[google-maps] Google Maps V3 - How to calculate the zoom level for a given bounds

I'm looking for a way to calculate the zoom level for a given bounds using the Google Maps V3 API, similar to getBoundsZoomLevel() in the V2 API.

Here is what I want to do:

// These are exact bounds previously captured from the map object
var sw = new google.maps.LatLng(42.763479, -84.338918);
var ne = new google.maps.LatLng(42.679488, -84.524313);
var bounds = new google.maps.LatLngBounds(sw, ne);
var zoom = // do some magic to calculate the zoom level

// Set the map to these exact bounds
map.setCenter(bounds.getCenter());
map.setZoom(zoom);

// NOTE: fitBounds() will not work

Unfortunately, I can't use the fitBounds() method for my particular use case. It works well for fitting markers on the map, but it does not work well for setting exact bounds. Here is an example of why I can't use the fitBounds() method.

map.fitBounds(map.getBounds()); // not what you expect

map.getBounds() is not momentary operation, so I use in similar case event handler. Here is my example in Coffeescript

@map.fitBounds(@bounds)
google.maps.event.addListenerOnce @map, 'bounds_changed', =>
  @map.setZoom(12) if @map.getZoom() > 12

Valerio is almost right with his solution, but there is some logical mistake.

you must firstly check wether angle2 is bigger than angle, before adding 360 at a negative.

otherwise you always have a bigger value than angle

So the correct solution is:

var west = calculateMin(data.longitudes);
var east = calculateMax(data.longitudes);
var angle = east - west;
var north = calculateMax(data.latitudes);
var south = calculateMin(data.latitudes);
var angle2 = north - south;
var zoomfactor;
var delta = 0;
var horizontal = false;

if(angle2 > angle) {
    angle = angle2;
    delta = 3;
}

if (angle < 0) {
    angle += 360;
}

zoomfactor = Math.floor(Math.log(960 * 360 / angle / GLOBE_WIDTH) / Math.LN2) - 2 - delta;

Delta is there, because i have a bigger width than height.

None of the highly upvoted answers worked for me. They threw various undefined errors and ended up calculating inf/nan for angles. I suspect perhaps the behavior of LatLngBounds has changed over time. In any case, I found this code to work for my needs, perhaps it can help someone:

function latRad(lat) {
  var sin = Math.sin(lat * Math.PI / 180);
  var radX2 = Math.log((1 + sin) / (1 - sin)) / 2;
  return Math.max(Math.min(radX2, Math.PI), -Math.PI) / 2;
}

function getZoom(lat_a, lng_a, lat_b, lng_b) {

      let latDif = Math.abs(latRad(lat_a) - latRad(lat_b))
      let lngDif = Math.abs(lng_a - lng_b)

      let latFrac = latDif / Math.PI 
      let lngFrac = lngDif / 360 

      let lngZoom = Math.log(1/latFrac) / Math.log(2)
      let latZoom = Math.log(1/lngFrac) / Math.log(2)

      return Math.min(lngZoom, latZoom)

}

Thanks to Giles Gardam for his answer, but it addresses only longitude and not latitude. A complete solution should calculate the zoom level needed for latitude and the zoom level needed for longitude, and then take the smaller (further out) of the two.

Here is a function that uses both latitude and longitude:

function getBoundsZoomLevel(bounds, mapDim) {
    var WORLD_DIM = { height: 256, width: 256 };
    var ZOOM_MAX = 21;

    function latRad(lat) {
        var sin = Math.sin(lat * Math.PI / 180);
        var radX2 = Math.log((1 + sin) / (1 - sin)) / 2;
        return Math.max(Math.min(radX2, Math.PI), -Math.PI) / 2;
    }

    function zoom(mapPx, worldPx, fraction) {
        return Math.floor(Math.log(mapPx / worldPx / fraction) / Math.LN2);
    }

    var ne = bounds.getNorthEast();
    var sw = bounds.getSouthWest();

    var latFraction = (latRad(ne.lat()) - latRad(sw.lat())) / Math.PI;

    var lngDiff = ne.lng() - sw.lng();
    var lngFraction = ((lngDiff < 0) ? (lngDiff + 360) : lngDiff) / 360;

    var latZoom = zoom(mapDim.height, WORLD_DIM.height, latFraction);
    var lngZoom = zoom(mapDim.width, WORLD_DIM.width, lngFraction);

    return Math.min(latZoom, lngZoom, ZOOM_MAX);
}

Demo on jsfiddle

Parameters:

The "bounds" parameter value should be a google.maps.LatLngBounds object.

