Azimuth and Quadrant Bearing Conversion

Converts between an azimuth (0 to 360 deg clockwise from north, the form all the coordinate math runs on) and a quadrant bearing (N or S, an angle 0 to 90 deg, E or W, the form deeds and plats are written in). First quadrant reads N az E; second, S the supplement E; third, S the excess over 180 W; fourth, N the deficit from 360 W. An azimuth of 138.5 deg is S 41 deg 30 min 00 sec E; SW 30 deg is azimuth 210. The cardinal azimuths 0/90/180/270 read as due north/east/south/west. Shown to the nearest second. Plane-direction bookkeeping only: no magnetic declination, which is a separate conversion and no grid convergence.

an azimuth A (0 to 360 deg clockwise from north) maps to a quadrant bearing by quadrant: A in [0,90] is N A E; A in [90,180] is S (180 minus A) E; A in [180,270] is S (A minus 180) W; A in [270,360] is N (360 minus A) W. The reverse runs each rule backward: N b E gives A = b, S b E gives A = 180 minus b, S b W gives A = 180 plus b, N b W gives A = 360 minus b. The cardinal azimuths 0/90/180/270 read as due north/east/south/west.

Azimuth and quadrant (deed) bearing are the two standard ways to write a plane direction in US surveying references (Ghilani/Wolf, Elementary Surveying; FM 5-233, public-domain), by name; the conversion is exact plane geometry.

The quadrant rules are elementary geometry stated in every surveying text and in free course notes and the public-domain FM 5-233; nothing here is tabulated or proprietary.

Estimate. AHJ and licensed professional govern.

Field names used by the API: mode, azimuth_deg, quadrant, quadrant_angle_deg

• Azimuth convention 0 to 360 deg measured clockwise from northstandard surveying convention
• Quadrant bearing N or S, an angle 0 to 90 deg, then E or Wdeed and plat convention
• Cardinals azimuth 0/90/180/270 read as due north/east/south/westboundary cases of the quadrant rules
• Scope no magnetic declination and no grid convergence; plane direction onlystated scope limit