Map scale

On a 1:25,000 map, 4 centimetres of paper stand for exactly 1 kilometre of ground.

Three ways to write a scale

No map can be as large as the land it shows, so every map is a reduction, and the scale tells you by how much. There are three common ways to write it. A ratio or representative fraction, such as 1:25,000, says that one unit on the map stands for 25,000 of the same unit on the ground. It works in any unit: one centimetre for 25,000 centimetres, or one inch for 25,000 inches. A verbal scale says it in words, such as one inch to one mile. A scale bar is a ruler printed on the map, marked in kilometres or miles.

The ratio is easiest to calculate with if you turn it into a convenient sentence. At 1:25,000, one centimetre on the map is 25,000 centimetres on the ground. There are 100 centimetres in a metre, so that is 250 metres. Four centimetres then make 1,000 metres, one kilometre. At 1:50,000, one centimetre is 500 metres and two centimetres make a kilometre. The USGS standard scale is 1:24,000, chosen because in inches it divides neatly: one inch on the map is 24,000 inches, which is exactly 2,000 feet.

Large scale, small scale

Map makers call 1:25,000 a larger scale than 1:250,000, which sounds backwards until you read the ratio as a fraction. One twenty-five-thousandth is a bigger number than one two-hundred-fifty-thousandth, and a house drawn at the larger scale is ten times wider on paper. Large-scale maps cover small areas in detail. The USGS notes that its 1:24,000 maps can show schools, cemeteries, campgrounds, ski lifts and even fence lines. Small-scale maps cover large areas and have to leave most of that out.

Korea’s national topographic maps are published at 1:5,000, 1:25,000 and 1:50,000, among other scales. The USGS series includes 1:24,000 (one inch to 2,000 feet), 1:63,360 for Alaska (one inch to exactly one mile, since a mile has 63,360 inches), 1:100,000 (about 1.6 miles per inch) and 1:250,000 (about 4 miles per inch). Notice that the USGS writes "about" for the last two. Only scales that divide neatly into the units you use give round numbers.

Why the scale bar survives a photocopier

In the scene the model land is 4 kilometres wide, and the scale bar in the corner of the map is drawn to match whatever size the map has on your screen. Set A and B at the two ends of one grid square and the distance should read close to 500 metres. Then try to place B exactly 1.5 kilometres from A along a grid line, using only the scale bar and your eye.