Lance Lance - 4 months ago 10
SQL Question

Querying MySQL for latitude and longitude coordinates that are within a given mile radius

I currently have a MySQL table that is structured as follows:

id name lon lat
----- ----- ----------- -----------
1 Mark -76.316528 40.036027
2 John -95.995102 41.25716
3 Paul -82.337036 29.645095
4 Dave -82.337036 29.645095
5 Chris -76.316528 40.036027


The way I currently query the DB to see if a user's location is within a certain mile radius of a given location is by doing this.

function Haversine($lat_from, $lon_from, $lat_to, $lon_to) {
$radius = 6371000;
$delta_lat = deg2rad($lat_to-$lat_from);
$delta_lon = deg2rad($lon_to-$lon_from);

$a = sin($delta_lat/2) * sin($delta_lat/2) +
cos(deg2rad($lat_from)) * cos(deg2rad($lat_to)) *
sin($delta_lon/2) * sin($delta_lon/2);
$c = 2*atan2(sqrt($a), sqrt(1-$a));

// Convert the distance from meters to miles
return ceil(($radius*$c)*0.000621371);
}

// Set the given location to NYC
$my_lon = -73.9844;
$my_lat = 40.7590;

// Query the DB for all of the users
$sql = "SELECT * FROM users";
$result = mysqli_query($con, $sql)or die(mysqli_error($con));
$count = mysqli_num_rows($result);
$i = 0;

while($row = mysqli_fetch_assoc($result)) {
$lon[$i] = $row['lon'];
$lat[$i] = $row['lat'];

$i++;
}

for($i=0;$i<$count;$i++) {
// Calculate the distance between each user's location and my location
$distance = Haversine($my_lat, $my_lon, $lat[$i], $lon[$i);

if($distance < 50) {
echo "Close enough";
}
}


This works well with only a few hundred rows in the table. But, now that I have tens of thousands of rows, checking so many rows has proven to be very time consuming. I'm wondering if there is a way to use the Haversine formula to only query rows that are within the 50 mile radius.

Answer

Spherical Law of Cosines Formula
(37 and -122 are the lat and lon of your radius center)

SELECT id, ( 3959 * acos( cos( radians(37) ) * cos( radians( lat ) ) 
    * cos( radians( long ) - radians(-122) ) + sin( radians(37) ) * sin(radians(lat)) ) ) AS distance 
FROM myTable
HAVING distance < 50
ORDER BY distance 

Features

  • Fastest
  • Precision similar to Harvesine Formula

Haversine Formula

SELECT id, 3956 * 2 * ASIN(SQRT(POWER(SIN((37 - abs(lat)) * pi()/180 / 2), 2)
       + COS(37 * pi()/180 ) * COS(abs(lat) * pi()/180)
       * POWER(SIN((-122 – long) * pi()/180 / 2), 2) )) as  distance
FROM myTable
HAVING distance < 50
ORDER BY distance

Features

  • Fast
  • More robust to floating point errors

Note that 3959 is the Earth radius in miles. Earth radius in km: 6971

You can find more information here