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Cartopics > Scale and measuring from maps

What is scale and why do we use it?

When we want to draw something to represent the Earth’s surface, it is not possible to show features at their full size. Therefore when we draw maps we ’scale’ things down so that a section of the Earth can be shown on a smaller area, such as a piece of paper or computer screen, with all the features still in proportion.
The scale of a map tells us the relationship between distances on the map and those on the ground. This makes the map more useful to us as we can apply the map to the real world by visualising what the map represents, and use the map effectively by taking measurements from it to calculate ground distances.

How do we show scale?

There are three main ways to represent scale, varying in simplicity and usefulness.
  • A representative fraction (RF) gives the relationship between one unit on the map and the number of ground units that one unit on the map represents. For example 1:100 000 means that 1 cm on the map shows 100 000 cm on the ground (1 km). This is a versatile method to use as it is possible to apply the fraction to any unit — centimetres, inches, feet, miles — even hand spans! However, it is not always easy to interpret as it can be hard to visualise 100 000 inches and, although this method allows for accurate calculation of distances, it can be laboured and complicated to convert it to a useful and understandable figure.
  • A map will sometimes carry a word statement (or statement of equivalency) such as ‘one inch to one mile’, meaning that one inch on the map shows one mile on the ground. This is a clear and concise statement which is easy to understand and helps the user to get an overall comprehension of distances without any calculations. However this is not always practical, as you may want to use different units or take more precise measurements than the unit shown. For example, you would need to know the relationship between inches and centimetres of you wanted to know a distance on a map in centimetres rather than inches.
One problem which can occur when using both of these types of scale representation is that, if the user wishes to scale the map up or down (using a photocopier for example), the stated map scale will be rendered useless as the map dimensions will have changed whilst the words or numbers have stayed the same. For example, a map of 1:100 000 scale would become 1: 50 000 if photocopied at 200%.
  • In order to avoid this a graphic scale bar can be used, which is a visual representation of the distances shown on a map. A line or block is divided up into equal sections which are numbered to show what distance that length is representing.
    scale bar
    A simple graphic scale bar

    There are many different forms of scale bar which vary from a straightforward, simple one as shown above, to more detailed bars with smaller divisions, allowing for more precise measuring. Many scale bars show both metric and imperial units, so are helpful to a wider user group.
    When this form of scale representation is shown on a map, it can be reduced or enlarged and its meaning and usefulness will stay the same. This is a simple, easy-to-use method which makes it easy to visualise and estimate distances on the map. However, depending on the number and size of divisions on the scale bar, it can be difficult to measure exact distances, particularly on small-scale maps.
Small or large scale?

It can be confusing to try to describe a map as large or small scale. A large-scale map shows a small area at a high level of detail, and as a general rule has an RF of between 1:1 (actual size) and 1:50 000. A small-scale map depicts a larger area so therefore cannot show as much detail. These are generally thought of as 1:50 000 or higher. A plan is a form of map which shows details of buildings, boundaries and roads, etc. with minimum use of symbols and with each object in its correct place, instead of using generalisation necessary in smaller-scale maps whereby objects are simplified and symbols used to represent them.

How do we use scale to measure from maps?

When measuring distances on a map, it is common to use a ruler, but this is obviously only useful for measuring straight lines. When measuring curved lines such as along a road it is possible to use a piece of string to mark the distance and then measure along the string with a ruler. You can also use a ‘map measurer’ with a small wheel linked by gears to a dial from which distances can be read.
To use an RF, the initial calculation is quite simple: Take the measurement from the map and multiply it by the fraction’s denominator. For example, you measure a distance on a map of scale 1:100 000 as being 4cm. 4 cm multiplied by 100 000 equals 400 000 cm (or 4 km since there are 100 000 cms in a km). However, these calculations are not always so simple when using unusual scale figures or units that are not multiples of ten, such as inches.
When using a word statement, taking measurements can be quite simple as the units described can be directly converted. For example, if a map states its scale as ‘one inch to one mile’, two inches would show two miles, three inches three miles and so on. However, if you wished to work in centimetres, it would be necessary to calculate the RF from the statement, so you would need to know that one mile equals 63 360 inches, therefore making the RF 1:63 360.
The easiest way to measure from a map is probably to use a scale bar. Once the distance has been measured on the map, the same distance can be measured along the scale bar to give the ground distance. No calculations are needed, but if the scale bar is not very detailed, the result may not be very accurate.

author:
Anna Thompson
Cartographic Editor, AA Publishing

Further reading:
Robinson, A.H. et al (1995), Elements of Cartography (6th ed.), New York and Chichester, John Wiley and Sons.
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