Bearing to Azimuth Calculator
The bearing to azimuth calculator converts a quadrant bearing, such as N30E, into a whole-circle azimuth measured clockwise from north, the form most modern survey and mapping software expects. The method is the set of four quadrant rules every surveyor learns. A quadrant bearing names a reference direction (north or south), an angle between 0 and 90 degrees, and a side (east or west). To convert it, you apply the rule for that quadrant: a north-east bearing keeps its angle, a south-east bearing becomes 180 minus the angle, a south-west bearing becomes 180 plus the angle, and a north-west bearing becomes 360 minus the angle. The result is a single azimuth from 0 to 360 degrees. Choose the quadrant and enter the angle to convert a deed call, set out a traverse leg, or move a record between bearing and azimuth conventions. The same logic finds a back azimuth by reversing the line, and the calculator updates the moment you change either the quadrant or the angle. Every figure here is computed deterministically from the quadrant rules shown in full below, with a worked example that reconciles exactly to the calculator so you can follow each step and trust the result rather than misreading a quadrant rule.
A quadrant bearing converts to a whole-circle azimuth by its quadrant rule: N-E keeps the angle, S-E is 180 minus, S-W is 180 plus, N-W is 360 minus. A bearing of N30E is an azimuth of 30.00°, measured clockwise from north.
Quadrant rules
N-E bearing: azimuth = angle
S-E bearing: azimuth = 180 - angle
S-W bearing: azimuth = 180 + angle
N-W bearing: azimuth = 360 - angle
Each quadrant rule rotates the quadrant angle into a single direction measured clockwise from north. The result is a whole-circle azimuth between 0 and 360 degrees.
Worked example
Convert the quadrant bearing N30E into an azimuth.
- The bearing is in the north-east quadrant
- The N-E rule is azimuth = angle
- Azimuth = 30°
The azimuth is 30.00 degrees, measured clockwise from north. These are the calculator's default inputs, so the result above matches the widget exactly.
Bearing to azimuth examples
The same 30 degree angle converted in each of the four quadrants.
| Bearing | Rule | Azimuth |
|---|---|---|
| N30E | angle | 30.00 |
| S30E | 180 - angle | 150.00 |
| S30W | 180 + angle | 210.00 |
| N30W | 360 - angle | 330.00 |
Survey and geodetic standards: US National Geodetic Survey (NOAA).
Bearing to azimuth calculator: frequently asked questions
What is the difference between a bearing and an azimuth?
A quadrant bearing measures direction as an angle east or west of north or south, written like N30E, and is always between 0 and 90 degrees. An azimuth measures direction as a single angle clockwise from north, from 0 to 360 degrees. Surveyors use both, and converting between them depends on which quadrant the bearing lies in.
How do I convert a quadrant bearing to an azimuth?
Apply the rule for the quadrant. A north-east bearing keeps its angle, so N30E is azimuth 30. A south-east bearing is 180 minus the angle. A south-west bearing is 180 plus the angle. A north-west bearing is 360 minus the angle. The result is a whole-circle azimuth measured clockwise from north.
What are the four quadrant rules?
For an N-E bearing the azimuth equals the angle. For an S-E bearing the azimuth equals 180 minus the angle. For an S-W bearing the azimuth equals 180 plus the angle. For an N-W bearing the azimuth equals 360 minus the angle. These four rules convert any quadrant bearing into a whole-circle azimuth.
Is azimuth measured from north or south?
In most surveying and mapping the azimuth is measured clockwise from north, which is the convention this calculator uses. Some astronomical and military conventions measure azimuth from south. Always confirm which reference a dataset uses, because a north and a south azimuth for the same line differ by 180 degrees.
What is a back azimuth?
A back azimuth is the reverse direction of a line, pointing from the far end back to the start. To find it, add 180 degrees to the forward azimuth if it is less than 180, or subtract 180 if it is 180 or more, so the result stays within 0 to 360 degrees. It represents the same line viewed from the opposite end.
Official sources
- Bearings, azimuths and geodetic standards: US National Geodetic Survey (NOAA). As at 25 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 25 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.