Converting...
Enter a quadrant bearing or whole-circle azimuth above, then click Convert.
What Is the Difference Between Bearing and Azimuth?
A quadrant bearing describes a direction by measuring the acute angle from the nearest cardinal direction toward the east or west. It is written as N 45° E, S 30°15′ W, and so on. Surveyors and deed drafters love quadrant bearings because the angle is always between 0° and 90° and the direction is unambiguous.
An azimuth is a whole-circle angle measured clockwise from north, ranging from 0° to 360°. Total stations, GPS receivers, and GIS software use azimuths because they are easier to compute with and feed directly into trigonometric formulas. Converting between the two notations is one of the most common tasks when retracing old property boundaries or importing survey data into CAD.
Quadrant Bearings vs Whole-Circle Azimuth
Quadrant bearing: angle measured from the nearest cardinal axis. Always written with N/S first and E/W last, e.g. N 45° E.
Whole-circle azimuth: angle measured clockwise from north through a full 360°, e.g. 45°.
Back azimuth: add 180° to the forward azimuth to reverse the line of sight.
How to Convert a Quadrant Bearing to an Azimuth
The conversion depends on which quadrant the bearing sits in. Start by converting the DMS angle to decimal degrees, then apply one of the four formulas:
- NE quadrant: azimuth = θ
- SE quadrant: azimuth = 180° − θ
- SW quadrant: azimuth = 180° + θ
- NW quadrant: azimuth = 360° − θ
For example, a bearing of N 45°30′ E lies in the NE quadrant, so the azimuth is 45.5°. A bearing of S 30°15′ W is in the SW quadrant, giving 180° + 30.25° = 210.25°. Our converter handles the DMS math automatically and shows both decimal and DMS azimuth output.
How to Calculate Back Azimuth
The back azimuth is the direction you face when looking back along the same line. Add 180° to the forward azimuth and, if the result is 360° or more, subtract 360°. The back bearing uses the same quadrant logic in reverse: if the forward bearing is N 45° E, the back bearing is S 45° W. This is indispensable for checking deed calls, closing traverse lines, and verifying total station setups.
Why Surveyors and Title Researchers Need Bearing ↔ Azimuth Conversion
Historical plats, metes-and-bounds deeds, and county records are almost always written in quadrant bearings. Modern survey instruments and GIS layers output azimuths. When you need to compare a 1905 deed call against a 2025 GPS survey, both directions must be expressed in the same system. A reliable converter saves manual calculation, reduces transcription errors, and keeps boundary retracements defensible.
Reading Bearings in Old Deeds and Plats
Older documents may omit degree symbols or write directions as North 45 East. Always confirm whether the angle is measured from true north or magnetic north; many 19th-century deeds reference magnetic north and require a declination correction before they can be plotted accurately. If you need the magnetic correction for a specific year and location, use the Magnetic Declination Calculator linked below.
Common Bearing ↔ Azimuth Conversions
| Quadrant Bearing | Whole-Circle Azimuth | Back Azimuth | Back Bearing |
|---|---|---|---|
| N 0° E | 0° | 180° | Due South |
| N 45° E | 45° | 225° | S 45° W |
| N 90° E | 90° | 270° | Due West |
| S 45° E | 135° | 315° | N 45° W |
| S 0° E | 180° | 0° | Due North |
| S 30° W | 210° | 30° | N 30° E |
| N 30° W | 330° | 150° | S 30° E |
Frequently Asked Questions
How do you convert N 45° E to azimuth?
Because the bearing is in the NE quadrant, the azimuth equals the angle itself: 45°. If the bearing were S 45° E, you would subtract from 180° to get 135°.
What is the back azimuth of 135 degrees?
Add 180° to 135° and the back azimuth is 315°. The back bearing is N 45° W, the exact opposite direction.
Can an azimuth be negative?
In standard whole-circle notation, no. Azimuths run from 0° to 360° clockwise from north. If a calculation gives a negative value, add 360° to bring it into the standard range.
Why do old property deeds use quadrant bearings?
Quadrant bearings keep the numeric angle small and clearly tied to a cardinal direction, which reduces ambiguity when deeds are copied by hand. Before electronic calculators, this made plat drafting faster and less error-prone.
What is the difference between true azimuth and magnetic azimuth?
True azimuth is referenced to geographic north. Magnetic azimuth is referenced to the direction a compass needle points, which shifts over time and location. Converting between them requires the local magnetic declination.
How do you convert an azimuth greater than 360?
Subtract 360° until the value falls between 0° and 360°. For example, 390° becomes 30°, which is the same direction as N 30° E.
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