I want to use this formula with php. I have a database with some values of latitute and longitude saved.
I want to find, with a certain value of latitude and longitude in input, all the distances (in km) from this point with each point in the database. To do this, I used the formula on googlemaps api:
( 6371 * acos( cos( radians(37) ) * cos( radians( lat ) ) * cos( radians( lng ) - radians(-122) ) + sin( radians(37) ) * sin( radians( lat ) ) ) )
Of course using that in php I replaced radians with deg2rad
.The values 37,-122 are my values of input and lat,lng are my values in the database.
Below there is my code. The problem is that there is something wrong but I don’t understand what. The value of distance is of course wrong.
//values of latitude and longitute in input (Rome - eur, IT) $center_lat = "41.8350"; $center_lng = "12.470"; //connection to database. it works (..) //to take each value in the database: $query = "SELECT * FROM Dati"; $result = mysql_query($query); while ($row = @mysql_fetch_assoc($result)){ $lat=$row['Lat']); $lng=$row['Lng']); $distance =( 6371 * acos((cos(deg2rad($center_lat)) ) * (cos(deg2rad($lat))) * (cos(deg2rad($lng) - deg2rad($center_lng)) )+ ((sin(deg2rad($center_lat))) * (sin(deg2rad($lat))))) ); }
For values for example: $lat= 41.9133741000 $lng= 12.5203944000
I have the output of distance=”4826.9341106926″
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Answer
The formula you used, seems to be the arccosine instead of the haversine formula. The haversine formula is indeed more appropriate to calculate the distance on a sphere, because it is less prone to rounding errors.
/** * Calculates the great-circle distance between two points, with * the Haversine formula. * @param float $latitudeFrom Latitude of start point in [deg decimal] * @param float $longitudeFrom Longitude of start point in [deg decimal] * @param float $latitudeTo Latitude of target point in [deg decimal] * @param float $longitudeTo Longitude of target point in [deg decimal] * @param float $earthRadius Mean earth radius in [m] * @return float Distance between points in [m] (same as earthRadius) */ function haversineGreatCircleDistance( $latitudeFrom, $longitudeFrom, $latitudeTo, $longitudeTo, $earthRadius = 6371000) { // convert from degrees to radians $latFrom = deg2rad($latitudeFrom); $lonFrom = deg2rad($longitudeFrom); $latTo = deg2rad($latitudeTo); $lonTo = deg2rad($longitudeTo); $latDelta = $latTo - $latFrom; $lonDelta = $lonTo - $lonFrom; $angle = 2 * asin(sqrt(pow(sin($latDelta / 2), 2) + cos($latFrom) * cos($latTo) * pow(sin($lonDelta / 2), 2))); return $angle * $earthRadius; }
P.S. I couldn’t find an error in your code, so is it just a typo that you wrote $lat= 41.9133741000 $lat= 12.5203944000
? Maybe you just calculated with $lat=12.5203944000 and $long=0 because you overwrote your $lat variable.
Edit:
Tested the code and it returned a correct result:
$center_lat = 41.8350; $center_lng = 12.470; $lat = 41.9133741000; $lng = 12.5203944000; // test with your arccosine formula $distance =( 6371 * acos((cos(deg2rad($center_lat)) ) * (cos(deg2rad($lat))) * (cos(deg2rad($lng) - deg2rad($center_lng)) )+ ((sin(deg2rad($center_lat))) * (sin(deg2rad($lat))))) ); print($distance); // prints 9.662174538188 // test with my haversine formula $distance = haversineGreatCircleDistance($center_lat, $center_lng, $lat, $lng, 6371); print($distance); // prints 9.6621745381693