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Leaflet - Calculate zoom level from radius in meters

I'm trying to find a way to calculate zoom level given a radius in meters.

For example, I want to show 100km radius within point x,y, how do I calculate the proper zoom level for that point?

Solution

  • This will depend on:

    • the number of tiles of your map
    • the latitude of your view

    The resolution (meters/pixel) of a web-Mercator map at zoom 0 (one tile for the whole map) is given by:

    resolution = cos(latitude_rad) * earth circumference / tile width

    with the latitude in radians, the earth circumference in meters (2 * pi * radius) and the map width given by:

    map width = 256 as the tiles are 256 pixel wide.

    At each zoom step, the width (in pixel) is doubled, so at zoom z: map width = 256*2^zoom

    so :

    resolution=cos(latitude_rad) * 2*pi* 6371008 / (256*2^zoom)

    but as you are using a certain number n of 256 pixel tiles:

    widthmap = cos(latitude_rad) * 2*pi* 6371008*n / (2^zoom)

    Now, to get the zoom from the distance:

    with latitude in degrees, radius is your circle in meters, and n the number of tiles to display:

    zoom = floor(log2 ((cos(latitude *pi/180) * 2*pi* 6371008*n)/radius))

    (floor as you want an integer and to make sure your whole circle is on the map)

    For example, at 45 degrees N/S, 100m and 1 tile will give you a zoom of 18.