Zoom Levels and Tile Grid

Service version: 2

Last edit: 2023.08.01

Purpose

TomTom Maps use the Spherical Mercator projection coordinate system (EPSG:3857).

Zoom levels

The world is divided into square tiles.

Maps Raster
- Map tiles has 23 zoom levels, numbered 0 through 22.
- Satellite tiles has 20 zoom levels, numbered 0 through 19.
- Hillshade tiles has 14 zoom levels, numbered 0 through 13.
Maps Vector has 23 zoom levels, numbered 0 through 22.

At zoom level 0, the entire world fits on a single tile:

Zoom level 1 uses 4 tiles to render the world: a 2 x 2 square.

Each subsequent zoom level quad divides the tiles of the previous one, creating a grid of 2^zoom x 2^zoom. For example, zoom level 22 is a grid 2²² x 2²², or 4,194,304 x 4,194,304 tiles (result: 17,592,186,044,416 in total).

To discover the real-world size of a single tile on a given zoom level, we can use the formula circumference of earth / 2^{zoom level} that produces number of meters per tile side, where the circumference of the earth equals 40,075,017 meters. The full data table of values for zoom levels is here:

zoom level	meters/pixel	meters/tile side
`0`	156543	40075017
`1`	78271.5	20037508
`2`	39135.8	10018754
`3`	19567.88	5009377.1
`4`	9783.94	2504688.5
`5`	4891.97	1252344.3
`6`	2445.98	626172.1
`7`	1222.99	313086.1
`8`	611.5	156543
`9`	305.75	78271.5
`10`	152.87	39135.8
`11`	76.44	19567.9
`12`	38.219	9783.94
`13`	19.109	4891.97
`14`	9.555	2445.98
`15`	4.777	1222.99
`16`	2.3887	611.496
`17`	1.1943	305.748
`18`	0.5972	152.874
`19`	0.2986	76.437
`20`	0.14929	38.2185
`21`	0.074646	19.10926
`22`	0.037323	9.55463

Tile grid

Tiles are called by zoom level and the x and y coordinates corresponding to the tile's position on the grid for that zoom level.

When determining which zoom level to use, remember that each location is in a fixed position on its tile.

This means that the number of tiles needed to display a given expanse of territory is dependent on the specific placement of zoom grid on the world.
For instance, if there are two points 900 meters apart, it may only take three tiles to display a route between them at zoom level 17.

However, if the western point is on the right side of its tile, and the eastern point on its left side, it may take four tiles as shown in the following diagram:

Once the zoom level is determined, the x and y coordinate values can be calculated:

The top-left tile in each zoom grid is
**x=0**
,
**y=0**
.
The bottom-right tile is at
**x=2 zoom -1**
,
**y=2 zoom -1**
.

Here is the zoom grid for zoom level 1:

Coordinates conversion

Convert latitude/longitude coordinates to tile z/x/y coordinates.

	Coordinates	Zoom level		Result
			Convert

Latitude/longitude to tile z/x/y

Select...

1function latLonToTileZXY(lat, lon, zoomLevel) {
const MIN_ZOOM_LEVEL = 0
const MAX_ZOOM_LEVEL = 22
const MIN_LAT = -85.051128779807
const MAX_LAT = 85.051128779806
const MIN_LON = -180.0
const MAX_LON = 180.0
8
if (
  zoomLevel == undefined ||
  isNaN(zoomLevel) ||
  zoomLevel < MIN_ZOOM_LEVEL ||
  zoomLevel > MAX_ZOOM_LEVEL
) {
  throw new Error(
    "Zoom level value is out of range [" +
      MIN_ZOOM_LEVEL.toString() +
      ", " +
      MAX_ZOOM_LEVEL.toString() +
      "]"
  )
}
23
if (lat == undefined || isNaN(lat) || lat < MIN_LAT || lat > MAX_LAT) {
  throw new Error(
    "Latitude value is out of range [" +
      MIN_LAT.toString() +
      ", " +
      MAX_LAT.toString() +
      "]"
  )
}
33
if (lon == undefined || isNaN(lon) || lon < MIN_LON || lon > MAX_LON) {
  throw new Error(
    "Longitude value is out of range [" +
      MIN_LON.toString() +
      ", " +
      MAX_LON.toString() +
      "]"
  )
}
43
let z = Math.trunc(zoomLevel)
let xyTilesCount = Math.pow(2, z)
let x = Math.trunc(Math.floor(((lon + 180.0) / 360.0) * xyTilesCount))
let y = Math.trunc(
  Math.floor(
    ((1.0 -
      Math.log(
        Math.tan((lat * Math.PI) / 180.0) +
          1.0 / Math.cos((lat * Math.PI) / 180.0)
      ) /
        Math.PI) /
      2.0) *
      xyTilesCount
  )
)
59
return z.toString() + "/" + x.toString() + "/" + y.toString()
61}

