Azimuth Calculator
Enter starting and ending coordinates in decimal degrees to get the precise great-circle distance, forward azimuth, and back azimuth between both points. The calculator defaults to U.S. customary units and uses the WGS84 ellipsoid for professional-grade accuracy.
Check your inputs
Please enter valid latitude and longitude values.
Starting point
Latitudes must be between −90° and 90°.
Positive latitudes are north of the equator. Use a minus sign for southern hemisphere coordinates.
Longitudes must be between −180° and 180°.
Positive longitudes are east of Greenwich. Use a minus sign for locations in the western hemisphere.
Final point
Latitudes must be between −90° and 90°.
Latitudes south of the equator are negative. Example: Sydney, Australia ≈ −33.8688°.
Longitudes must be between −180° and 180°.
Longitudes east of Greenwich are positive. Example: Cairo, Egypt ≈ 31.2357°.
Results
No calculation yet
Enter two coordinate pairs to see azimuth and distance instantly.
What is azimuth?
Azimuth is the clockwise angle between true north and the direction from your starting point to your destination, measured along Earth’s surface. Surveyors, aviators, sailors, and hikers rely on azimuths to align maps with real-world directions. Because azimuths always reference true north (0°), a value of 90° points east, 180° points south, and 270° points west. Bearings such as 230.96° mean you should travel southwest with a slight southerly emphasis.
Our calculator pairs azimuth with great-circle distance—the shortest path over the Earth’s curvature. That path follows a geodesic, so the numbers stay accurate even over intercontinental ranges. For routine fieldwork or long-haul route planning, having both distance and azimuth prevents cumulative drift that appears when you approximate Earth as a flat plane.
The tool accepts decimal degrees because they are the standard output from GPS devices and GIS software. If you have degrees/minutes/seconds (DMS), simply convert them to decimals or use four decimal places to capture street-level precision.
How the azimuth calculator works
This calculator uses the Vincenty inverse solution on the WGS84 ellipsoid, the same mathematical model used by GPS and modern aerial charts. Vincenty’s method iteratively solves the shape of the geodesic between two latitude/longitude pairs, returning both the great-circle distance and the forward/back azimuths. It is accurate to 0.5 millimeters for most pairs of points.
We also display the well-known Haversine formulation for educational context. The Haversine equation estimates the central angle between two points on a sphere:
Haversine distance
a = sin²(Δφ / 2) + cos φ₁ · cos φ₂ · sin²(Δλ / 2)
d = 2R · atan2(√a, √(1 − a))
φ = latitude in radians, λ = longitude in radians, R ≈ 6 371 km
The forward azimuth (initial bearing) uses the spherical formula, consistent with navigational textbooks and the screenshot provided:
Forward azimuth
θ = atan2( sin Δλ · cos φ₂, cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ )
The result is normalized to 0° – 360°.
If Vincenty fails to converge (a rare case near antipodal points), the calculator gracefully falls back to the Haversine estimate and applies the spherical azimuth equations so you always receive a trustworthy answer.
Navigation tips for accurate bearings
- • Use at least four decimal places: Coordinates rounded to 0.0001° are accurate to roughly 11 meters (36 feet).
- • Confirm your datum: GPS receivers default to WGS84. If you are using NAD27 or other datums, convert them first to avoid offset errors.
- • Check for identical points: The azimuth is undefined when both locations are the same—our validator alerts you before calculating.
- • Account for local declination: Magnetic compasses measure magnetic north; convert using NOAA’s declination if you are aligning the azimuth to a compass bearing.
- • Combine with elevation data: When topography matters, pair this azimuth with elevation profiles or DEM data for a full 3D picture.
These habits keep your routes consistent whether you are plotting a cross-country flight path, designing a solar array, or simply planning a long-distance hike with accurate direction cues.
Distance and azimuth use cases
Field & Survey Work
Survey crews stake out property lines, utility easements, or remote infrastructure using forward and back azimuths to stay aligned with legal descriptions.
Shared azimuths let separated teams verify they are working on the same alignment even miles apart.
Outdoor Navigation
Backcountry hikers translate GPS coordinates into compass legs, reducing detours in dense forests or open desert terrain.
Sailors and aviators plan great-circle routes to save fuel, especially on transoceanic travel.
Engineering & Renewable Energy
Solar array orientation, microwave link planning, and wind farm layouts all rely on precise bearings to maximize performance.
Combining azimuth with distance ensures that support structures and transmitters stay aligned over long spans.
Frequently asked questions
What is the difference between azimuth and bearing?
An azimuth is always measured clockwise from true north and spans 0° to 360°. A bearing can be expressed as a quadrant value (for example, S 50° W) or as an azimuth. Our calculator outputs azimuths and also provides the compass quadrant description so you can record the direction in either style.
How accurate is the distance calculation?
We use the Vincenty inverse method on the WGS84 ellipsoid, the same approach recommended by NOAA, NGS, and ICAO. Accuracy is typically better than 0.5 millimeters. If Vincenty cannot converge (extremely rare near exact antipodes), we fall back to the Haversine solution and clearly note it.
Can I enter degrees, minutes, and seconds (DMS)?
The inputs expect decimal degrees. To convert from DMS, divide minutes by 60 and seconds by 3600, then add them to the degrees. Example: 40° 26′ 46″ N becomes 40 + 26/60 + 46/3600 ≈ 40.4461°.
What is the back azimuth?
The back azimuth is the direction from Point B back to Point A. It is 180° opposite the forward azimuth when traveling the same great-circle path. Surveyors use the back azimuth to verify that traverses close accurately.
Why does the azimuth change along a great-circle route?
On a sphere or ellipsoid, a great-circle path curves relative to lines of longitude. The initial azimuth is your starting direction, but the bearing gradually shifts as you progress. Airlines continuously adjust heading to stay on the shortest path.
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