pracma (version 1.9.9)

haversine: Haversine Formula


Haversine formula to calculate the arc distance between two points on earth (i.e., along a great circle).


haversine(loc1, loc2, R = 6371.0)


loc1, loc2
Locations on earth; for format see Details.
Average earth radius R = 6371 km, can be changed on input.


Returns the distance in km.


The Haversine formula is more robust for the calculating the distance as with the spherical cosine formula. The user may want to assume a slightly different earth radius, so this can be provided as input.

The location can be input in two different formats, as latitude and longitude in a character string, e.g. for Frankfurt airport as '50 02 00N, 08 34 14E', or as a numerical two-vector in degrees (not radians).

Here for latitude 'N' and 'S' stand for North and South, and for longitude 'E' or 'W' stand for East and West. For the degrees format, South and West must be negative.

These two formats can be mixed.


Entry 'Great_circle_distance' in Wikipedia.

See Also

Implementations of the Haversine formula can also be found in other R packages, e.g. 'geoPlot' or 'geosphere'.


Run this code
FRA = '50 02 00N, 08 34 14E'  # Frankfurt Airport
ORD = '41 58 43N, 87 54 17W'  # Chicago O'Hare Interntl. Airport
fra <- c(50+2/60, 8+34/60+14/3600)
ord <- c(41+58/60+43/3600, -(87+54/60+17/3600))

dis <- haversine(FRA, ORD)    # 6971.059 km
fprintf('Flight distance Frankfurt-Chicago is %8.3f km.\n', dis)

dis <- haversine(fra, ord)
fprintf('Flight distance Frankfurt-Chicago is %8.3f km.\n', dis)

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