1std::string latLonToTileZXY(double lat, double lon, unsigned int z)
2{
constexpr unsigned int MAX_ZOOM_LEVEL = 22;
constexpr double MIN_LAT = -85.051128779807;
constexpr double MAX_LAT = 85.051128779806;
constexpr double MIN_LON = -180.0;
constexpr double MAX_LON = 180.0;
8
if (z > MAX_ZOOM_LEVEL) {
  throw std::invalid_argument("Zoom level value is out of range [0, " +
                              std::to_string(MAX_ZOOM_LEVEL) + "]");
}
13
if (!std::isfinite(lat) || (lat < MIN_LAT) || (lat > MAX_LAT)) {
  throw std::invalid_argument("Latitude value is out of range [" +
                              std::to_string(MIN_LAT) + ", " + std::to_string(MAX_LAT) + "]");
}
18
if (!std::isfinite(lon) || (lon < MIN_LON) || (lon > MAX_LON)) {
  throw std::invalid_argument("Longitude value is out of range [" +
                                  std::to_string(MIN_LON) + ", " + std::to_string(MAX_LON) + "]");
}
23
const int xyTilesCount = 1 << z;
int x = floor((lon + 180.0) / 360.0 * xyTilesCount);
int y = floor((1.0 - log(tan(lat * M_PI / 180.0) + 1.0 / cos(lat * M_PI / 180.0)) / M_PI) /
              2.0 * xyTilesCount);
28
return std::to_string(z) + "/" + std::to_string(x) + "/" + std::to_string(y);
30}

1public static String latLonToTileZXY(double lat, double lon, int z)
2{
  final int MIN_ZOOM_LEVEL = 0;
  final int MAX_ZOOM_LEVEL = 22;
  final double MIN_LAT = -85.051128779807;
  final double MAX_LAT = 85.051128779806;
  final double MIN_LON = -180.0;
  final double MAX_LON = 180.0;
9
  if ((z < MIN_ZOOM_LEVEL) || (z > MAX_ZOOM_LEVEL))
  {
      throw new IllegalArgumentException("Zoom level value is out of range [" +
                                         Integer.toString(MIN_ZOOM_LEVEL) + ", " +
                                         Integer.toString(MAX_ZOOM_LEVEL) + "]");
  }
16
  if (!Double.isFinite(lat) || (lat < MIN_LAT) || (lat > MAX_LAT))
  {
      throw new IllegalArgumentException("Latitude value is out of range [" +
                                         Double.toString(MIN_LAT) + ", " +
                                         Double.toString(MAX_LAT) + "]");
  }
23
  if (!Double.isFinite(lon) || (lon < MIN_LON) || (lon > MAX_LON))
  {
      throw new IllegalArgumentException("Longitude value is out of range [" +
                                         Double.toString(MIN_LON) + ", " +
                                         Double.toString(MAX_LON) + "]");
  }
30
  int xyTilesCount = (int)Math.pow(2, z);
  int x = (int) Math.floor((lon + 180.0) / 360.0 * xyTilesCount);
  int y = (int) Math.floor((1.0 - Math.log(Math.tan(lat * Math.PI / 180.0) + 1.0 / Math.cos(lat * Math.PI / 180.0)) / Math.PI) / 2.0 * xyTilesCount);
34
  return Integer.toString(z) + "/" + Integer.toString(x) + "/" + Integer.toString(y);
36}

Convert tile z/x/y coordinates to latitude/longitude coordinates.

	Tile coordinates		Result
		Convert

Tile z/x/y to latitude/longitude

Select...

