Quadrant Bearing & Azimuth Converter
Convert surveyor-style quadrant bearings (e.g. N45°30'15"E) to azimuths and back. Paste one bearing per line for batch conversion of an entire traverse — perfect for converting plat descriptions, field notes, and textbook problems.
Results will appear here as you type.
Accepted input formats
N45°30'15"E — DMS with symbolsN 45 30 15 E — DMS with spacesN45-30-15 E — DMS with hyphensN45°30'E — degrees and minutesN45°E or N45.5°E — decimal045 30 15 — azimuth in DMSQuick conversion reference
Cardinal directions and 45° diagonals — useful as a sanity check while you work through a traverse.
| Quadrant bearing | Azimuth | Notes |
|---|---|---|
| N (Due North) | 000°00'00" | Cardinal |
| N45°00'00"E | 045°00'00" | NE diagonal |
| E (Due East) | 090°00'00" | Cardinal |
| S45°00'00"E | 135°00'00" | SE diagonal |
| S (Due South) | 180°00'00" | Cardinal |
| S45°00'00"W | 225°00'00" | SW diagonal |
| W (Due West) | 270°00'00" | Cardinal |
| N45°00'00"W | 315°00'00" | NW diagonal |
Worked traverse example
A four-leg closed traverse expressed in quadrant bearings, paired with the azimuth values the tool produces. Paste the left-hand column into the converter to verify.
| Leg | Quadrant bearing | Azimuth (DMS) |
|---|---|---|
| AB | N45°30'15"E | 045°30'15.00" |
| BC | S22°15'00"W | 202°15'00.00" |
| CD | S88°15'30"W | 268°15'30.00" |
| DA | N15°00'00"W | 345°00'00.00" |
Common use cases
Plat and deed description input
US land surveying records express boundary lines as quadrant bearings (N45°30'E, S22°15'W). Paste a metes-and-bounds description and get the azimuths to enter into GIS or CAD.
Total station / GPS data preparation
Total stations and field controllers usually accept azimuth inputs. Convert legacy bearing field notes into azimuths before loading them into the instrument.
Civil engineering coursework
Surveying textbook problems give traverse legs as quadrant bearings and ask for azimuths (or vice versa) before computing latitudes/departures. Batch paste the problem set; check your work in seconds.
Boundary mapping in QGIS / ArcGIS
QGIS and ArcGIS expect bearings in azimuth (0–360°) when constructing lines from a length+direction list. Convert the deed bearings first to avoid quadrant-conversion errors.
COGO inputs
Coordinate geometry (COGO) routines in AutoCAD Civil 3D, Carlson, and TBC accept either format, but consistent azimuth input avoids quadrant entry mistakes. Batch-prep the whole traverse first.
Traverse closure verification
When recomputing a historical traverse, convert all legs to azimuth, sum the interior angles, and check closure. The batch mode lets you handle dozens of legs in one paste.
Conversion formulas
For completeness — the tool applies these automatically, but the underlying math is straightforward:
Where {d} is the interior angle expressed in decimal degrees (degrees + minutes/60 + seconds/3600). Azimuth values returned by the tool are always in the range [0°, 360°).
Frequently asked questions
How do I convert a bearing like N45°30'15"E to azimuth?
Paste the bearing into the input box above and the azimuth is computed instantly. The math: for N{d}E the azimuth equals d, for S{d}E it equals 180 − d, for S{d}W it equals 180 + d, and for N{d}W it equals 360 − d. The tool handles the conversion plus DMS arithmetic for you.
Can I convert a whole traverse at once?
Yes. Paste one bearing per line — the tool processes each line independently and gives you a column of azimuths. Works for traverse closures, plat descriptions, field-book exports, or textbook problem sets where you need to convert a list of bearings.
What input formats are accepted?
DMS with symbols (N45°30'15"E), DMS with spaces (N 45 30 15 E), DMS with hyphens (N45-30-15 E), degrees + minutes only (N45°30'E), decimal degrees (N45.5°E), and azimuths in either decimal (045.5) or DMS (045°30'15"). Case is ignored and whitespace is tolerant.
How do I convert an azimuth back to a quadrant bearing?
Switch to the "Azimuth → Quadrant bearing" tab and paste your azimuth values. The tool returns bearings in the same N{D}°{M}'{S}"E quadrant format used on plats and deeds. You can also click the Swap direction button to flip the current input/output.
Why are quadrant bearings still used if azimuths are simpler?
Quadrant bearings are the traditional notation in US land surveying, deed descriptions, and plat documents — anything that traces back to a metes-and-bounds legal description will be in quadrant form. GIS systems, total stations, and modern survey software almost always use azimuth internally, so converting between the two is a routine task.
Does this tool handle DMS arithmetic correctly?
Yes. Degrees, minutes, and seconds are aggregated into decimal degrees with full precision before the quadrant conversion, then converted back to DMS for display. Rounding edge cases (such as 59.999...") are handled so the output always has minutes < 60 and seconds < 60.
What is the difference between this and the regular bearing/azimuth converter?
The regular bearing/azimuth converter at /bearing-azimuth-converter handles the modern −180 to 180 signed bearing convention used by some APIs and navigation tools, one pair at a time. This page is for surveyor-style quadrant bearings (N/S + degrees + E/W) and supports batch traverse conversion — the format you encounter in deeds, plats, traverse field notes, and most US land-surveying coursework.
Is my data uploaded to a server?
No. All parsing and conversion happens entirely in your browser using client-side JavaScript. Nothing is sent to any server — safe to use for confidential survey data or proprietary plat descriptions.