Difference between Reduced Bearing (RB) and Whole Circle Bearing (WCB

 

Difference between Reduced Bearing (RB) and Whole Circle Bearing (WCB)

In surveying, we need to determine the direction of a line. For this, we use the bearing system. There are two main types of bearings:

1. Whole Circle Bearing (WCB)

2. Reduced Bearing (RB)

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1️⃣ Whole Circle Bearing (WCB)

Definition:
WCB is measured clockwise from North to the line.

Key Points:

• Always measured clockwise from North.

• Angle ranges from 0° to 360°.

• Uses only one reference direction: North.

Examples:

• Line 60° clockwise from North → WCB = 60°

• Line towards South → WCB = 180°

• Line towards West → WCB = 270°

Advantages:

• Easier for calculations and mathematics.

• Useful in computer software and mapping.

Disadvantages:

• Can be confusing in the field due to large numbers.

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2️⃣ Reduced Bearing (RB)

Definition:
RB is measured from the nearest North or South line towards East or West.

Key Points:

• Always ranges between 0° and 90°.

• Written as N θ E, N θ W, S θ E, S θ W

  • θ = angle measured from North or South

Examples:

• N 45° E → 45° from North towards East

• S 30° W → 30° from South towards West

Advantages:

• Easy to understand in the field.

• Simple for drawing maps and diagrams.

Disadvantages:

• Slightly difficult for calculations.

• Often needs conversion to WCB for math or mapping.

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3️⃣ Comparison Table

Feature	RB	WCB
Reference	Nearest North/South	North only
Angle	0° – 90°	0° – 360°
Notation	N θ E, N θ W, S θ E, S θ W	0° – 360° clockwise from North
Field Use	Easy	Slightly difficult
Calculation	Slightly difficult	Easy
Conversion	Required to WCB	Not required

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4️⃣ RB → WCB Conversion Rules

RB	WCB
N θ E	θ
S θ E	180° − θ
S θ W	180° + θ
N θ W	360° − θ

Examples:

• N 60° E → WCB = 60°

• S 40° E → WCB = 140°

• S 30° W → WCB = 210°

• N 20° W → WCB = 340°

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5️⃣ WCB → RB Conversion Rules

WCB	RB
0° – 90°	N θ E
90° – 180°	S (180 − θ) E
180° – 270°	S (θ − 180) W
270° – 360°	N (360 − θ) W

Examples:

• WCB = 30° → RB = N 30° E

• WCB = 150° → RB = S 30° E

• WCB = 210° → RB = S 30° W

• WCB = 330° → RB = N 30° W

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6️⃣ Visual Idea / Easy Understanding

• WCB: Angle clockwise from North, 0° – 360°

• RB: Angle from nearest North/South towards East/West, 0° – 90°

Examples:

• North-East line → WCB = 45°, RB = N 45° E

• South-West line → WCB = 225°, RB = S 45° W

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7️⃣ Why Two Systems?

• RB → Easy in field work (small angles).

• WCB → Easy for calculations and mapping (360° system).

• Surveyors often note RB in the field and convert to WCB for calculations.

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8️⃣ Common Exam Questions

• Convert RB → WCB

• Convert WCB → RB

• Draw the direction of a line

• Calculate angle between two lines

Tip: RB < 90°, WCB = 0–360°. Remember conversion rules for exams.

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9️⃣ Key Points – Simplified

• RB (Reduced/Quadrantal Bearing): 0° – 90°

• WCB (Whole Circle Bearing): 0° – 360°

• RB: Easy in field, WCB: Easy in calculation

• Conversion rules are important → often asked in exams

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