How to Use Azimuth / Bearing Calculator
The Azimuth Bearing Calculator finds the compass heading from any origin point to any destination on Earth.
- Enter the origin coordinates — Input the latitude and longitude of your starting location in decimal degrees.
- Enter the destination coordinates — Input the latitude and longitude of where you want to head toward.
- Read the bearing — The Azimuth Bearing Calculator instantly returns the standard azimuth (0°–360°), the quadrant bearing (e.g. N 45° E), and the 16-point compass direction.
Latitude values range from −90 to 90 (negative = South); longitude values range from −180 to 180 (negative = West).
Formula & Theory — Azimuth / Bearing Calculator
The Azimuth Bearing Calculator computes the initial forward bearing using spherical trigonometry:
y = sin(Δλ) · cos(φ2)
x = cos(φ1) · sin(φ2) − sin(φ1) · cos(φ2) · cos(Δλ)
θ = atan2(y, x)
bearing = (θ in degrees + 360) mod 360
| Symbol | Meaning |
|---|---|
| φ1, φ2 | Latitudes of origin and destination in radians |
| λ1, λ2 | Longitudes of origin and destination in radians |
| Δλ | λ2 − λ1 (longitude difference) |
| θ | Raw bearing in radians from atan2 |
| bearing | Final azimuth normalised to [0°, 360°) |
The Azimuth Bearing Calculator normalises the atan2 output so that North = 0°, East = 90°, South = 180°, and West = 270°, conforming to standard compass convention.
Quadrant Bearing Notation
The Azimuth Bearing Calculator also converts the decimal azimuth to quadrant notation. For example, a bearing of 45° is expressed as N 45° E, meaning 45° from North toward East. Quadrant notation is widely used in land surveying and traditional navigation.
Use Cases for Azimuth / Bearing Calculator
The Azimuth Bearing Calculator is valuable across many disciplines:
- Marine navigation — Set the correct heading before leaving port.
- Aviation — Compute initial track angle for flight planning.
- Hiking & orienteering — Determine the compass bearing to a summit or waypoint.
- Surveying — Establish reference bearings for boundary measurements.
- Astronomy — Find the direction to a celestial object rising or setting on the horizon.
- Telecommunications — Align directional antennas toward a tower or satellite.
Whenever you know two coordinates and need to know which direction to travel, the Azimuth Bearing Calculator provides an instant, precise answer in both modern and traditional formats.