Map Control: Zoom Levels -> Resolution

A common question we get is, "What is the resolution or scale at a particular zoom level in Virtual Earth or Windows Live Local?"  Well, that is actually a little more complex of answer than you might expect.  We use Mercator projection across the maps in the Virtual Earth Map Control so they can be be cut up into image tiles for quick delivery to clients and reliable stitching back together of the images.  But, because it is a cylindrical projection, the map gets distorted as you approach the poles--just look at Antarctica to see the effect.  So, we measure the effective resolution at the equator where there is the least distortion.  

The resolution at the equator for each zoom level (see this earlier post to find your current zoom level in Windows Live Local):

Meters/Pixel Zoom Level
78271.52 1
39135.76 2
19567.88 3
9783.94 4
4891.97 5
2445.98 6
1222.99 7
611.50 8
305.75 9
152.87 10
76.44 11
38.22 12
19.11 13
9.55 14
4.78 15
2.39 16
1.19 17
0.60 18
0.30 19

How did we arrive at these seemingly convoluted numbers? Well, honestly, we picked a view that we thought looked good at one of the closest zoom levels bottom and then just did some math to generate the rest--hence the kind of wacky numbers at higher zoom levels.

But, remember I said it was complicated? Well to get the resolution where you are looking on the map, you actually have to do some quick math as it varies by latitude. To get the resolution where you are:

Map resolution = 156543.04 meters/pixel * cos(latitude) / (2 ^ zoomlevel)

But, what about Scale--this is just resolution?

For you cartographers or junior explorers out there, who think not in resolution but in map scale ratios, you can do a little more math to convery it correctly.  To convert the map resolution into scale, you need to know (or assume) the screen resolution.  Then the formula becomes:

Map scale = 1 : (ScreenRes pixels/inch * 39.37 inches/meter * 156543.04 meters/pixel * cos(latitude * pi/180) / (2 ^ zoomlevel))

For example, assuming a ScreenRes of 100 pixels/inch, the map scale at level 10 and latitude 40 degrees is:

Map scale = 1 : (100 pixels/inch * 39.37 inches/meter * 156543.04 meters/pixel * cos(40 * pi/180) / (2 ^ 10))
Map scale = 1 : (100 * 39.37 * 156543.04 * 0.766 / 1024)
Map scale = 1 : 461028.73

You can thank Joe, a Tech Lead on Virtual Earth, for the excellent explanation.

Comments (8)

  1. We are happy to announce the availability of version 3 of the Virtual Earth Map Control.  This exciting…

  2. bradser says:

    Comment:  I think the "* pi/180" is missing from the Map resolution calculation.

    Question:  Isn’t the map resolution above the east-west resolution?  Shouldn’t the north-south resolution be constant?  If so, do you just do away with the cos multiplication altogether?

  3. joesch says:

    On the comment, you’re right — it should be cos(latitude * pi/180).

    On the question, the map resolution applies to both the X and Y axes (east-west and north-south).  In the Mercator projection, the X and Y scale factors are always equal.

    It’s true that the number of meters per degree is constant in the north-south direction, but in the Mercator projection, the number of meters per pixel varies with the latitude, in both the north-south and east-west directions.  See for an illustration with grid lines.

  4. We are happy to announce the availability of version 3 of the Virtual Earth Map Control. This exciting

  5. jpelak says:


    Are there any API calls on VE available or planned to provide zoom level -> meters/pixel@equator values?  I’m hardcoding(!) this table into a mapping app now – would much rather get this from you.



  6. jpelak says:

    resolved my own question…

    this works great – many thanks for the post!

  7. While the MapPoint Web Service SDK is highly cool and nice and lightweight, I gotten lots of requests

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