Bearing Calculator
Find the direction from one point on Earth to another. Enter two latitude and longitude pairs to get the initial and final great-circle bearing, the compass point, the distance and a list of waypoints along the route.
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Decimal degrees (south negative) or D M S with N/S
Decimal degrees (west negative) or D M S with E/W
How to use the Bearing Calculator
- Enter point A, your starting position, as latitude and longitude. Use negative values for south and west, or type 40°38'29"N style values.
- Enter point B, the destination.
- Choose a distance unit: kilometers, miles or nautical miles.
- Press Calculate to see the initial bearing, the final bearing, the compass direction and the distance.
- Use the waypoint table to follow the great-circle route in steps, or download it as CSV.
Bearing formulas used
- Initial bearing: θ = atan2(sin Δλ · cos φ₂, cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ), normalized with (θ + 360) mod 360.
- Final bearing: compute the initial bearing from B to A and add 180°.
- Haversine distance: a = sin²(Δφ/2) + cos φ₁ · cos φ₂ · sin²(Δλ/2); c = 2 · atan2(√a, √(1 − a)); d = R · c with R = 6,371.0088 km.
- Rhumb line: Δψ = ln(tan(π/4 + φ₂/2) / tan(π/4 + φ₁/2)); bearing = atan2(Δλ, Δψ).
- Ellipsoid: Vincenty's inverse formula on WGS 84 (a = 6,378,137 m, f = 1/298.257223563), iterated to 10⁻¹² radians.
Example: from New York JFK (40.6413° N, 73.7781° W) to London Heathrow (51.4700° N, 0.4543° W) the initial bearing is about 51° (northeast), but the aircraft arrives heading about 108° (east-southeast). The great-circle distance is about 5,540 km, while a constant-heading rhumb line of 78° would be about 5,760 km.
Compass points and bearings
| Point | Name | Center bearing | Range |
|---|---|---|---|
| N | North | 0° | 348.75° - 11.25° |
| NNE | North-northeast | 22.5° | 11.25° - 33.75° |
| NE | Northeast | 45° | 33.75° - 56.25° |
| ENE | East-northeast | 67.5° | 56.25° - 78.75° |
| E | East | 90° | 78.75° - 101.25° |
| ESE | East-southeast | 112.5° | 101.25° - 123.75° |
| SE | Southeast | 135° | 123.75° - 146.25° |
| SSE | South-southeast | 157.5° | 146.25° - 168.75° |
| S | South | 180° | 168.75° - 191.25° |
| SSW | South-southwest | 202.5° | 191.25° - 213.75° |
| SW | Southwest | 225° | 213.75° - 236.25° |
| WSW | West-southwest | 247.5° | 236.25° - 258.75° |
| W | West | 270° | 258.75° - 281.25° |
| WNW | West-northwest | 292.5° | 281.25° - 303.75° |
| NW | Northwest | 315° | 303.75° - 326.25° |
| NNW | North-northwest | 337.5° | 326.25° - 348.75° |
Tips
- Surveyor (quadrant) bearings such as N 51.35° E start from north or south and turn toward east or west. The calculator shows both styles.
- For short distances (a few kilometers) the great-circle and rhumb line bearings are practically identical, so a single compass heading works.
- Crossing the antimeridian (180° longitude) is handled automatically: the route always takes the shorter way around.
- Get coordinates from a map app by long-pressing a location, or from your phone's GPS with the GPS Coordinates tool.
Frequently asked questions
How do you calculate the bearing between two points?
The initial bearing from point A to point B on a sphere is θ = atan2(sin Δλ · cos φ₂, cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ), where φ is latitude, λ is longitude and Δλ is the difference in longitude. The result is converted to degrees and normalized to 0-360° measured clockwise from true north.
What is the difference between initial and final bearing?
A great circle, the shortest route on a sphere, crosses each meridian at a different angle. The initial bearing is the heading you start on at point A; the final bearing is the heading you are on when you arrive at point B. They are only equal when you travel along a meridian or the equator.
What is a rhumb line?
A rhumb line (loxodrome) is a path that keeps the same compass bearing the whole way. It is easier to steer and appears as a straight line on a Mercator map, but it is longer than the great-circle route, sometimes by several percent on long east-west trips.
Is the bearing true or magnetic?
The calculator gives true bearings, measured from geographic north. To follow one with a magnetic compass, adjust for the local magnetic declination: subtract east declination or add west declination. The Magnetic Declination Calculator gives the value for your location.
What is a back bearing?
The back bearing (reciprocal bearing) points from B back toward A at the start of the line. It is the bearing plus 180°, wrapped to 0-360°. For example the back bearing of 51° is 231°.
How accurate is the distance?
The great-circle distance uses a spherical Earth with the mean radius of 6,371 km, which is accurate to about 0.5%. The ellipsoidal value uses Vincenty's formula on the WGS 84 ellipsoid, accurate to within millimeters for most point pairs.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.