How do map scales show the relationship between a map and real distances on the ground?

In cartography, map scale defines the relationship between the size of a representation on a map and the actual size of the corresponding area on the ground. This relationship is typically expressed in three primary ways:1

• Representative Fraction or Ratio: This expresses the scale as a fraction (e.g., 1/63,360) or a ratio (e.g., 1:63,360), indicating that one unit of measurement on the map equals a specific number of the same units on the Earth's surface.12
• Verbal Scale: This describes the relationship in words, such as "one-inch-to-one-mile," meaning one inch on the map represents one mile on the ground.1
• Linear or Bar Scale: Most maps include a graphic bar scale in the margins or title blocks, allowing users to measure distances directly on the map and compare them to the ground distance.1

It is important to note that a larger denominator indicates a smaller scale; for example, 1:1,000,000 is a smaller scale than 1:100,000. While linear scales are most common, areal scales may occasionally be used, where the denominator is the square of the linear scale's denominator.1