# haversine: Haversine Formula In pracma: Practical Numerical Math Functions

## Description

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

## Usage

 `1` ```haversine(loc1, loc2, R = 6371.0) ```

## Arguments

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

## Details

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.

## Value

Returns the distance in km.

Hans W. Borchers

## References

Entry 'Great_circle_distance' in Wikipedia.

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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) ```

### Example output

```Flight distance Frankfurt-Chicago is 6971.059 km.
Flight distance Frankfurt-Chicago is 6971.059 km.
```

pracma documentation built on Dec. 11, 2021, 9:57 a.m.