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Whole Circle Bearing to Reduced Bearing (WCB to RB) | Surveying

Updated: Jan 19


Whole Circle Bearing to Reduced Bearing Conversion in surveying
Conversion of WCB to RB example

In Whole Circle Bearing - Bearings are measured clockwise from north of reference meridian; In Reduced Bearing - Bearings are measured either clockwise or anti-clockwise from north/south whichever is close to the line.


Let us see a few basic concepts before we jump on the conversion steps. If you already know them, skip directly to the WCB to RB conversion steps


What is bearing?

Bearing is the direction of survey lines with respect to a meridian

Bearing is as simple as the direction of survey lines w.r.t. a meridian.


Meridian is a fixed reference line.


The bearing system is of two types - Whole circle bearing and reduced bearing. We can convert from one system to another.


Whole Circle Bearing (WCB)


Bearings are measured clockwise from north of reference meridian.


It is also known as the Azimuthal System

  • It varies from 0 degrees to 360 degrees in the clockwise direction

  • North will be zero degrees; East will be 90 degrees; South will be 180 degrees and West will be 270 degrees.

  • Prismatic compass uses the WCB system

Examples of WCB


Line from origin to A (OA) : The angle is measured from the north to OA represented by θ in the figure.


Line from origin to B (OB): The angle is measured from the north to OB represented by ϕ in the figure.


Whole Circle Bearing (WCB)
Whole Circle Bearing (WCB)

Reduced Bearing (RB)


Bearings are measured either clockwise/anti-clockwise from north/south whichever is close to the line.

It is also known as Quadrantal Bearing (QB)

  • Angles vary from 0 degrees to 90 degrees

  • It is measured from either clockwise/anti-clockwise from north/south (If the line is closer to south and going towards west, it is read as Sβ°W)

  • Four quadrants are possible namely NE, SE, SW and NW

  • Surveyor's compass used RB system

Examples of RB


Line from origin to A (OA) : The angle is measured from the north to OA because OA is closer to the north. It is represented by NαE in the figure.


Line from origin to B (OB): The angle is measured from the south to OB because OB is closed to the south. It is represented by SβW in the figure.


Reduced Bearing (RB)
Reduced Bearing (RB)

Conversion from Whole Circle Bearing to Reduced Bearing


It is very easy to convert if we draw diagrams as shown below.

  1. In this example, WCB = 240°

  2. It lies in the third quadrant as the angle is between 180° and 270°

  3. So, the quadrant position reading as per RB is SW

  4. The angle will be 240° - 180° = 60°

  5. RB = S60°W

There are pin-pointed formulas to convert WCB to RB