Calculate distance, bearing and more between two
latitude/longitude points
Top of FormDistanceThis page helps you to calculate great-circle
distances betweentwo pointsusing the Haversine formula.The formula
assumes that theearth is a sphere, (we know that it is "egg"
shaped) but it is accurate enough*for our purposes.Enter the
coordinates into the text boxes to try it out. It accepts a variety
of formats: deg-min-sec suffixed with N/S/E/W (e.g. 404455N, 73 59
11W), or signed decimal degrees without compass direction, where
negative indicates west/south (e.g. 40.7486, -73.9864):Lat 1:Long
1:Lat 2:Long 2:And you cansee it on a map(thanks to Google
Maps)Haversine formula:R = earths radius (mean radius = 6,371km)lat
= lat2 lat1long = long2 long1a = sin(lat/2) +
cos(lat1).cos(lat2).sin(long/2)c = 2.atan2(a, (1a))d = R.c(Note
that angles need to be in radians to pass to trig functions).
TheHaversineformula remains particularly well-conditioned for
numerical computation even at small distances
Spherical lawof cosines:d =
acos(sin(lat1).sin(lat2)+cos(lat1).cos(lat2).cos(long2long1)).R
Excel:=ACOS(SIN(Lat1)*SIN(Lat2)+COS(Lat1)*COS(Lat2)*COS(Lon2-Lon1))*6371
BearingFormula: =atan2(sin(long).cos(lat2),cos(lat1).sin(lat2)
sin(lat1).cos(lat2).cos(long) )
Since atan2 returns values in the range - ... +, to normalise
the result to a compass bearing, multiply by 180/ then use (+360) %
360, where % is modulo.This is the initial bearing which if
followed in a straight line along a great-circle arcwill take you
from the start point to the end point; in general, the bearing you
are following will have varied by the time you get to the end
pointFor final bearing, take the initial bearing from the end point
to the start point and reverse it (using = (+180) % 360).
MidpointFormula:Bx = cos(lat2).cos(long)By =
cos(lat2).sin(long)latm= atan2(sin(lat1) + sin(lat2),
((cos(lat1)+Bx) + By))lonm= lon1+ atan2(By, cos(lat1)+Bx)
Just as the initial bearing may vary from the final bearing, the
midpoint may not be located half-way between
latitudes/longitudes.Bottom of Form