The "mapDim" parameter value should be an object with "height" and "width" properties that represent the height and width of the DOM element that displays the map. You may want to decrease these values if you want to ensure padding. That is, you may not want map markers within the bounds to be too close to the edge of the map.

If you are using the jQuery library, the mapDim value can be obtained as follows:

var $mapDiv = $('#mapElementId');
var mapDim = { height: $mapDiv.height(), width: $mapDiv.width() };

If you are using the Prototype library, the mapDim value can be obtained as follows:

var mapDim = $('mapElementId').getDimensions();

Return Value:

The return value is the maximum zoom level that will still display the entire bounds. This value will be between 0 and the maximum zoom level, inclusive.

The maximum zoom level is 21. (I believe it was only 19 for Google Maps API v2.)

Explanation:

Google Maps uses a Mercator projection. In a Mercator projection the lines of longitude are equally spaced, but the lines of latitude are not. The distance between lines of latitude increase as they go from the equator to the poles. In fact the distance tends towards infinity as it reaches the poles. A Google Maps map, however, does not show latitudes above approximately 85 degrees North or below approximately -85 degrees South. (reference) (I calculate the actual cutoff at +/-85.05112877980658 degrees.)

This makes the calculation of the fractions for the bounds more complicated for latitude than for longitude. I used a formula from Wikipedia to calculate the latitude fraction. I am assuming this matches the projection used by Google Maps. After all, the Google Maps documentation page I link to above contains a link to the same Wikipedia page.

Other Notes:

1. Zoom levels range from 0 to the maximum zoom level. Zoom level 0 is the map fully zoomed out. Higher levels zoom the map in further. (reference)
2. At zoom level 0 the entire world can be displayed in an area that is 256 x 256 pixels. (reference)
3. For each higher zoom level the number of pixels needed to display the same area doubles in both width and height. (reference)
4. Maps wrap in the longitudinal direction, but not in the latitudinal direction.

Here a Kotlin version of the function:

fun getBoundsZoomLevel(bounds: LatLngBounds, mapDim: Size): Double {
        val WORLD_DIM = Size(256, 256)
        val ZOOM_MAX = 21.toDouble();

        fun latRad(lat: Double): Double {
            val sin = Math.sin(lat * Math.PI / 180);
            val radX2 = Math.log((1 + sin) / (1 - sin)) / 2;
            return max(min(radX2, Math.PI), -Math.PI) /2
        }

        fun zoom(mapPx: Int, worldPx: Int, fraction: Double): Double {
            return floor(Math.log(mapPx / worldPx / fraction) / Math.log(2.0))
        }

        val ne = bounds.northeast;
        val sw = bounds.southwest;

        val latFraction = (latRad(ne.latitude) - latRad(sw.latitude)) / Math.PI;

        val lngDiff = ne.longitude - sw.longitude;
        val lngFraction = if (lngDiff < 0) { (lngDiff + 360) } else { (lngDiff / 360) }

        val latZoom = zoom(mapDim.height, WORLD_DIM.height, latFraction);
        val lngZoom = zoom(mapDim.width, WORLD_DIM.width, lngFraction);

        return minOf(latZoom, lngZoom, ZOOM_MAX)
    }

The calculation of the zoom level for the longitudes of Giles Gardam works fine for me. If you want to calculate the zoom factor for latitude, this is an easy solution that works fine:

double minLat = ...;
double maxLat = ...;
double midAngle = (maxLat+minLat)/2;
//alpha is the non-negative angle distance of alpha and beta to midangle
double alpha  = maxLat-midAngle;
//Projection screen is orthogonal to vector with angle midAngle
//portion of horizontal scale:
double yPortion = Math.sin(alpha*Math.pi/180) / 2;
double latZoom = Math.log(mapSize.height / GLOBE_WIDTH / yPortion) / Math.ln2;

