Azimuth Bearing Converter
The azimuth bearing converter translates between whole-circle azimuth (0 to 360 degrees) and quadrant bearing notation (N 45 E, S 30 W, etc.) used in US land surveying and legal property descriptions. Enter an azimuth and get the equivalent quadrant bearing, or enter a quadrant bearing components and get the azimuth. The converter also computes the back bearing. Understanding both notations is essential for reading deeds, traversing survey plats, and working with older survey data.
Azimuth to quadrant bearing conversion
0-90 deg (NE): N (azimuth) E
90-180 deg (SE): S (180 - azimuth) E
180-270 deg (SW): S (azimuth - 180) W
270-360 deg (NW): N (360 - azimuth) W
Special cases: 0/360 = North, 90 = East, 180 = South, 270 = West. Back azimuth = (azimuth + 180) mod 360.
Bearing notation in US deeds
- Quadrant bearings in deeds are written as: N 45 30 E (North, 45 degrees 30 minutes East).
- The first letter (N or S) gives the primary compass direction. The number is degrees from north or south. The last letter (E or W) gives the secondary direction.
- The angle in a quadrant bearing is always between 0 and 90 degrees.
- When working with modern GIS data in azimuths, convert quadrant bearings using the reverse formulas before computing coordinates.
Azimuth bearing converter: frequently asked questions
What is the difference between azimuth and bearing?
An azimuth is measured clockwise from north through 360 degrees (0 to 360). A quadrant bearing uses four compass quadrants: N, S, E, W. It is expressed as N 45 E (45 degrees east of north) or S 30 W (30 degrees west of south), with angles always 0-90 degrees from north or south.
How do I convert azimuth to quadrant bearing?
NE quadrant (0-90): bearing = N (azimuth) E. SE quadrant (90-180): bearing = S (180 - azimuth) E. SW quadrant (180-270): bearing = S (azimuth - 180) W. NW quadrant (270-360): bearing = N (360 - azimuth) W.
How do I convert quadrant bearing to azimuth?
N x E: azimuth = x. S x E: azimuth = 180 - x. S x W: azimuth = 180 + x. N x W: azimuth = 360 - x. Where x is the angle from north or south in the quadrant bearing.
Which system is used in US land surveying?
US land surveying and legal descriptions traditionally use quadrant bearings (also called surveyor's bearings). Modern GPS and GIS software typically uses azimuths (whole-circle bearings). The two systems must be converted carefully when mixing sources.
What is a back bearing?
A back bearing is the reverse direction: 180 degrees from the forward bearing. In azimuth: back azimuth = (azimuth + 180) mod 360. In quadrant notation, swap N/S and E/W: N 45 E becomes S 45 W.
Official sources
- NOAA National Geodetic Survey: NGS surveying standards and bearing notation.
- BLM GLO Records: BLM GLO historical survey records.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.