Bearing calculator
Which way to point: the initial and final great-circle bearing between two places, and the single constant heading of the rhumb line.
40.7494°, -73.9819° · America/New York
48.8667°, 2.3333° · Europe/Paris
Initial bearingFinal bearingRhumb line
How bearing is calculated
The initial great-circle bearing θ from point 1 to point 2 is
θ = atan2( sin Δλ · cos φ₂ , cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ )
normalised to 0–360°. The final bearing is the reverse bearing from point 2 back to point 1, plus 180°. The rhumb-line heading uses the Mercator “stretched latitude” ψ = ln tan(π/4 + φ/2), so that the heading is simply atan2(Δλ, Δψ).
New York to Paris starts out at about 54° (north-east) and arrives at about 112° (east-south-east), while the constant rhumb heading is about 81°.
Compass points in degrees
| Point | Degrees | Point | Degrees |
|---|---|---|---|
| N | 0° | S | 180° |
| NE | 45° | SW | 225° |
| E | 90° | W | 270° |
| SE | 135° | NW | 315° |
Frequently asked questions
What is the bearing between two points?
The compass direction from the first point to the second, measured clockwise from true north in degrees (0° = north, 90° = east, 180° = south, 270° = west).
Why are the initial and final bearings different?
Along a great circle the direction relative to north keeps changing because meridians converge at the poles. Only routes along the equator or straight north–south keep the same bearing throughout.
What is the difference between true and magnetic bearing?
True bearing is measured from geographic north, which is what this calculator returns. A magnetic compass points to magnetic north; the angle between them (magnetic declination) varies by place and year, from 0° to more than 20°. Look up local declination from NOAA’s World Magnetic Model before using a hand compass.
What is a rhumb line bearing?
The single constant heading that gets you from A to B if you never change course. It is easier to steer but the path is longer than the great circle.