//return min (max zoom) of both zoom levels
double zoom = Math.min(lngZoom, latZoom);

Thanks, that helped me a lot in finding the most suitable zoom factor to correctly display a polyline. I find the maximum and minimum coordinates among the points I have to track and, in case the path is very "vertical", I just added few lines of code:

var GLOBE_WIDTH = 256; // a constant in Google's map projection
var west = <?php echo $minLng; ?>;
var east = <?php echo $maxLng; ?>;
*var north = <?php echo $maxLat; ?>;*
*var south = <?php echo $minLat; ?>;*
var angle = east - west;
if (angle < 0) {
    angle += 360;
}
*var angle2 = north - south;*
*if (angle2 > angle) angle = angle2;*
var zoomfactor = Math.round(Math.log(960 * 360 / angle / GLOBE_WIDTH) / Math.LN2);

Actually, the ideal zoom factor is zoomfactor-1.

Since all of the other answers seem to have issues for me with one or another set of circumstances (map width/height, bounds width/height, etc.) I figured I'd put my answer here...

There was a very useful javascript file here: http://www.polyarc.us/adjust.js

I used that as a base for this:

var com = com || {};
com.local = com.local || {};
com.local.gmaps3 = com.local.gmaps3 || {};

com.local.gmaps3.CoordinateUtils = new function() {

   var OFFSET = 268435456;
   var RADIUS = OFFSET / Math.PI;

   /**
    * Gets the minimum zoom level that entirely contains the Lat/Lon bounding rectangle given.
    *
    * @param {google.maps.LatLngBounds} boundary the Lat/Lon bounding rectangle to be contained
    * @param {number} mapWidth the width of the map in pixels
    * @param {number} mapHeight the height of the map in pixels
    * @return {number} the minimum zoom level that entirely contains the given Lat/Lon rectangle boundary
    */
   this.getMinimumZoomLevelContainingBounds = function ( boundary, mapWidth, mapHeight ) {
      var zoomIndependentSouthWestPoint = latLonToZoomLevelIndependentPoint( boundary.getSouthWest() );
      var zoomIndependentNorthEastPoint = latLonToZoomLevelIndependentPoint( boundary.getNorthEast() );
      var zoomIndependentNorthWestPoint = { x: zoomIndependentSouthWestPoint.x, y: zoomIndependentNorthEastPoint.y };
      var zoomIndependentSouthEastPoint = { x: zoomIndependentNorthEastPoint.x, y: zoomIndependentSouthWestPoint.y };
      var zoomLevelDependentSouthEast, zoomLevelDependentNorthWest, zoomLevelWidth, zoomLevelHeight;
      for( var zoom = 21; zoom >= 0; --zoom ) {
         zoomLevelDependentSouthEast = zoomLevelIndependentPointToMapCanvasPoint( zoomIndependentSouthEastPoint, zoom );
         zoomLevelDependentNorthWest = zoomLevelIndependentPointToMapCanvasPoint( zoomIndependentNorthWestPoint, zoom );
         zoomLevelWidth = zoomLevelDependentSouthEast.x - zoomLevelDependentNorthWest.x;
         zoomLevelHeight = zoomLevelDependentSouthEast.y - zoomLevelDependentNorthWest.y;
         if( zoomLevelWidth <= mapWidth && zoomLevelHeight <= mapHeight )
            return zoom;
      }
      return 0;
   };

   function latLonToZoomLevelIndependentPoint ( latLon ) {
      return { x: lonToX( latLon.lng() ), y: latToY( latLon.lat() ) };
   }

   function zoomLevelIndependentPointToMapCanvasPoint ( point, zoomLevel ) {
      return {
         x: zoomLevelIndependentCoordinateToMapCanvasCoordinate( point.x, zoomLevel ),
         y: zoomLevelIndependentCoordinateToMapCanvasCoordinate( point.y, zoomLevel )
      };
   }

   function zoomLevelIndependentCoordinateToMapCanvasCoordinate ( coordinate, zoomLevel ) {
      return coordinate >> ( 21 - zoomLevel );
   }

   function latToY ( lat ) {
      return OFFSET - RADIUS * Math.log( ( 1 + Math.sin( lat * Math.PI / 180 ) ) / ( 1 - Math.sin( lat * Math.PI / 180 ) ) ) / 2;
   }

   function lonToX ( lon ) {
      return OFFSET + RADIUS * lon * Math.PI / 180;
   }

};

You can certainly clean this up or minify it if needed, but I kept the variable names long in an attempt to make it easier to understand.

