Compass Surveying Calculator
Complete Guide to Compass Surveying Bearings
In civil engineering and land surveying, determining the exact direction of a survey line is fundamental for traversing and boundary layout. The direction is defined by its horizontal angle relative to a fixed meridian (usually Magnetic North). Surveyors utilize two primary systems to read and record these angles: Whole Circle Bearing (WCB) and Reduced Bearing (RB).
1. Whole Circle Bearing (WCB)
In this system, the bearing of a line is measured clockwise continuously from Magnetic North. The value can be anywhere from 0° to 360°.
- Instrument Used: Prismatic Compass.
- Advantage: Much easier for plotting traverses and calculating interior angles without worrying about direction letters (N, S, E, W).
2. Reduced Bearing (RB) / Quadrantal Bearing
In this system, the bearing is measured either from North or South (whichever is closer) towards East or West. The angle never exceeds 90° and must always be accompanied by the quadrant letters (e.g., N 45° E).
- Instrument Used: Surveyor's Compass.
- Advantage: Essential for calculating consecutive coordinates (Latitudes and Departures) in a closed traverse.
Conversion Formulas Table
To convert manually, identify which of the four quadrants the survey line falls into:
| Quadrant | WCB Range | Rule for RB | Rule for WCB |
|---|---|---|---|
| I (North-East) | 0° - 90° | RB = WCB | WCB = RB |
| II (South-East) | 90° - 180° | RB = 180° - WCB | WCB = 180° - RB |
| III (South-West) | 180° - 270° | RB = WCB - 180° | WCB = 180° + RB |
| IV (North-West) | 270° - 360° | RB = 360° - WCB | WCB = 360° - RB |
When subtracting degrees and minutes manually, remember that 1 Degree = 60 Minutes. If you need to subtract 145° 30' from 180°, you cannot use standard decimal math. You must "borrow" 1 degree and convert it to 60 minutes. Therefore, 180° becomes 179° 60'.
Solved Numerical Examples
1. Check Quadrant: 145° is between 90° and 180° (II Quadrant, South-East).
2. Formula: RB = 180° - WCB
3. Math Setup: 179° 60' - 145° 30'
4. Result: S 34° 30' E
1. Check Quadrant: North-West is the IV Quadrant.
2. Formula: WCB = 360° - RB
3. Math Setup: 359° 60' - 25° 15'
4. Result: 334° 45'
Advanced Concepts: Declination & Attraction
Magnetic Declination
A compass needle does not point to the geographic North Pole (True North); it points to the Magnetic North Pole. The horizontal angle between True North and Magnetic North at any given location is called Magnetic Declination.
- Declination East: True Bearing = Magnetic Bearing + Declination
- Declination West: True Bearing = Magnetic Bearing - Declination
Local Attraction
If you are surveying near steel structures, high-voltage power lines, or underground iron pipes, the magnetic needle will deflect from its normal position. This error is known as Local Attraction. Civil engineers detect this in a closed traverse by checking the Fore Bearing (FB) and Back Bearing (BB) of a line. If the difference between FB and BB is not exactly 180°, the station is affected by local attraction.