Azimuth Calculator
Calculate the forward azimuth and back azimuth between any two coordinates. Enter Point A and Point B to get the bearing angle (0–360° from North), compass direction, and great-circle distance. Built for surveyors, pilots, drone operators, and GIS professionals.
Enter coordinates for Point A and Point B above, then click Calculate Azimuth.
Or use a city-pair preset to see an example result instantly.
How Azimuth Is Measured
The diagram below shows how forward azimuth is the clockwise angle from North at Point A to the direction of Point B, and how the back azimuth is exactly 180° different.
What Is an Azimuth Angle?
An azimuth is a horizontal angle measured clockwise from true North (0°) to the direction of a target or destination. It is expressed as a single number between 0° and 360°: due East is 90°, due South is 180°, and due West is 270°. A full circle returns to 360°, which is identical to 0° (North).
Azimuth is the standard unit of direction in geodesy, navigation, astronomy, and military operations because it avoids the ambiguity of compass-quadrant notation. Instead of saying "South-Southwest", a surveyor writes "202.5°" — a single unambiguous value. Pilots file flight plans with magnetic azimuth headings; artillery crews use grid azimuth to aim. GIS software stores bearing as azimuth because it converts directly to trigonometry without extra parsing.
This calculator computes geodetic azimuth — the true bearing at Point A along the great-circle arc to Point B on the WGS84 ellipsoid. For short distances (under ~10 km) geodetic azimuth and plane azimuth are nearly identical. For intercontinental routes the difference can be several degrees.
How to Calculate Azimuth from Latitude and Longitude
The standard formula uses atan2 applied to the east and north components of the displacement vector between two points on a sphere. All angles are converted to radians first.
// Convert inputs to radians
φ1 = lat1 × π / 180
φ2 = lat2 × π / 180
Δλ = (lng2 − lng1) × π / 180
// East and north components
x = sin(Δλ) × cos(φ2)
y = cos(φ1) × sin(φ2) − sin(φ1) × cos(φ2) × cos(Δλ)
// Azimuth, normalised to [0°, 360°)
θ = atan2(x, y)
azimuth = (θ × 180/π + 360) mod 360
Note the argument order: atan2(x, y) where x is the east component and y is the north component. This is opposite to the standard mathematical convention of atan2(y, x). Using the wrong order rotates every azimuth by 90° and produces incorrect results.
The back azimuth (the bearing from Point B back to Point A) is simply the forward azimuth plus 180°, wrapped into the [0°, 360°) range:
Forward Azimuth vs Back Azimuth — What Is the Difference?
The forward azimuth is the initial bearing at Point A looking toward Point B. The back azimuth is the initial bearing at Point B looking back toward Point A. They differ by exactly 180° because looking from one end of a straight path gives the opposite direction of looking from the other end.
Both values are essential in field work. A surveyor measuring a traverse leg records the forward azimuth to set the instrument, then checks the back azimuth from the next station to verify closure. A hiker following an azimuth of 127° (SE) should expect to return on a bearing of 307° (NW). Emergency services navigating to a caller's coordinate use the forward azimuth to reach the location and the back azimuth to communicate an exit route.
| Property | Forward Azimuth | Back Azimuth |
|---|---|---|
| Definition | Bearing at A toward B | Bearing at B toward A |
| Formula | atan2(x, y), normalised | (forward + 180) mod 360 |
| Use case | Navigate to destination | Return to origin, closure check |
| Example | 127.57° (SE) | 307.57° (NW) |
Azimuth vs Bearing — Are They the Same Thing?
Both "azimuth" and "bearing" describe horizontal direction, but the notation differs by discipline. Azimuth is always a single number from 0° to 360° measured clockwise from North. Quadrant bearing (used in land surveying) is expressed as an angle from 0° to 90° within a named quadrant: "N 52° 26′ E" or "S 37° 34′ W".
To convert quadrant bearing to azimuth: NE quadrant → bearing as-is; SE quadrant → 180° minus bearing; SW quadrant → 180° plus bearing; NW quadrant → 360° minus bearing. Azimuth is used in GIS, navigation, and astronomy. Quadrant bearing is common in COGO (coordinate geometry) and traditional land survey plats. This calculator always outputs azimuth (0°–360°), which is directly usable in software tools like QGIS, ArcGIS, and flight-planning applications.
| Quadrant Bearing | Azimuth Equivalent | Compass Direction |
|---|---|---|
| N 45° E | 45.00° | Northeast (NE) |
| S 45° E | 135.00° | Southeast (SE) |
| S 45° W | 225.00° | Southwest (SW) |
| N 45° W | 315.00° | Northwest (NW) |
| N 30° E | 30.00° | NNE–NE range |
| S 60° W | 240.00° | WSW |
Real-World Uses of Azimuth Calculations
Land Surveying
Traverse closure checks, property boundary bearings, and COGO point location all rely on azimuth. The forward azimuth from a control point sets the total station orientation; the back azimuth verifies it.
