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XRTech Bearing–Azimuth
Input Bearing → Az
Accepts: N30E · N 30° 20' E · N45.5E · S45W
NE: Az = α  ·  SE: Az = 180° − α
SW: Az = 180° + α  ·  NW: Az = 360° − α
FORMAT
N S E W NE SE SW NW 0 90 180 270 144°
Result
Azimuth144°
DMS144° 00' 00.0"
Radians2.5133
Direction
BearingS 36° E
DMS BearingS 36° 00' 00.0" E
QuadrantSE
Reciprocal
Back Azimuth324°
Back BearingN 36° W
144°Azimuth
324°Back Az
SEQuadrant
0Saved
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Current Calculation
ModeBearing→Az
InputS 36° E
Angle (α)36°
QuadrantSE
All Formats
Decimal °144.0000°
DMS144° 00' 00.0"
Radians2.5133
Grad (gon)160.000
Compass Components
sin(Az)0.6947
cos(Az)−0.7193
Bearing → Azimuth
NE: Az = α
SE: Az = 180 − α
SW: Az = 180 + α
NW: Az = 360 − α
Azimuth → Bearing
0–90: N α° E
90–180: S (180−Az)° E
180–270: S (Az−180)° W
270–360: N (360−Az)° W
Back Azimuth
Back = (Az + 180) mod 360
Coordinates → Azimuth
Az = atan2(ΔE, ΔN) × 180/π
Note: surveying uses atan2(ΔE, ΔN) not atan2(ΔN, ΔE)
Magnetic Correction
True = Magnetic + Declination
East = + / West = −
xrtechgroup.com — Bearing & Azimuth Engineering Calculator Real-time · DMS · Batch · Export

Bearing to Azimuth Conversion — Complete Engineering Guide

Converting bearing to azimuth is a daily task for land surveyors, civil engineers, pilots, and GIS professionals. The bearing system uses four quadrant notations (NE, SE, SW, NW) with angles from 0° to 90°. Azimuth is a continuous 0° to 360° measurement clockwise from north. This free online bearing to azimuth calculator handles all formats, including DMS (degrees, minutes, seconds), decimal degrees, and radians, with a live rotating compass.

Bearing to Azimuth Formula

The conversion depends entirely on which quadrant the bearing falls in. Apply the correct formula using the angle within the quadrant (α, always 0° to 90°):

QuadrantBearing ExampleFormulaAzimuth Result
NEN 45° EAzimuth = α45°
SES 45° EAzimuth = 180° − α135°
SWS 45° WAzimuth = 180° + α225°
NWN 45° WAzimuth = 360° − α315°

All results are normalized to the 0°–360° range. Back azimuth is calculated automatically as (Azimuth + 180°) mod 360°.

How to Convert Bearing to Azimuth — Step by Step

Step 1: Read the quadrant from the bearing. "S 36° E" is the SE quadrant, angle = 36°.

Step 2: Apply the SE formula. Azimuth = 180° − 36° = 144°.

Step 3: Back azimuth = (144° + 180°) mod 360° = 324°.

The tool above accepts free-text bearing input in any common format: N30E, S 45° 30' W, N 45.5 E, or the manual DMS builder in the left panel.

Azimuth to Bearing Conversion

Surveyors often need the reverse: converting a total station or GPS azimuth back to quadrant bearing notation for use in legal property descriptions. Switch to the "Az → Bearing" tab and enter any azimuth from 0° to 360°. The tool outputs the full quadrant bearing in both decimal and DMS format. For example, 225.5° converts to S 45° 30' W.

Batch Bearing to Azimuth Converter

The Batch mode lets you paste a column of bearings — one per line — and converts all of them at once into a table showing azimuth, DMS, bearing, back azimuth, and radians. This is a major time saver for surveyors entering traverse data or GIS analysts processing boundary descriptions. Export the full table to CSV with one click.

Back Azimuth Calculator

The back azimuth is the reciprocal direction: add 180° to the forward azimuth and apply modulo 360°. A forward azimuth of 127.458° gives a back azimuth of 307.458°. Surveyors use back azimuths to verify traverse closure — if the computed back azimuth from the endpoint matches the measured back sight, the measurement is confirmed.

Magnetic Declination Correction

Compass instruments read magnetic bearings, which differ from true (geodetic) bearings by the magnetic declination at your location. The correction is: True Bearing = Magnetic Bearing + Declination. East declination is positive, west is negative. In Seattle, declination is approximately +15.5° East, so a compass reading of 90° gives a true bearing of 105.5°. This tool includes preset declination values and shows both needles on the compass — orange for magnetic, green for true.

Output Format Options

Switch between three output formats using the buttons in the left panel footer. Decimal Degrees (144.0000°) is standard for most software. DMS (144° 00' 00.0") matches traditional surveying documentation. Radians (2.5133) is needed for GIS calculations and trigonometry. Grad (gon) values are also shown in the Info tab, used in European surveying systems.

Who Uses Bearing and Azimuth Conversions?

Land surveyors convert azimuth output from total stations to quadrant bearing notation for property deed descriptions, which legally require the N/S format in most jurisdictions.

Civil engineers use azimuths for highway horizontal alignment, pipeline routing, and construction staking. Traverse calculations accumulate azimuth through each course.

Pilots apply magnetic declination to convert compass readings to true course before filing flight plans. A 15° error over a two-hour flight at 140 knots misses the destination by 72 nautical miles.

GIS analysts need radians and atan2-based azimuth from coordinate pairs for spatial analysis and feature orientation calculations.

Frequently Asked Questions

What is the difference between bearing and azimuth?
A bearing splits the compass into four 90° quadrants (NE, SE, SW, NW) and uses notation like "S 36° E." An azimuth is a continuous 0°–360° angle measured clockwise from north. Both describe the same direction. Azimuth is the standard in modern instruments. Bearing is still required for legal property descriptions in many countries.
How do I convert bearing to azimuth manually?
Identify the quadrant from the bearing notation, then apply: NE → Az = angle. SE → Az = 180° − angle. SW → Az = 180° + angle. NW → Az = 360° − angle. For "S 36° E" (SE, angle 36°): Az = 180° − 36° = 144°.
Why does coordinate-to-azimuth use atan2(ΔE, ΔN) not atan2(ΔN, ΔE)?
Standard mathematics measures angles counterclockwise from east (positive x-axis). Surveying measures azimuth clockwise from north. Swapping the arguments to atan2(ΔE, ΔN) correctly places 0° at north and 90° at east, matching the azimuth convention.
What is back azimuth and when is it used?
Back azimuth = (Forward Az + 180°) mod 360°. It represents the direction from your destination back to your starting point. Surveyors use it to close traverses and verify measurements. A forward azimuth of 127° gives a back azimuth of 307°.
How accurate do bearing measurements need to be?
Property surveys typically require 0.5°–5° precision. Control surveys may need 1 arc-second. Rough navigation accepts 5°–10°. This tool outputs results to four decimal places in decimal degrees and to 0.1 arc-second in DMS to match any precision requirement.

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