Map Projections: Properties: Preserving Distances

Map Projections

Useful Map Properties: Distances and Scale

Can Distances be Accurately Measured?

Scale constrast across an equidistant cylindrical map

In this equidistant cylindrical map, all arrow lines have the same length; however, actual world distances (measured in km) between the ends of each arrow vary enormously. The included graphical scale (blue) is only useful along the Equator and meridians (where scale is constant, for this projection at least); also, only along those lines each arrow actually follows a straight route on Earth.

Any practical map shrinks Earth features down to a manageable size. The general rate of reduction is called a scale, and frequently a small "ruler" superimposed on the map eases distance evaluation. For instance, on a 1:100000-scale map, two points separated by 1 unit could represent two cities actually 100000 units apart. With a scale 10 times "larger" - 1:10000 - the same two cities would appear separated by 10 units on the map (therefore, if the same region is presented in different maps, smaller-scale versions can be more portable but probably less precise and detailed).

However, only a true globe would allow a similar conclusion for any pair of points on its surface. In flat maps, most likely the scale will not be constant, changing with direction and location. As a result, although useful for rough estimation, scaling rulers and numeric ratios are misleading except in very large scales or, conversely, small mapped areas (more elaborate small-scale maps have a set of rulers and guides for their use).


On the map on the left, the center C of the blue cross looks 41% farther from the tips (like B) of the red line than from its center D. Actually, every point on the line is equally far from the cross. Distance between A and B is actually zero, since both lie on a pole. The map on the right puts those facts in a better perspective, in more than one sense.

Actually, there is another reason why distances across a map can deceive the unwary reader: the shortest distance between two points on a sphere is rarely represented by a straight line on a map.

Lines (straight or not) in the map with constant scale and length proportional to corresponding lines on Earth are called standard lines. Map projections with a well-defined, nontrivial set of standard lines are sometimes called equidistant.


In a Sanson-Flamsteed equatorial map, all parallels are standard lines: if segment A is twice the length of B, corresponding lines on Earth follow the same proportion. Although the straight vertical distances between parallels follow this rule, distances along meridians do not, except for the central one.	In this cylindrical equidistant map, only vertical lines and the Equator preserve a constant scale. Since all parallels are equally long in the map, horizontal scale increases quickly towards the top and bottom, reaching infinity at the poles.

An azimuthal equidistant map preserves distances along any lines through the central point. This important projection must be custom-made for every location of interest.	The cordiform Werner projection also has standard lines radiating from the center. In addition, every arc centered in that point is also a standard line.