Initial Bearing Calculator
Calculate the initial compass bearing (forward azimuth) of the great-circle route between two coordinates.
How it works
θ = atan2( sin Δλ·cos φ₂ , cos φ₁·sin φ₂ − sin φ₁·cos φ₂·cos Δλ )
The initial bearing (or forward azimuth) is the compass direction you set out on to follow the shortest great-circle path. Because a great circle curves relative to the meridians, the bearing changes continuously along the route, so this is only the starting heading — a rhumb line, by contrast, keeps a constant bearing.
Worked example
From New York to London the formula gives θ = atan2(y, x) ≈ 51.2° after normalising to 0–360°, i.e. roughly north-east.
Sources: Bearing — Movable Type Scripts
Frequently asked questions
Why does the bearing change during the trip?
A great circle is the shortest path on a sphere but it crosses each meridian at a different angle, so the compass heading drifts. Long flights adjust heading continuously or in steps.
What is the difference from a rhumb line?
A rhumb line holds a single constant bearing and plots as a straight line on a Mercator map, but it is longer than the great circle. This calculator gives the great-circle initial bearing.
Is 0° north or east?
Bearings are measured clockwise from true north, so 0° is north, 90° is east, 180° is south and 270° is west.
Related calculators
Educational estimate. Uses a spherical-Earth model; results differ slightly from ellipsoidal (WGS84) calculations.