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Surveying

Quadrant Bearings in Surveying

Updated · GeoCAD Bridge engineering team · 8 min read

Summary

A quadrant bearing gives a direction as an angle of 0° to 90° measured from north or south towards east or west, for example N 30° E or S 45° W. Surveying calculations use whole-circle azimuths (0° to 360° clockwise from north), so bearings are converted using four simple rules.

Definition

Quadrant bearing: a horizontal direction stated as N or S, an angle up to 90°, then E or W.

  • Range 0°–90°
  • Measured from N or S
  • NE: Az = β
  • SE: Az = 180° − β

Bearing to azimuth

Conversion rules used by GeoCAD Bridge.
QuadrantAzimuth from bearing βExample
NEAz = βN 30°00′ E → 30°00′
SEAz = 180° − βS 30°00′ E → 150°00′
SWAz = 180° + βS 30°00′ W → 210°00′
NWAz = 360° − βN 30°00′ W → 330°00′

Azimuth to bearing

  • 0°–90°: N Az E
  • 90°–180°: S (180° − Az) E
  • 180°–270°: S (Az − 180°) W
  • 270°–360°: N (360° − Az) W

Back bearings

The back bearing swaps both letters and keeps the angle: the back bearing of N 30° E is S 30° W. For azimuths, add or subtract 180°.

FAQ

What is the difference between a bearing and an azimuth?

A bearing is a quadrant angle up to 90° with N/S and E/W letters; an azimuth is a single angle from 0° to 360° clockwise from north.

Are bearings grid, true or magnetic?

Any of the three. Always state the reference: grid north for map projections, true north for geodetic work, magnetic north for compass readings.

Tools

Articles

References

  1. Ghilani, C. D. & Wolf, P. R. Elementary Surveying: An Introduction to Geomatics, 15th ed., Pearson, 2018 (traverse computations and adjustments).
  2. Uren, J. & Price, W. F. Surveying for Engineers, 5th ed., Palgrave Macmillan, 2010.

Cite this page

GeoCAD Bridge. “Quadrant Bearings in Surveying.” GeoCAD Bridge Knowledge Center, updated 2026-10-05. https://www.geocadbridge.com/knowledge/survey-bearings/