The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes.
a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2) c = 2 ⋅ atan2( √a, √(1−a) ) d = R ⋅ c
Where: φ (Phi) is latitude, λ (Lambda) is longitude, R is earth’s radius (mean radius = 6,371km);
Note that angles need to be in radians to pass to trig functions!
var R = 6371e3; // metres var φ1 = lat1.toRadians(); var φ2 = lat2.toRadians(); var Δφ = (lat2-lat1).toRadians(); var Δλ = (lon2-lon1).toRadians(); var a = Math.sin(Δφ/2) * Math.sin(Δφ/2) + Math.cos(φ1) * Math.cos(φ2) * Math.sin(Δλ/2) * Math.sin(Δλ/2); var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); var d = R * c;
3959 * acos(cos(radians('.$lat.')) * cos(radians(a.lat)) * cos(radians(a.lon) - radians('.$lon.')) + sin(radians('.$lat.')) * sin(radians(a.lat)))) as distance