Simple calculations for working with lat lon and km distance

Question

Is there a simple calculation I can do which will convert km into a value which I can add to a lat or lon float to calculate a bounding box for searches  It doesn t need to be completely accurate   For instance  if I were given a lat lon for London  England  51 5001524  -0 1262362  and I wanted calculate what the lat would be 25km east west from that point  and what the lon would be 25km north south of that point  what would I need to do to convert the 25km into a decimal to add to the values above   I m looking for a general rule-of-thumb  ie  1km      - 0 XXX  Edit   My original search for  lat lon  didn t return this result   How to calculate the bounding box for a given lat lng location   The accepted answer seems adequate for my requirements

User · Answer

Thanks Jim Lewis for his great answer and I would like to illustrate this solution by my function in Swift:

func getRandomLocation(forLocation location: CLLocation, withOffsetKM offset: Double) -> CLLocation {
        let latDistance = (Double(arc4random()) / Double(UInt32.max)) * offset * 2.0 - offset
        let longDistanceMax = sqrt(offset * offset - latDistance * latDistance)
        let longDistance = (Double(arc4random()) / Double(UInt32.max)) * longDistanceMax * 2.0 - longDistanceMax

        let lat: CLLocationDegrees = location.coordinate.latitude + latDistance / 110.574
        let lng: CLLocationDegrees = location.coordinate.longitude + longDistance / (111.320 * cos(lat / .pi / 180))
        return CLLocation(latitude: lat, longitude: lng)
    }

In this function to convert distance I use following formulas:

latDistance / 110.574
longDistance / (111.320 * cos(lat / .pi / 180))

User · Answer

The approximate conversions are    Latitude  1 deg   110 574 km Longitude  1 deg   111 320 cos latitude  km   This doesn t fully correct for the Earth s polar flattening - for that you d probably want a more complicated formula using the WGS84 reference ellipsoid  the model used for GPS    But the error is probably negligible for your purposes   Source  http   en wikipedia org wiki Latitude  Caution  Be aware that latlong coordinates are expressed in degrees  while the cos function in most  all   languages typically accepts radians  therefore a degree to radians conversion is needed

User · Answer

Interesting that I didn t see a mention of UTM coordinates    https   en wikipedia org wiki Universal Transverse Mercator coordinate system   At least if you want to add km to the same zone  it should be straightforward  in Python   https   pypi org project utm     utm from latlon and utm to latlon

User · Answer

If you re using Java  Javascript or PHP  then there s a library that will do these calculations exactly  using some amusingly complicated  but still fast  trigonometry   http   www jstott me uk jcoord

User · Answer

Why not use properly formulated geospatial queries     Here is the SQL server reference page on the STContains geospatial function   https   docs microsoft com en-us sql t-sql spatial-geography stcontains-geography-data-type view sql-server-ver15  or if you do not waant to use box and radian conversion   you cna always use the distance function to find the points that you need   DECLARE  CurrentLocation geography   SET  CurrentLocation    geography  Point 12 822222  80 222222  4326   SELECT     Round  GeoLocation STDistance  CurrentLocation   0  AS Distance FROM  Landmark  WHERE GeoLocation STDistance  CurrentLocation   lt   2000 -- 2 Km   There should be similar functionality for almost any database out there   If you have implemented geospatial indexing correctly your searches would be way faster than the approach you are using

User · Answer

http   www jstott me uk jcoord  - use this library              LatLng lld1   new LatLng 40 718119  -73 995667               LatLng lld2   new LatLng 51 499981  -0 125313               Double distance   lld1 distance lld2               Log d TAG   Distance in kilometers     distance

[algorithm] Simple calculations for working with lat/lon and km distance?

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