Case 1
- Start latitude
- 52.52°
- Start longitude
- 13.405°
- End latitude
- 48.1351°
- End longitude
- 11.582°
195.57°
Open with these valuesInitial Bearing Calculator
195.57°
Result: 195.57 °Enter two pairs of decimal degrees and read the direction you would set off in, measured clockwise from true North. Berlin to Munich is 195.57°, just west of due south. It is the INITIAL bearing: along a great circle the direction keeps turning, so you arrive on a different one.
The numbers at a glance
Held fixed: Start latitude 52.5200 °, Start longitude 13.4050 °, End latitude 48.1351 °.
| End longitude (°) | Result (°) |
|---|---|
| 0.0000 | 248.15 |
| 5.0000 | 234.04 |
| 10.0000 | 207.69 |
| 11.5820Your value | 195.57 |
| 15.0000 | 166.31 |
| 20.0000 | 133.58 |
Worked examples
Case 2
- Start latitude
- 51.5074°
- Start longitude
- -0.1278°
- End latitude
- 48.8566°
- End longitude
- 2.3522°
148.12°
Open with these valuesCase 3
- Start latitude
- -33.8688°
- Start longitude
- 151.2093°
- End latitude
- 35.6762°
- End longitude
- 139.6503°
350.05°
Open with these valuesHow it's calculated
bearing = atan2(sin Δλ · cos φ₂, cos φ₁·sin φ₂ − sin φ₁·cos φ₂·cos Δλ)
- StepEnter the coordinates you start from, in decimal degrees.
- StepEnter the coordinates you are aiming at; south and west are negative.
- ResultRead the bearing: 0° is North, 90° East, 180° South, 270° West.
Reference table
| Start lat, lon — end lat, lon | Direction | Bearing |
|---|---|---|
| 0, 0, 10, 0 | Straight up the meridian | 0 |
| 0, 0, 0, 10 | Due east along the equator | 90 |
| 51.5074, -0.1278, 48.8566, 2.3522 | London → Paris | 148.12 |
| 52.52, 13.405, 48.1351, 11.582 | Berlin → Munich | 195.57 |
| 0, 0, 0, -10 | Due west along the equator | 270 |
| 40.7128, -74.006, 34.0522, -118.2437 | New York → Los Angeles | 273.69 |
| -33.8688, 151.2093, 35.6762, 139.6503 | Sydney → Tokyo | 350.05 |
Questions
What is the initial bearing between two points?
It is the forward azimuth: the compass direction from the start point at the very beginning of the shortest great-circle path, measured clockwise from true North. Berlin to Munich comes out at about 195.57°.
Why is it called the initial bearing?
Along a great circle the compass direction changes continuously, so the bearing you set off on differs from the one you arrive on. The effect is tiny over short hops and large over intercontinental ones — which is why long flights look curved on a flat map.
How do I read the bearing as a compass direction?
Bearings run clockwise from North: 0° or 360° is North, 90° East, 180° South, 270° West. In between, 45° is northeast, 135° southeast, 225° southwest and 315° northwest. A bearing of 195.57° is just west of due south.
Is this true North or magnetic North?
True, geographic North. A magnetic compass points to magnetic North, which differs by the local declination. To steer by a handheld compass, look up the declination where you are and adjust the bearing accordingly.
Can I use negative latitudes and longitudes?
Yes. Latitude runs from −90 to +90 with south negative, longitude from −180 to +180 with west negative, and zero marks the equator and the prime meridian. The atan2 form picks the correct compass quadrant in every hemisphere.
Sources and last check
Information, not professional advice.