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I'm having trouble understanding the meaning of the concept of scale when it comes to maps on screen, i.e. either in a Desktop GIS or in a WebMap.

When it comes to paper maps, the idea is very clear. The Scale is the ratio of a particular distance on the map, to the same distance on the ground.

But when it comes to maps on screen, the same concept cannot be applied. Firstly different screens do not have the same pixel size. It might be that a 14 inch monitor and a 24 inch monitor could have the same resolution (in terms of pixels). Then comes the issue of dpi. An iOS device with retina display has a dpi several times that of my work-station monitor. So 1 cm on my screen might show a different distance than 1 cm on your screen.

So what does the scale of a map in digital cartography mean? What does it mean, when I see the scale of a map is 1:180,000 in ArcMap?


Aside
This question came about because of several ArcMap Documents I received from a client who publishes paper maps.
The paper map is published at 1:180,000, but at that scale the map looks terrible. It's only when I zoom in, does the map look good. With trial and error, I found that the map looks best on screen at about 3 times the scale, i.e. at 1:60,000

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2 Answers

ArcMap assumes a logical DPI of 96 for the purposes of calculating and displaying scale, so you are right in that holding a ruler up to your screen and attempting to perform measurements based on that scale would in all likelihood be incorrect, unless your monitor is actually 96 DPI (physical DPI) and you are using its native resolution.

I am not sure if this is a common assumption for other mapping platforms, but I did find a ScreenDpi property in the ArcGIS Web ADF documentation with an interesting, if somewhat unclear, explanation:

This is the dots per inch (dpi) assumed as the screen resolution. Used for calculating the correct scale thresholds for scale dependent elements such as ScaleDependentRenderer, Layer, and AcetateElement.

The default is 96 dots (or pixels) per inch. Note that with the higher resolutions of screens common today, this figure is probably incorrect. In this case, scale thresholds, such as when a layer becomes visible as users zoom in or out, will not occur at precisely the scale set in a MinScale or MaxScale property. This is most noticeable when the computer image is projected onto a large screen, when scales are obviously distorted from the nominal values.

Tip: on Windows computers, the screen DPI can be adjusted with the Display Properties dialog, accessible by right-clicking on the desktop. On the Settings tab, click the Advanced button. In the advanced dialog, in the General tab, the drop-down list for DPI setting allows setting a custom DPI for the screen by comparison with a physical ruler. Note that setting to a non-default number may cause text and layout issues with some programs, especially Web pages.

The Wikipedia articles on DPI and PPI have some good background information as well.

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Just to add to that, remember that most web maps are using Web Mercator which obviously causes extreme distortions at the poles therefore the scale bar on most web maps is adjusted to show the scale at the centre of the current view rather than anywhere that you can see on the map. –  ChrisInCambo May 24 '13 at 1:51
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The concept of scale in web mapping has no real meaning, as blah238 writes it's meant to imitate scale on paper maps, ie.that you can measure your map on-screen with a ruler and then convert to "real life distance". ArcMap assumes 96 DPI, OpenLayers assumes 72 DPI (by default), so on screens with these resolutions you might be in the ballpark when using a ruler. But try on a Smartphone screen (or a retina screen) and you will be way off.

So, the morale is: try avoiding showing the user scale numbers, use a scale bar or more generic terms, such as "street level", "city level" etc. And, when creating scale dependent style rules, be aware of the possible error and check your results

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