The scale of a nautical chart is a way to convert inches on paper to inches in the real world. Chart scales are expressed as ratios (1:100,000 for example), so the unit of measure does not matter. On a chart whose scale is 1:100,000, one inch on paper represents 100,000 inches in the real world. Also, one foot on paper represents 100,000 feet, and one meter represents 100 kilometers.

Typical nautical chart scales range from 1:2,000 (sometimes referred to as “Berthing-scale” or a “Berthing chart”) to 1:10,000,000 (“Planning-scale”). Between these extremes, charts can be collected into groups like these: Harbor, Approach, Coastal, General, and Overview.

When comparing one scale to another, the “larger” scale
chart is the one with the smaller number following the colon. This may seem
counterintuitive, but it’s because the scale ratio is like a fraction. At
1:100,000 scale, the image on the chart is 1/100,000^{th} the size of
the area it represents. A 1:2,000 scale chart is 1/2,000^{th} the size.
Since 1/100,000^{th} is smaller than 1/2,000^{th}, the second
chart is at a larger scale than the first.

## The Mercator Projection

In 1569, Belgian geographer and cartographer Gerardus Mercator devised a way to convert the spherical, three-dimensional surface of the earth into a rectangular, two-dimensional map. This conversion—or “projection”—is called the Mercator projection. It became the standard map projection for nautical charts because routes following an unchanging compass bearing are straight, and therefore are easy to plot on the chart.

One limitation to the Mercator projection is that it cannot represent the North or South poles. In fact, any latitudes above 85° are very difficult to represent. This is because vertical scale (the scale of true North-South lines) increases further from the equator, and becomes infinite at the poles; horizontal scale (the scale of true East-West lines) stays constant. A scale of 1:infinity is impossible to accomplish because one inch on paper would represent an infinite number of inches in the real world. At a latitude of 85°N, one inch horizontally (East-West) covers the same distance as nearly 12 inches vertically (North-South). At 60°N, that ratio drops to two inches vertically for every one inch horizontally. At 37°N, it’s just 1 ¼ inches up to match one inch over.

Charts covering the poles and very high latitudes typically use the Gnomonic projection. With the Gnomonic projection, any straight line drawn on the map is on a great circle—that is, straight lines will follow a ring around the globe, like the equator. Directions are true only from the center point of projection, which makes plotting routes on a Gnomonic chart tricky. Scale increases very rapidly as the distance away from the center point of the chart increases. Also, distortion of shapes and areas increases away from the center point.

## Calculating Distance

Ships sail routes made up of segments following a particular compass bearing. These segments are called loxodromes, or, more commonly, rhumb lines. Scale is key in determining the distance between two points on a chart along a (straight) rhumb line.

Suppose ship will sail from the Port of Boston to the Port of Sines in Portugal using NGA Chart 120 (Nort Atlantic Ocean, Southern Sheet). The ship will take a route along a single rhumb line plotted from one port to the other. That line, when plotted on NGA Chart 120, is 83.76cm long. The chart’s scale is 1:6,331,100. Multiplying 83.76 by 6,331,100 equals 530,292,936. So, 83.76cm on paper represents 530,292,936cm in the real world. Converting to more relevant units, 530,292,936cm is 5,302,929 meters, or 5,303km.