Aviation & Maritime
Pilots file flight-plan magnetic headings derived from true azimuth corrected for declination. Ships plot courses as compass bearings. Both use azimuth as the base calculation before applying variation.
Drone Operations
UAV operators flying beyond-visual-line-of-sight missions use azimuth to plan corridors and set waypoint headings. Ground control stations display azimuth to the home point for return-to-home verification.
GIS & Spatial Analysis
Tools like QGIS and ArcGIS accept azimuth directly in "bearing" or "direction" fields. Line feature orientation, viewshed analysis, and aspect calculations all express direction as azimuth values between 0° and 360°.
Emergency Services
Search and rescue teams record a caller's GPS coordinate and use the azimuth from the nearest road to plan approach corridors. Helicopter crews calculate the bearing from base to scene to set the autopilot heading.
Astronomy
The solar azimuth (bearing to the Sun) is used to orient solar panels, plan building shading analysis, and determine sunrise/sunset compass positions. Our Solar Angle Calculator uses the same azimuth convention.
16-Point Compass Reference
The 360° circle is divided into 16 sectors of 22.5° each. Each sector maps to a compass point abbreviation and full name.
| Abbrev | Full Name | Azimuth Range (°) |
|---|---|---|
| N | North | 348.75 – 11.25 |
| NNE | North-Northeast | 11.25 – 33.75 |
| NE | Northeast | 33.75 – 56.25 |
| ENE | East-Northeast | 56.25 – 78.75 |
| E | East | 78.75 – 101.25 |
| ESE | East-Southeast | 101.25 – 123.75 |
| SE | Southeast | 123.75 – 146.25 |
| SSE | South-Southeast | 146.25 – 168.75 |
| S | South | 168.75 – 191.25 |
| SSW | South-Southwest | 191.25 – 213.75 |
| SW | Southwest | 213.75 – 236.25 |
| WSW | West-Southwest | 236.25 – 258.75 |
| W | West | 258.75 – 281.25 |
| WNW | West-Northwest | 281.25 – 303.75 |
| NW | Northwest | 303.75 – 326.25 |
| NNW | North-Northwest | 326.25 – 348.75 |
Frequently Asked Questions
What is the difference between azimuth and bearing?
Azimuth is always a single clockwise angle from 0° to 360° measured from North. Bearing (or "quadrant bearing") in traditional land surveying is an angle from 0° to 90° within a named quadrant — for example "N 52° E" or "S 37° W". Both describe the same direction using different notation. GIS software and navigation instruments universally use azimuth because it avoids the extra parsing step.
How do I calculate azimuth from latitude and longitude?
Convert both coordinates to radians. Compute x = sin(Δlon) × cos(lat2) and y = cos(lat1) × sin(lat2) − sin(lat1) × cos(lat2) × cos(Δlon). Then azimuth = atan2(x, y) in radians, converted to degrees and normalised to [0°, 360°) by adding 360° if negative. This formula is accurate on a spherical Earth; for the WGS84 ellipsoid the difference is under 0.3° even for intercontinental distances.
What does a 270° azimuth mean?
270° points due West. The four cardinal azimuths are: 0° (North), 90° (East), 180° (South), 270° (West). An azimuth of 270° means you are heading directly toward the setting sun. The back azimuth from 270° is 90°, meaning East.
What is back azimuth and when do I use it?
The back azimuth is the bearing from Point B back to Point A — always 180° different from the forward azimuth. It is used in surveying traverse closure (checking that the return leg closes the loop), in field navigation to retrace a route, and in antenna alignment where you need to point equipment back toward a transmitter. for example, if the forward azimuth from your camp to the summit is 047° (NE), the back azimuth to return is 227° (SW).
How accurate is the atan2 azimuth formula?
The spherical atan2 formula gives the initial bearing on a perfect sphere of radius 6,371 km. Compared to the rigorous Vincenty formula on the WGS84 ellipsoid, the error is typically under 0.1° for distances under 1,000 km and under 0.3° for intercontinental distances near the equator. Near the poles the spherical formula degrades, but for the vast majority of practical navigation and GIS use cases the difference is negligible.
What is true north vs magnetic north in azimuth calculations?
This calculator computes true azimuth — the bearing relative to geographic North Pole. Compass needles point to magnetic north, which differs from true north by the magnetic declination (also called magnetic variation). To convert a true azimuth to a magnetic compass heading, subtract the declination (if East declination) or add it (if West declination). Use our Magnetic Declination Calculator to find the declination for any coordinate.
Related Calculators
Distance & Bearing Calculator
Forward bearing + Haversine distance between two points
Haversine Distance Calculator
Great-circle distance between two WGS84 coordinates
Solar Angle Calculator
Compute solar azimuth and altitude for any date and location
Magnetic Declination Calculator
True north vs magnetic north offset for any coordinate
Coordinate Converter
Convert between decimal degrees, DMS, MGRS, and UTM