1function tileZXYToLatLon(zoomLevel, x, y) {
const MIN_ZOOM_LEVEL = 0
const MAX_ZOOM_LEVEL = 22
4
if (
  zoomLevel == undefined ||
  isNaN(zoomLevel) ||
  zoomLevel < MIN_ZOOM_LEVEL ||
  zoomLevel > MAX_ZOOM_LEVEL
) {
  throw new Error(
    "Zoom level value is out of range [" +
      MIN_ZOOM_LEVEL.toString() +
      "," +
      MAX_ZOOM_LEVEL.toString() +
      "]"
  )
}
19
let z = Math.trunc(zoomLevel)
let minXY = 0
let maxXY = Math.pow(2, z) - 1
23
if (x == undefined || isNaN(x) || x < minXY || x > maxXY) {
  throw new Error(
    "Tile x value is out of range [" +
      minXY.toString() +
      "," +
      maxXY.toString() +
      "]"
  )
}
33
if (y == undefined || isNaN(y) || y < minXY || y > maxXY) {
  throw new Error(
    "Tile y value is out of range [" +
      minXY.toString() +
      "," +
      maxXY.toString() +
      "]"
  )
}
43
let lon = (x / Math.pow(2, z)) * 360.0 - 180.0
45
let n = Math.PI - (2.0 * Math.PI * y) / Math.pow(2, z)
let lat = (180.0 / Math.PI) * Math.atan(0.5 * (Math.exp(n) - Math.exp(-n)))
48
return lat.toString() + "/" + lon.toString()
50}

1public static String  tileZXYToLatLon(int z, int x, int y)
2{
  final int MIN_ZOOM_LEVEL = 0;
  final int MAX_ZOOM_LEVEL = 22;
5
  if ((z < MIN_ZOOM_LEVEL) || (z > MAX_ZOOM_LEVEL))
  {
      throw new IllegalArgumentException("Zoom level value is out of range [" +
                                         Integer.toString(MIN_ZOOM_LEVEL) + ", " +
                                         Integer.toString(MAX_ZOOM_LEVEL) + "]");
  }
12
  int minXY = 0;
  int maxXY = (int)(Math.pow(2, z) - 1);
  if ((x < minXY) || (x > maxXY))
  {
      throw new IllegalArgumentException("Tile x value is out of range [" +
                                         Integer.toString(minXY) + ", " +
                                         Integer.toString(maxXY) + "]");
  }
21
  if ((y < 0) || (y > maxXY))
  {
      throw new IllegalArgumentException("Tile y value is out of range [" +
                                         Integer.toString(minXY) + ", " +
                                         Integer.toString(maxXY) + "]");
  }
28
  double lon = (double)x / Math.pow(2, z) * 360.0 - 180.0;
30
  double n = Math.PI - 2.0 * Math.PI * (double)y / Math.pow(2, z);
  double lat = 180.0 / Math.PI * Math.atan(0.5 * (Math.exp(n) - Math.exp(-n)));
33
  return Double.toString(lat) + "/" + Double.toString(lon);
35}

Convert tile z/x/y coordinates to latitude/longitude bounding box.

	Tile coordinates		Result
		Convert

Tile z/x/y to latitude/longitude bounding box

Select...

1function tileZXYToLatLonBBox(zoomLevel, x, y) {
const MIN_ZOOM_LEVEL = 0
const MAX_ZOOM_LEVEL = 22
4
if (
  zoomLevel == undefined ||
  isNaN(zoomLevel) ||
  zoomLevel < MIN_ZOOM_LEVEL ||
  zoomLevel > MAX_ZOOM_LEVEL
) {
  throw new Error(
    "Zoom level value is out of range [" +
      MIN_ZOOM_LEVEL.toString() +
      "," +
      MAX_ZOOM_LEVEL.toString() +
      "]"
  )
}
19
let z = Math.trunc(zoomLevel)
let minXY = 0
let maxXY = Math.pow(2, z) - 1
23
if (x == undefined || isNaN(x) || x < minXY || x > maxXY) {
  throw new Error(
    "Tile x value is out of range [" +
      minXY.toString() +
      "," +
      maxXY.toString() +
      "]"
  )
}
33
if (y == undefined || isNaN(y) || y < minXY || y > maxXY) {
  throw new Error(
    "Tile y value is out of range [" +
      minXY.toString() +
      "," +
      maxXY.toString() +
      "]"
  )
}
43
let lon1 = (x / Math.pow(2, z)) * 360.0 - 180.0
45
let n1 = Math.PI - (2.0 * Math.PI * y) / Math.pow(2, z)
let lat1 = (180.0 / Math.PI) * Math.atan(0.5 * (Math.exp(n1) - Math.exp(-n1)))
48
let lon2 = ((x + 1) / Math.pow(2, z)) * 360.0 - 180.0
50
let n2 = Math.PI - (2.0 * Math.PI * (y + 1)) / Math.pow(2, z)
let lat2 = (180.0 / Math.PI) * Math.atan(0.5 * (Math.exp(n2) - Math.exp(-n2)))
53
return (
  lat1.toString() +
  "/" +
  lon1.toString() +
  "/" +
  lat2.toString() +
  "/" +
  lon2.toString()
)
63}

