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Haversine Distance Calculator

Computes the great-circle (as-the-crow-flies) distance between two points on a spherical Earth with the haversine formula, in kilometres, miles and nautical miles, together with the initial bearing, compass direction and the midpoint of the route.

When to use

You need the straight-line distance between two GPS coordinates or cities, e.g. for flight distance, range checks or geofencing.

Do not use when: You need road distance, or ellipsoidal accuracy better than about 0.5 % (use a geodesic method such as Vincenty or Karney on WGS-84); for bearings and compass points use compass-bearing.

Formula

a = sin²(Δφ/2) + cos φ1 · cos φ2 · sin²(Δλ/2); c = 2 · atan2(√a, √(1−a)); d = R · c with R = 6371.0088 km; θ = atan2(sin Δλ · cos φ2, cos φ1 · sin φ2 − sin φ1 · cos φ2 · cos Δλ)

Spherical model with the IUGG mean Earth radius; real distances on the WGS-84 ellipsoid differ by up to about 0.3–0.5 %. The bearing is the initial heading; on long routes it changes continuously along the great circle.

Inputs

Parameter	Type	Unit	Required	Description
`lat1`	number	°	yes	Latitude of point 1 in decimal degrees (north positive, south negative). Range: ≥ -90, ≤ 90
`lon1`	number	°	yes	Longitude of point 1 in decimal degrees (east positive, west negative). Range: ≥ -180, ≤ 180
`lat2`	number	°	yes	Latitude of point 2 in decimal degrees (north positive, south negative). Range: ≥ -90, ≤ 90
`lon2`	number	°	yes	Longitude of point 2 in decimal degrees (east positive, west negative). Range: ≥ -180, ≤ 180

Outputs

Output	Type	Unit	Description
`distance_km`	number	km	Great-circle distance on a sphere of radius 6,371.0088 km.
`distance_miles`	number	mi	Same distance in statute miles (1 mi = 1.609344 km).
`distance_nautical_miles`	number	nmi	Same distance in nautical miles (1 nmi = 1.852 km).
`central_angle_degrees`	number	°	Angle subtended at the Earth's centre.
`initial_bearing_degrees`	number	°	Forward azimuth at point 1, clockwise from true north (0–360).
`compass_direction`	string		16-point compass direction of the initial bearing.
`midpoint_lat`	number	°	Latitude of the great-circle midpoint.
`midpoint_lon`	number	°	Longitude of the great-circle midpoint.

Example

Sydney → Tokyo: {"lat1":-33.8688,"lon1":151.2093,"lat2":35.6762,"lon2":139.6503} → {"distance_km":7825.83,"distance_miles":4862.74,"distance_nautical_miles":4225.61,"central_angle_degrees":70.3793,"initial_bearing_degrees":350.05,"compass_direction":"N (north)","midpoint_lat":0.9083,"midpoint_lon":145.4933}

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} → {"distance_km":968.85,"distance_miles":602.02,"initial_bearing_degrees":9.12,"midpoint_lat":54.3623,"midpoint_lon":-4.5307}

GET https://tttkmbb.com/api/v1/calculate/haversine-distance?lat1=-33.8688&lon1=151.2093&lat2=35.6762&lon2=139.6503

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/haversine-distance (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/haversine-distance · Markdown: https://tttkmbb.com/time/haversine-distance.md · JSON definition: https://tttkmbb.com/time/haversine-distance.json
MCP: server https://tttkmbb.com/mcp, tool calculate_haversine_distance
OpenAPI operationId: calculate_haversine_distance
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)
Haversine formula (Wikipedia) (reference)
Earth radius – IUGG mean radius R1 = 6,371.0088 km (Wikipedia) (reference)

FAQ

How accurate is the haversine formula?

It is exact for a sphere and numerically stable for short distances. Because the Earth is an oblate ellipsoid, results differ from geodesic (Vincenty/Karney) distances by up to about 0.5 %, i.e. roughly 30 km on a 7,800 km flight.

Which sign convention do the coordinates use?

Decimal degrees: north and east positive, south and west negative. Use coordinate-converter to turn degrees-minutes-seconds into decimals first.

Related calculators

Compass Bearing Calculator — Initial and final bearing with compass points for the same route.
Coordinate Converter — Convert DMS coordinates to the decimal degrees this calculator needs.
Length Converter — Convert the distance to other length units.