If you are wondering where OFFSET came from, apparently 268435456 is half of earth's circumference in pixels at zoom level 21 (according to http://www.appelsiini.net/2008/11/introduction-to-marker-clustering-with-google-maps).

Work example to find average default center with react-google-maps on ES6:

const bounds = new google.maps.LatLngBounds();
paths.map((latLng) => bounds.extend(new google.maps.LatLng(latLng)));
const defaultCenter = bounds.getCenter();
<GoogleMap
 defaultZoom={paths.length ? 12 : 4}
 defaultCenter={defaultCenter}
>
 <Marker position={{ lat, lng }} />
</GoogleMap>

For version 3 of the API, this is simple and working:

var latlngList = [];
latlngList.push(new google.maps.LatLng(lat, lng));

var bounds = new google.maps.LatLngBounds();
latlngList.each(function(n) {
    bounds.extend(n);
});

map.setCenter(bounds.getCenter()); //or use custom center
map.fitBounds(bounds);

and some optional tricks:

//remove one zoom level to ensure no marker is on the edge.
map.setZoom(map.getZoom() - 1); 

// set a minimum zoom 
// if you got only 1 marker or all markers are on the same address map will be zoomed too much.
if(map.getZoom() > 15){
    map.setZoom(15);
}

For swift version

func getBoundsZoomLevel(bounds: GMSCoordinateBounds, mapDim: CGSize) -> Double {
        var bounds = bounds
        let WORLD_DIM = CGSize(width: 256, height: 256)
        let ZOOM_MAX: Double = 21.0
        func latRad(_ lat: Double) -> Double {
            let sin2 = sin(lat * .pi / 180)
            let radX2 = log10((1 + sin2) / (1 - sin2)) / 2
            return max(min(radX2, .pi), -.pi) / 2
        }
        func zoom(_ mapPx: CGFloat,_ worldPx: CGFloat,_ fraction: Double) -> Double {
            return floor(log10(Double(mapPx) / Double(worldPx) / fraction / log10(2.0)))
        }
        let ne = bounds.northEast
        let sw = bounds.southWest
        let latFraction = (latRad(ne.latitude) - latRad(sw.latitude)) / .pi
        let lngDiff = ne.longitude - sw.longitude
        let lngFraction = lngDiff < 0 ? (lngDiff + 360) : (lngDiff / 360)
        let latZoom = zoom(mapDim.height, WORLD_DIM.height, latFraction);
        let lngZoom = zoom(mapDim.width, WORLD_DIM.width, lngFraction);
        return min(latZoom, lngZoom, ZOOM_MAX)
    }

Dart Version:

  double latRad(double lat) {
    final double sin = math.sin(lat * math.pi / 180);
    final double radX2 = math.log((1 + sin) / (1 - sin)) / 2;
    return math.max(math.min(radX2, math.pi), -math.pi) / 2;
  }

  double getMapBoundZoom(LatLngBounds bounds, double mapWidth, double mapHeight) {
    final LatLng northEast = bounds.northEast;
    final LatLng southWest = bounds.southWest;

    final double latFraction = (latRad(northEast.latitude) - latRad(southWest.latitude)) / math.pi;

    final double lngDiff = northEast.longitude - southWest.longitude;
    final double lngFraction = ((lngDiff < 0) ? (lngDiff + 360) : lngDiff) / 360;

    final double latZoom = (math.log(mapHeight / 256 / latFraction) / math.ln2).floorToDouble();
    final double lngZoom = (math.log(mapWidth / 256 / lngFraction) / math.ln2).floorToDouble();

    return math.min(latZoom, lngZoom);
  }