer: D. It is quoted with quadrant letters, e.g. N 40° E. (Key point: Reduced bearing)

3. WCB 215°30' converts to:
   A. S 35°30' W
   B. S 35°30' E
   C. N 35°30' W
   D. S 125°30' W
   Answer: A. Third quadrant: QB = WCB - 180° = 35°30', S 35°30' W. (Key point: Conversion)

4. S 62° E has WCB:
   A. 242°
   B. 118°
   C. 62°
   D. 298°
   Answer: B. SE quadrant: WCB = 180° - 62° = 118°. (Key point: Reverse conversion)

## Related in Surveying I

- [Local attraction: AB 69°30′ compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-ab-69-30-reordered) — Surveying I, chapter 4
- [Types of bearing in surveying](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atypes-of-bearing-meridian-designation-path) — Surveying I, chapter 4
- [Bearings and local attraction explained](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Abearings-and-local-attraction-terms) — Surveying I, chapter 4, asked 2×
- [Link traverse M2 to M8 bearings](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alink-traverse-m2-to-m8) — Surveying I, chapter 4
- [Local attraction with quadrantal bearings](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alocal-attraction-quadrantal-bearings-s11-30w) — Surveying I, chapter 4