To convert a bearing to an azimuth, type it as a quadrant bearing such as S 45°30' E; to convert an azimuth to a bearing, type the angle, such as 134.5. The converter detects which one you entered, returns the other with the back azimuth and back bearing, and accepts decimal degrees or degrees-minutes-seconds. It converts lists too and runs in your browser.
- Free, no signup
- Both directions, auto-detected
- Back azimuth and back bearing
- Runs in your browser
Calculate many at once
One value per line. Quadrant bearings (N/S first, E/W last) are read as bearings; plain numbers and DMS are read as azimuths from 0 to 360°.
How to convert between bearing and azimuth
- Type the value. A quadrant bearing starts with N or S and ends with E or W, for example
S 45°30'00" EorN 30 W. An azimuth is a number from 0 to 360, for example134.5or225°15'30". - Click Convert. The page shows what it read, the azimuth in decimal degrees and DMS, the quadrant bearing, the back azimuth and the back bearing.
- Check the quadrant. The quadrant angle is always 90° or less. The letters tell you the quadrant: NE, SE, SW or NW.
- Or convert a list. Paste many, one per line, and download the results as a CSV.
Azimuth and quadrant bearing
Both describe a direction from north. They differ in how:
- Azimuth is one angle from 0° to 360°, measured clockwise from north. East is 90°, south 180°, west 270°.
- Quadrant bearing (also called a surveyor's or reduced bearing) is an angle of at most 90° measured from north or south toward east or west, for example
N 45° E.
Many navigation texts call the azimuth a bearing, and a three-figure bearing like 045° is an azimuth. If you are working from a land survey deed, bearings are almost always quadrant bearings.
The conversion rules
| Quadrant | Quadrant bearing → azimuth | Azimuth → quadrant bearing |
|---|---|---|
| North-east | azimuth = α | N α E, for 0° to 90° |
| South-east | azimuth = 180° - α | S (180° - az) E, for 90° to 180° |
| South-west | azimuth = 180° + α | S (az - 180°) W, for 180° to 270° |
| North-west | azimuth = 360° - α | N (360° - az) W, for 270° to 360° |
Here α is the angle in the quadrant bearing. The back azimuth is the azimuth plus or minus 180°, and the back bearing swaps both letters: the back bearing of N 30° E is S 30° W.
Worked examples
| You type | Azimuth | Quadrant bearing | Back azimuth |
|---|---|---|---|
S 45°30'00" E | 134.5° | S 45°30'00" E | 314.5° |
N 30° W | 330° | N 30°00'00" W | 150° |
225 | 225° | S 45°00'00" W | 45° |
N 12°30' E | 12.5° | N 12°30'00" E | 192.5° |
due east | 90° | Due East | 270° |
Common mistakes
- Quadrant angle over 90°.
N 120° Eis not valid. The page rejects it and tells you why. - Wrong subtraction in the south quadrants. South-east is 180° minus the angle, south-west is 180° plus the angle. Mixing them up flips the direction.
- Forgetting the letters.
45alone is an azimuth of 45°. Add letters (N 45 E) if you mean a quadrant bearing. - Treating magnetic and true as the same. The converter changes the notation only. It does not apply declination.
What this converter does and does not do
- Notation only. It converts how a direction is written. It does not change reference north, so true, magnetic and grid bearings stay what they are.
- Azimuth range. Azimuths from 0 to 360 are accepted; 360 is treated as 0. Negative values are rejected.
- Runs in your browser. Nothing is sent to a server.
Related calculators
To compute a bearing from coordinates, use bearing between two points. For the length of the line use distance between coordinates. Traverses are covered in the bearing and distance guide.
Frequently asked questions
How do I convert a bearing to an azimuth?
For N α E the azimuth is α, for S α E it is 180° - α, for S α W it is 180° + α, and for N α W it is 360° - α. Or type the quadrant bearing and let the page do it.
How do I convert an azimuth to a quadrant bearing?
Find the quadrant from the azimuth: 0-90° is NE, 90-180° is SE, 180-270° is SW and 270-360° is NW. Then use the angle from north or south as in the rules table.
What is the difference between bearing and azimuth?
An azimuth is 0 to 360° clockwise from north. A quadrant bearing is an angle up to 90° from north or south toward east or west. In navigation, "bearing" often means azimuth.
What is a back azimuth?
The direction in the opposite sense: add 180° if the azimuth is below 180°, otherwise subtract 180°. The back bearing swaps N/S and E/W.
Can I enter degrees, minutes and seconds?
Yes. S 45°30'15" E, S 45 30 15 E and S 45-30-15 E are all read.
What does due east or due north mean here?
Due north is azimuth 0°, due east 90°, due south 180° and due west 270°. The converter reads these words and the single letters N, E, S and W.
Why was my quadrant bearing rejected?
Usually the angle exceeds 90°, the letters are in the wrong order (the first must be N or S and the last E or W) or a part could not be read as a number.
Does the converter handle magnetic declination?
No. It converts notation only. Apply declination separately if you are working from compass readings.
How is 360 degrees treated?
As 0°, due north. Values above 360 and negative values are rejected.
Can I convert a list at once?
Yes. Paste one entry per line into the batch box, click Convert list, then copy the results or download them as a CSV. Lines that cannot be read are flagged with the reason instead of being skipped silently.
Does it send my coordinates to a server?
No. The conversion runs in your browser, and once the page has loaded it needs no connection.
Related tools and guides
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Request a consultationLast updated 2026-10-15. Published by Sagarmekhla GIS Consultancy.