# Difference between Whole Circle Bearing(WCB) andReduced(Quadrantal)Bearing System(RBS)

 S.NO. Whole Circle Bearing(WCB) Reduced(Quadrantal) Bearing System 1. Bearings (angles) are taken towards the clockwise direction from magnetic north. Bearing are always taken from magnetic north or south whichever is nearer. 2. Bearings are always taken in a clockwise direction. Bearings are taken in clockwise or anticlockwise direction. 3. Bearings vary from 0° to 360° Bearings vary from 0° to 90° 4. Example:- 166°45́ Ex:-N 89°45́ E, N 55° W, S 69° E, S 77° W

Bearing represents the measurement of angles w.r.t clockwise(examples: S 77° W or N 89°45́ E) or anticlockwise( S 69° E and N 55° W) direction or angles w.r.t north direction in surveying, where angle simply represent a degree in geometry.
How to convert the reduced bearing system to whole circle bearing?
Suppose we have given N43°E means bearing is from North towards East so we do nothing i.e. 43°(WCB).—–>FIRST QUADRANT
Suppose we have given S43°E means bearing is from South towards East so we subtract from 180° i.e. 180°-43°=137°(WCB).—–>SECOND QUADRANT
Suppose we have given S43°W means bearing is from South towards West so we add 180° i.e. 180°+43°=223°(WCB).—–>THIRD QUADRANT
Suppose we have given N43°W means bearing is from North towards West so we subtract from 360° i.e. 360°-43°=317°(WCB).—–>FOURTH QUADRANT.
Explaination: Whole circle bearing and quadrantal bearing are two different systems used to measure and express directions or bearings in surveying and navigation. While both systems are used to determine the direction of a point relative to a reference, they differ in terms of the range of values and the method of representation.

Whole circle bearing, also known as azimuth or azimuthal angle, is a system that measures angles clockwise from a fixed reference direction, usually the north direction. In this system, the circle is divided into 360 degrees, with each degree further divided into minutes and seconds. The whole circle bearing is expressed as a three-digit number, where the first two digits represent the degrees, the next two digits represent the minutes, and the last two digits represent the seconds. For example, a whole circle bearing of 120° 30′ 45″ indicates a direction that is 120 degrees clockwise from the reference direction.

On the other hand, quadrantal bearing divides the circle into four quadrants: northeast (NE), southeast (SE), southwest (SW), and northwest (NW). It uses cardinal directions (north, south, east, west) along with intermediate directions (northeast, southeast, southwest, northwest) to express bearings. Quadrantal bearings are typically used in aviation and marine navigation. The quadrant is determined based on the angle formed between the reference direction (usually north) and the line connecting the reference point to the point of interest. The quadrant is then combined with one or two cardinal or intermediate directions to express the bearing. For example, a quadrantal bearing of NE indicates a direction that lies in the northeast quadrant.

The main difference between whole circle bearing and quadrantal bearing lies in their range of values. Whole circle bearing covers a full 360-degree range, allowing for precise measurement and representation of any direction. Quadrantal bearing, on the other hand, only covers a 90-degree range within each quadrant. This means that quadrantal bearing provides a more generalized representation of direction, but it is less precise compared to whole circle bearing.

In terms of representation, whole circle bearing uses a numerical format with degrees, minutes, and seconds, while quadrantal bearing uses a combination of cardinal and intermediate directions along with the quadrant. The choice between the two systems depends on the specific application and the level of precision required. Whole circle bearing is commonly used in land surveying and geodesy, where high accuracy is essential. Quadrantal bearing, on the other hand, is often used in navigation systems where simplicity and ease of use are prioritized.

In conclusion, whole circle bearing and quadrantal bearing are two different systems used to express directions or bearings. Whole circle bearing provides a precise measurement of direction using degrees, minutes, and seconds, covering a full 360-degree range. Quadrantal bearing, on the other hand, divides the circle into four quadrants and uses cardinal and intermediate directions to represent bearings within each quadrant. While whole circle bearing offers higher accuracy and precision, quadrantal bearing provides a simpler representation suitable for navigation purposes.

Top 3 Authoritative Reference Publications or Domain Names Used:

1. “Surveying: Principles and Applications” by Barry F. Kavanagh
2. “Fundamentals of Surveying” by S.K. Roy