What this calculator does
Azimuth is the compass bearing from an observer to a target, measured in degrees clockwise from true north, running from 0 up to 360. Given the latitude and longitude of two points, this azimuth calculator works out the direction you would need to face at the first point to look directly at the second, using the standard great-circle bearing formula from navigation and surveying.
Azimuth is not the same as a straight line drawn on a flat map, because the Earth is a sphere and lines of longitude converge towards the poles. The formula below accounts for that curvature, which is why the bearing from London to Paris, for example, is not simply "read the angle off a rectangular map". It also returns the back azimuth, the bearing you would face for the return trip, which is not just the forward bearing plus or minus 180 degrees on a curved path in general, though the difference is small over short distances.
The formula
Convert both latitudes and longitudes to radians, then use atan2 with the difference in longitude and both latitudes to get the initial bearing in radians. Converting that back to degrees and adding 360 before taking the remainder puts the result in the standard 0 to 360 degree compass range. The back azimuth, the bearing from the target back to the observer, is the forward azimuth plus 180 degrees, wrapped the same way.
| Term | Meaning |
|---|---|
| Azimuth | The compass bearing from the observer to the target, in degrees clockwise from true north (0 to 360). |
| Latitude / longitude | The coordinates of each point in decimal degrees, positive for north/east, negative for south/west. |
| Back azimuth | The bearing from the target back to the observer, roughly the forward azimuth plus or minus 180 degrees. |
The inputs explained
| Field | What to enter |
|---|---|
| Observer latitude | The observer's latitude in decimal degrees, negative for the southern hemisphere. |
| Observer longitude | The observer's longitude in decimal degrees, negative for west of the Greenwich meridian. |
| Target latitude | The target's latitude in decimal degrees. |
| Target longitude | The target's longitude in decimal degrees. |
When to use it
Orienteering and land navigation
Given the coordinates of a known point and a destination, the azimuth is the compass bearing to walk, before accounting for magnetic declination at that location.
Aiming an antenna or telescope
Satellite dishes and some telescope mounts need a horizontal bearing to point at, worked out from the coordinates of the observer and the target or satellite's ground position.
Checking a flight or shipping heading
The initial great-circle bearing between two airports or ports gives the compass heading a straight-line route would start on, before wind, air traffic corridors or shipping lanes adjust it.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Azimuth from London to several European cities
The bearing from London to a range of target cities at increasing distance and direction.
| Target latitude | Azimuth to target | Compass direction |
|---|---|---|
| 48.8566 | 148.1° | SSE |
| 41.9028 | 169.0° | S |
| 52.5200 | 55.5° | NE |
| 55.7558 | 18.1° | NNE |
| 40.4168 | 170.3° | S |
Azimuth and back azimuth between two fixed points
A single pair of points, showing the forward and back bearings side by side.
| Observer latitude (unchanged) | Azimuth to target | Back azimuth (target to observer) |
|---|---|---|
| -33.8688 | 230.3° | 50.3° |
Questions
What is azimuth measured from?
True north, not magnetic north, moving clockwise so that east is 90 degrees, south is 180 and west is 270. A magnetic compass reading needs the local magnetic declination applied to match this figure.
Why is the azimuth not just the reverse of the back azimuth minus 180?
Because the shortest path between two points on a sphere is a curved great-circle arc, not a straight line, the bearing measured at each end of that arc differs from a simple 180-degree flip, except along the equator or between points on the same meridian.
Can azimuth be negative or above 360 degrees?
Not as returned here. The formula is wrapped to always fall between 0 and 360 degrees, which is the standard convention for compass bearings.
Does this calculator account for elevation or altitude?
No, it works purely from latitude and longitude, giving the horizontal (ground-plane) bearing. Astronomical or satellite-pointing azimuth calculations that also need elevation angle require the height of the target as well as its position.
For the same two points expressed in degrees-minutes-seconds format instead of decimal degrees, see the degrees, minutes, seconds converter, or the distance formula calculator for straight-line distance.