Both describe a horizontal direction, and both start from north, which is why they get used interchangeably in conversation and then cause trouble in a calculation. The difference is the reference frame: an azimuth is one continuous angle measured clockwise from north, while a bearing names a quadrant and measures the angle from whichever of north or south is nearer, towards east or west. Deeds, older survey plans and some jurisdictions use bearings; computation and most modern software use azimuths.
An azimuth is measured clockwise from north and runs from 0° through east at 90°, south at 180°, west
at 270°, and back to 360° at north. There is no quadrant bookkeeping and no sign convention — the
direction north-east is simply 45°, and the direction west-south-west is 247.5°. Because it is a
single continuous quantity, an azimuth is what coordinate geometry uses: ΔE = d sin A
and ΔN = d cos A turn a distance and an azimuth directly into a change in coordinates.
A quadrant bearing, sometimes called a reduced bearing, states the quadrant first and gives an angle
between 0° and 90° inside it. It is written with the north or south reference first and the east or
west direction last, as in N 45°30′ E — 45°30′ east of north. The four possible forms are
NE, SE, SW and NW, and the angle is always the deviation from the meridian, never an absolute angle.
The style is not arbitrary. A quadrant bearing makes the direction readable at a glance: you can see from the letters whether a line runs easterly or westerly without comparing numbers to 90 and 270, and in a metes-and-bounds description where a dozen lines are read aloud in sequence, that matters.
| Quadrant | Bearing | Azimuth | Rule |
|---|---|---|---|
| North-east | N θ E | θ | Azimuth = θ |
| South-east | S θ E | 180° − θ | Azimuth = 180° − θ |
| South-west | S θ W | 180° + θ | Azimuth = 180° + θ |
| North-west | N θ W | 360° − θ | Azimuth = 360° − θ |
Worked both ways: a bearing of N 45°30′ E is azimuth 45.5°. A bearing of
S 60° E is 180° − 60° = 120°. An azimuth of 225° falls in the south-west quadrant, so the
bearing is S 45° W, because 225° − 180° = 45°. And an azimuth of 330° is
N 30° W, because 360° − 330° = 30°.
Going from azimuth to bearing, the quadrant is decided first — NE for 0–90, SE for 90–180, SW for 180–270, NW for 270–360 — and then the angle inside that quadrant is computed by the inverse of the rule above. Exact multiples of 90° are the awkward case, since the angle inside the quadrant is 0° and the bearing degenerates to a pure cardinal direction, which is why software often reports them as azimuths regardless of the setting.
The direction of a line depends on which end you stand at. The forward azimuth and the back azimuth
differ by 180°: back = forward + 180° if the forward azimuth is below 180°, and
back = forward − 180° if it is above. For bearings the rule is neater — the letters
swap, so N 45° E reverses to S 45° W and the angle stays the same.
This is one place where the bearing convention earns its keep: reading a description of a closed parcel, the reverse of each line appears in the next line's letters, and any line that does not reverse correctly is immediately visible as a transcription error. The same check exists for azimuths, but as arithmetic rather than as pattern-matching.
True north, magnetic north or grid north? A bearing or azimuth is meaningless without knowing which north it refers to. True north is the geographic pole, magnetic north is where a compass needle points and it drifts with the magnetic declination, and grid north is the direction of the grid's north axis on a projected map, which differs from true north by the grid convergence. Deeds written with a compass give magnetic bearings with the declination stated at the time of survey. Modern computation uses grid or true azimuths. Converting between them without the declination and convergence is not possible.
The three errors that come up most often are mixing conventions within one calculation, forgetting that a magnetic bearing from an old deed does not equal a modern azimuth, and applying a back-bearing rule twice so that the direction silently reverts. All three produce results that are internally consistent and externally wrong. If a coordinate closes neatly but the shape is rotated relative to the ground, declination or a swapped convention is the first thing to check.
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