1std::string tileZXYToLatLonBBox(unsigned int z, unsigned int x, unsigned int y)
2{
constexpr unsigned int MAX_ZOOM_LEVEL = 22;
if (z > MAX_ZOOM_LEVEL)
{
  throw std::invalid_argument("Zoom level value is out of range [0, " +
                              std::to_string(MAX_ZOOM_LEVEL) + "]");
}
9
const long maxXY = (1 << z) - 1;
if (x > maxXY)
{
  throw std::invalid_argument("Tile x value is out of range [0, " +
                             std::to_string(maxXY) + "]");
}
16
if (y > maxXY)
{
  throw std::invalid_argument("Tile y value is out of range [0, " +
                              std::to_string(maxXY) + "]");
}
22
const int xyTilesCount = 1 << z;
const double lon1 = static_cast<double>(x) / xyTilesCount * 360.0 - 180.0;
25
const double n1 = M_PI - 2.0 * M_PI * static_cast<double>(y) / xyTilesCount;
const double lat1 = 180.0 / M_PI * atan(0.5 * (exp(n1) - exp(-n1)));
28
const double lon2 = static_cast<double>(x + 1) / xyTilesCount * 360.0 - 180.0;
30
const double n2 = M_PI - 2.0 * M_PI * static_cast<double>(y + 1) / xyTilesCount;
const double lat2 = 180.0 / M_PI * atan(0.5 * (exp(n2) - exp(-n2)));
33
return std::to_string(lat1) + "/" + std::to_string(lon1) + "/" + std::to_string(lat2) + "/" + std::to_string(lon2);
35}

1public static String  tileZXYToLatLonBBox(int z, int x, int y)
2{
  final int MIN_ZOOM_LEVEL = 0;
  final int MAX_ZOOM_LEVEL = 22;
5
  if ((z < MIN_ZOOM_LEVEL) || (z > MAX_ZOOM_LEVEL))
  {
      throw new IllegalArgumentException("Zoom level value is out of range [" +
                                         Integer.toString(MIN_ZOOM_LEVEL) + ", " +
                                         Integer.toString(MAX_ZOOM_LEVEL) + "]");
  }
12
  int minXY = 0;
  int maxXY = (int)(Math.pow(2, z) - 1);
  if ((x < minXY) || (x > maxXY))
  {
      throw new IllegalArgumentException("Tile x value is out of range [" +
                                         Integer.toString(minXY) + ", " +
                                         Integer.toString(maxXY) + "]");
  }
21
  if ((y < 0) || (y > maxXY))
  {
      throw new IllegalArgumentException("Tile y value is out of range [" +
                                         Integer.toString(minXY) + ", " +
                                         Integer.toString(maxXY) + "]");
  }
28
  double lon1 = (double)x / Math.pow(2, z) * 360.0 - 180.0;
30
  double n1 = Math.PI - 2.0 * Math.PI * (double)y / Math.pow(2, z);
  double lat1 = 180.0 / Math.PI * Math.atan(0.5 * (Math.exp(n1) - Math.exp(-n1)));
33
  double lon2 = (double)(x + 1) / Math.pow(2, z) * 360.0 - 180.0;
35
  double n2 = Math.PI - 2.0 * Math.PI * (double)(y + 1) / Math.pow(2, z);
  double lat2 = 180.0 / Math.PI * Math.atan(0.5 * (Math.exp(n2) - Math.exp(-n2)));
38
  return Double.toString(lat1) + "/" + Double.toString(lon1) + "/" + Double.toString(lat2) + "/" + Double.toString(lon2);
40}