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Compass Bearing Calculator

Computes the initial (forward) and final bearing of the great-circle route between two latitude/longitude points, the back bearing for the return trip, the matching 16-point compass directions and the distance.

When to use

You need the heading from one coordinate to another for navigation, antenna or solar alignment, or want a bearing expressed as a compass point such as NNE.

Do not use when: You only need the distance (use haversine-distance) or a bearing relative to magnetic north (apply the local magnetic declination separately).

Formula

θ_initial = atan2(sin Δλ · cos φ2, cos φ1 · sin φ2 − sin φ1 · cos φ2 · cos Δλ) mod 360; θ_final = (θ_initial(point 2 → point 1) + 180) mod 360; compass point = round(θ / 22.5) mod 16

Bearings are relative to true north on a spherical Earth. The 16-wind compass rose assigns 22.5° sectors centred on each point (N = 348.75°–11.25°).

Inputs

Parameter	Type	Unit	Required	Description
`lat1`	number	°	yes	Latitude of start point in decimal degrees (north positive, south negative). Range: ≥ -90, ≤ 90
`lon1`	number	°	yes	Longitude of start point in decimal degrees (east positive, west negative). Range: ≥ -180, ≤ 180
`lat2`	number	°	yes	Latitude of destination in decimal degrees (north positive, south negative). Range: ≥ -90, ≤ 90
`lon2`	number	°	yes	Longitude of destination in decimal degrees (east positive, west negative). Range: ≥ -180, ≤ 180

Outputs

Output	Type	Unit	Description
`initial_bearing_degrees`	number	°	Heading at the start point, clockwise from true north (0–360).
`initial_compass_point`	string		16-point compass direction of the initial bearing.
`final_bearing_degrees`	number	°	Heading on arrival at the destination.
`final_compass_point`	string		16-point compass direction of the final bearing.
`back_bearing_degrees`	number	°	Initial bearing of the return route (final bearing + 180°).
`distance_km`	number	km	Great-circle distance (haversine, R = 6371.0088 km).
`distance_miles`	number	mi	Same distance in statute miles.

Example

Kansas City → St Louis: {"lat1":39.099912,"lon1":-94.581213,"lat2":38.627089,"lon2":-90.200203} → {"initial_bearing_degrees":96.51,"initial_compass_point":"E (east)","final_bearing_degrees":99.26,"back_bearing_degrees":279.26,"distance_km":382.9}

Movable Type example: 50°03′59″N 5°42′53″W → 58°38′38″N 3°04′12″W: {"lat1":50.06639,"lon1":-5.71472,"lat2":58.64389,"lon2":-3.07} → {"initial_bearing_degrees":9.12,"initial_compass_point":"N (north)","final_bearing_degrees":11.28,"final_compass_point":"NNE (north-northeast)","back_bearing_degrees":191.28,"distance_km":968.85}

GET https://tttkmbb.com/api/v1/calculate/compass-bearing?lat1=39.099912&lon1=-94.581213&lat2=38.627089&lon2=-90.200203

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/compass-bearing (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/compass-bearing · Markdown: https://tttkmbb.com/time/compass-bearing.md · JSON definition: https://tttkmbb.com/time/compass-bearing.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="compass-bearing"
OpenAPI operationId: calculate_compass_bearing
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Veness C – Calculate distance, bearing and more between latitude/longitude points (Movable Type Scripts) (reference)
Points of the compass (Wikipedia) (reference)

FAQ

Why do the initial and final bearings differ?

A great circle is not a line of constant heading: except along the equator or a meridian, the heading drifts as you travel. The difference grows with distance and latitude.

Is this a magnetic bearing?

No, it is relative to true north. Subtract the local magnetic declination (east positive) to obtain a magnetic compass heading.

Related calculators

Haversine Distance Calculator — Distance, central angle and midpoint of the same route.
Coordinate Converter — Convert DMS coordinates to decimal degrees first.
Angle Converter — Convert bearings between degrees, radians and mils.