Map scale

A real town is very, very big.

A map of the town fits on one sheet of paper. Everything is made smaller by the same amount. The scale tells you how much smaller.

A map is a small model of a big place. To fit a whole town, country or even the world onto a page or a screen, the mapmaker shrinks everything by the same amount, so the distances between places stay in the right proportion.

The map's scale tells you how much it has been shrunk. Ordnance Survey, Britain's national mapping agency, explains it like this: the scale shows how much you would have to enlarge your map to get the actual size of the land. Once you know the scale, you can use the map to work out real distances.

National Geographic describes maps as scaled-down models of places: whatever a map's size, the distances between points are, relative to the map, intended as accurate representations of real distances. The relationship between map distance and ground distance is the map's scale, expressed by visual scales and by representative fractions.

Ordnance Survey frames scale as the amount by which you would have to enlarge the map to reach the land's actual size. That makes scale a ratio, not a unit: it works the same in centimeters, inches or any other measure. Understanding scale lets a reader turn a measurement on paper into a distance on the ground, compare maps of different kinds, and choose the right map for a walk, a drive or a study of a whole continent.

Some maps write their scale as numbers, like 1 : 25,000.

It means 1 step on the map is the same as 25,000 steps in real life. That is a lot of shrinking!

Many maps write their scale as a ratio, such as 1:25,000. It means that 1 unit on the map stands for 25,000 of the same units on the ground. So 1 centimeter on the map is 25,000 centimeters in real life, which is 250 meters.

The ratio works with any unit. On a 1:1,000,000 map, 1 centimeter stands for 1,000,000 centimeters, or 10 kilometers. On a 1:50,000 map, 1 inch stands for 50,000 inches, a little more than three-quarters of a mile.

A representative fraction states scale as a ratio that is independent of units. National Geographic's examples: at 1:1,000,000, one centimeter on the map represents 1,000,000 centimeters on Earth, or 10 kilometers; at 1:50,000, one inch represents 50,000 inches, just over three-quarters of a mile. Ordnance Survey's example: at 1:25 000, every 1 cm represents 25,000 cm, or 250 m.

Converting is a matter of multiplying and changing units: 25,000 cm ÷ 100 = 250 m, and 50,000 in ÷ 63,360 in per mile ≈ 0.79 mile. Because the units cancel, the same 1:25,000 map can be read in centimeters or inches; only the conversion to meters, feet or miles changes. A larger second number means each map unit stands for more ground, so the map shows more area in less detail.

Many maps have a scale bar. It looks like a little ruler.

Measure between two places with a piece of string. Then hold the string against the scale bar to see how far apart they really are.

The most common kind of drawn scale is a bar scale, which looks like a ruler printed on the map. Its marks stand for real distances, such as kilometers or miles. Ordnance Survey's walking maps even write the scale out for you: "4 cm to 1 km," and their grid lines are exactly 4 centimeters apart, so each grid square is 1 kilometer across.

To measure a distance, lay a piece of thin string between two places. For a straight line, "as the crow flies," stretch it tight. To follow a winding road, bend the string along the road. Then hold the string against the scale bar to read the real distance.

A bar scale is a horizontal line marked in uniform increments that represent kilometers, miles or other distances, so a ruler measurement on the map converts directly into ground distance (National Geographic). Ordnance Survey prints the scale of its 1:25 000 maps as "4 cm to 1 km" and spaces its grid lines exactly 4 cm apart, making every grid square 1 km by 1 km; its 1:50 000 maps are 2 cm to 1 km.

Ordnance Survey's method for measuring distance distinguishes a straight line, as the crow flies, from a winding route such as a country lane: lay thin string along the route, bending it to follow every curve, mark the length, then lay the string against the scale bar, which is usually at the foot of the sheet.

A map of your street shows lots of things, like houses and paths.

A map of the whole world shows much less. Each map is good for a different job.

