Azimuth Calculator — Bearing Between Two Points
Enter the latitude and longitude of two locations to get the azimuth (clockwise bearing from true North) from the first point to the second, plus the back-bearing and great-circle distance.
°
°
°
°
NNW — measured clockwise from true North
- 1
Longitude difference
-0.1278° − 2.3522° = -2.48° - 2
x component
sin(-2.48°) × cos(51.5074°) = -0.026932East-facing component of the bearing vector. - 3
y component
cos(48.8566°) × sin(51.5074°) − sin(48.8566°) × cos(51.5074°) × cos(-2.48°) = 0.046688 - 4
Raw angle θ
atan2(-0.026932, 0.046688) = -29.9789°atan2 result converted from radians to degrees. - 5
Azimuth
(-29.9789 + 360) mod 360 = 330.02
How does this calculator work?
Azimuth = (atan2(sin(Δλ)·cos(φ₂), cos(φ₁)·sin(φ₂) − sin(φ₁)·cos(φ₂)·cos(Δλ)) + 360°) mod 360°. Enter the latitude and longitude of two points (decimal degrees) to get the compass bearing from the first to the second, the back-bearing, and the great-circle distance.
Formula
How this is calculated
Azimuth is the horizontal angle measured clockwise from true North to the direction of a target — 0° is North, 90° East, 180° South, 270° West. Given two points on the Earth's surface described by latitude (φ) and longitude (λ), the initial bearing is computed using the forward-azimuth formula of spherical trigonometry: the angle θ = atan2(sin(Δλ)·cos(φ₂), cos(φ₁)·sin(φ₂) − sin(φ₁)·cos(φ₂)·cos(Δλ)), then normalised to 0–360° by adding 360° and taking the remainder.
This gives the bearing at the origin point — the direction you would face at the start to head toward the destination along the shortest path (a great circle). Because a great circle curves relative to the compass, the instantaneous bearing changes continuously along the route. The back-bearing (azimuth + 180°) is the direction from the destination back to the origin.
The great-circle distance is computed separately using the haversine formula, which gives the shortest surface distance between the two points on a spherical Earth (radius ≈ 6371 km). The result is accurate to within about 0.5% compared to the actual WGS-84 ellipsoid — sufficient for most navigation, mapping and surveying purposes.
Frequently asked questions
They are the same concept: both measure the horizontal angle clockwise from North (0–360°). "Azimuth" is the preferred term in astronomy, surveying and military contexts; "compass bearing" or just "bearing" is more common in marine and general navigation. This calculator returns the true (geodetic) bearing, not the magnetic bearing, which differs by the local magnetic declination.
On a spherical Earth, the shortest path between two points is a great circle, which curves relative to lines of constant latitude. If you fly from London to New York on a great circle, you start heading roughly NW but end up heading SW — the bearing shifts continuously. The value this calculator gives is the initial bearing at the origin only.
Degrees = integer part. Minutes = (decimal part) × 60; take the integer part. Seconds = (remainder) × 60. For example, 48.8566° N = 48° 51' 23.76" N. Many GPS and mapping apps accept either format — decimal degrees are simpler for calculation.
Also known as
TG we-Calculate Editorial Team. (2026). Azimuth Calculator — Bearing Between Two Points [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/azimuth-calculator
TG we-Calculate Editorial Team. "Azimuth Calculator — Bearing Between Two Points." TG we-Calculate. 2026. https://we-calculate.com/calculator/azimuth-calculator.
TG we-Calculate Editorial Team, "Azimuth Calculator — Bearing Between Two Points," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/azimuth-calculator
@misc{wecalculate_azimuth_calculator, title = {Azimuth Calculator — Bearing Between Two Points}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/azimuth-calculator}}, year = {2026}, note = {TG we-Calculate} }
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