This bearing to azimuth converter converts between the two ways of describing direction that survey
plans mix freely. A quadrant bearing such as N 45°30′ E states the angle
from north or south towards east or west; a whole-circle azimuth such as
45.5° measures clockwise from north all the way round to 360°. Enter either
form and the converter returns the other, plus the 16-point compass direction.
Enter decimal degrees or degrees, minutes and seconds: 45.5 and 45 30 00 are the same angle.
| Quadrant bearing | Azimuth | Quadrant bearing | Azimuth |
|---|---|---|---|
| N 0° E | 0° | S 0° E | 180° |
| N 45° E | 45° | S 45° E | 135° |
| N 90° E | 90° | S 90° E | 90° |
| N 45° W | 315° | S 45° W | 225° |
| N 90° W | 270° | S 90° W | 270° |
Whole-circle azimuths and quadrant bearings describe the same direction in different ways. An azimuth is always measured clockwise from north, from 0° up to 360°. A quadrant bearing instead measures the acute angle away from the nearest north–south line and names that line and the direction, so it always reads between 0° and 90°.
The conversion therefore depends on the quadrant. In the north-east quadrant the two are identical: bearing N θ E equals azimuth θ. In the south-east quadrant the azimuth is 180° − θ, in the south-west quadrant it is 180° + θ, and in the north-west quadrant it is 360° − θ. Working the other way, take the azimuth modulo 90° to get the quadrant angle and read the quadrant directly from the azimuth value.
To find the back azimuth — the direction of the same line viewed from its other end — add 180° and subtract 360° if the total exceeds a full circle. The reverse of an azimuth of 45° is therefore 225°.
A bearing to azimuth converter is needed because two conventions sit side by side. A quadrant bearing names the reference line and the direction of travel, so it reads N 45°30′ E or S 12°45′ W and never exceeds 90°. A whole-circle bearing, usually called an azimuth, is a single number measured clockwise from north between 0° and 360°. Neither notation is more correct; each simply suits a different document.
This page works as a bearing to azimuth converter in the forward direction and as an azimuth to bearing calculator in reverse. Enter the quadrant bearing, choose whether it is measured from north or south and towards east or west, and the whole-circle azimuth comes back with a 16-point compass direction plus the back azimuth for the same line read from the far end. The arithmetic is exact, so N 45°30′ E gives 45.5° and the reverse conversion returns the bearing you started with.
Going the other way — quadrant bearing to azimuth — is one rule per quadrant. A bearing in the north-east quadrant (NE) becomes the azimuth itself; a south-east bearing (SE) becomes 180° − θ; a south-west bearing (SW) becomes 180° + θ; and a north-west bearing (NW) becomes 360° − θ. Every result lands inside 0–360°, which is the range a COGO or traverse program expects when bearings and azimuths appear together on the same plan.
Survey plans, deeds and field books are inconsistent about direction notation, so a conversion is needed whenever two sources are compared:
Use the rule for the quadrant: N theta E is azimuth theta, S theta E is 180 minus theta, S theta W is 180 plus theta, and N theta W is 360 minus theta. For example N 45 degrees 30 minutes E becomes an azimuth of 45.5 degrees, and S 30 degrees E becomes 150 degrees.
Azimuths from 0 to 90 degrees are north-east bearings and use the azimuth itself. Azimuths from 90 to 180 degrees are south-east: subtract the azimuth from 180. From 180 to 270 degrees they are south-west: subtract 180. From 270 to 360 degrees they are north-west: subtract the azimuth from 360. An azimuth of 135.25 degrees is therefore S 44 degrees 45 minutes E.
A back azimuth is the direction of the same line measured from the opposite end. It is always the forward azimuth plus or minus 180 degrees: add 180 if the azimuth is 180 or less, subtract 180 if it is greater. A forward azimuth of 45 degrees has a back azimuth of 225 degrees.
No. A quadrant bearing is by definition an acute angle measured from either north or south, so it always lies between 0 and 90 degrees. Values above 90 degrees only appear in whole-circle azimuths, which is one of the reasons the two notations get confused.
Yes. You can enter either decimal degrees such as 45.5 or a degrees-minutes-seconds value such as 45 30 00, and every result is given in both formats.
Not exactly. An azimuth is an exact angle measured from true north, while a compass bearing is measured from magnetic north and drifts as the magnetic declination changes. The 16-point compass direction shown here is a rounded headline value for the azimuth, not a magnetic compass reading.
A bearing is a direction stated relative to north or south and towards east or west, so it is always an acute angle between 0 and 90 degrees; an azimuth is the same direction written as a single clockwise angle from north between 0 and 360 degrees. Feed either one into this bearing to azimuth converter and the other form, the compass point and the back azimuth are returned.
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