Here is a puzzle: a map of your neighborhood is called a large-scale map, and a map of the whole world is a small-scale map. That seems backward! It is because on a neighborhood map, things like houses and roads appear relatively large. On a world map, everything appears small.

Different scales suit different jobs. Ordnance Survey says its 1:25,000 maps are very useful for walking, but if you used one in a car you would quickly drive off the edge. Maps at 1:250,000 (note the extra zero) show much more land, in far less detail.

National Geographic explains that the size of the area depicted, not the size of the paper, determines how a scale is described. A map showing a place in great detail, such as a neighborhood street map, is a large-scale map, because objects appear relatively large; a map of a continent or the world is a small-scale map, because objects appear small. In ratio terms, 1:25,000 is a larger scale than 1:250,000, because 1/25,000 is the larger fraction.

Ordnance Survey ties scale to purpose: its 1:25 000 maps are very useful for walking, while 1:250 000 maps show much more land in far less detail. USGS draws the same line for U.S. mapping: maps at 1:24,000 show an area in detail useful for engineering and local planning; 1:50,000 to 1:100,000 maps cover larger areas for land management; and 1:250,000 to 1:1,000,000 maps cover very large areas for regional and statewide planning.

In the United States, many detailed maps have a scale of 1 to 24,000.

One inch on these maps is the same as 2,000 feet on the ground. That is a long way to walk!

The U.S. Geological Survey (USGS) has been the United States' main civilian mapping agency since 1879. Its best-known maps, called 7.5-minute quadrangles, are drawn at a scale of 1:24,000. One inch on them equals 24,000 inches, or 2,000 feet, on the ground. In Alaska, these maps use 1:25,000.

USGS makes maps at smaller scales too. At 1:100,000, 1 centimeter equals 1 kilometer. At 1:250,000, 1 inch is about 4 miles, and at 1:1,000,000, 1 inch is about 16 miles.

USGS 7.5-minute topographic maps, the primary series since 1947, are bounded by 7.5 minutes of latitude and longitude and, for the contiguous 48 states and Hawaii, published at 1:24,000: one inch equals 24,000 inches, or 2,000 feet. Alaska's 7.5-minute maps use 1:25,000. A USGS 1994 guide lists further series: 1:50,000 (1 cm = 0.5 km) and 1:100,000 (1 cm = 1 km) for land management, and 1:250,000 (1 inch ≈ 4 miles), 1:500,000 (≈ 8 miles) and 1:1,000,000 (≈ 16 miles) for regional and statewide planning.

The arithmetic checks out: 24,000 in ÷ 12 = 2,000 ft; 250,000 in ÷ 63,360 ≈ 3.95 mi; 1,000,000 in ÷ 63,360 ≈ 15.8 mi. USGS also notes that scale interacts with projection: its large-scale 1:24,000 maps, drawn on the Transverse Mercator, are nearly correct in every respect, while a small-scale world map on the Mercator shows extreme distortion at high latitudes. Since 2009, USGS has produced computer-generated US Topo maps from national databases.

When you zoom in on a map on a phone, the scale changes.

Zoom out, and you see the whole world. Zoom in, and you see your own street. The screen stays the same size!

Digital maps on phones and computers let you zoom in and out, and every zoom changes the map's scale. Looking at the whole world, you are viewing a small-scale map. Zoom all the way in to your hometown, and it becomes a large-scale map, even though the screen is the same size.

Globes have a scale too. Because the whole Earth must fit on a ball, even the largest globe has a very small scale and shows only a little detail. So a globe cannot show small things like the streets of your town.

National Geographic points out that zooming a digital map changes its scale: a phone showing the whole world displays a small-scale map, and zooming to a hometown turns it into a large-scale map while the screen stays the same size.

Scale also limits globes. USGS lists among the globe's disadvantages that even the largest globe has a very small scale and shows relatively little detail. Scale, projection and purpose therefore work together: a small-scale world map must pick a projection and accept distortion, while a large-scale map of a small area, such as a USGS 1:24,000 quadrangle, can be nearly true in every respect.