Measuring Distance and Area from a map.

Calculating distance from a map scale

Suppose we have a map with a scale of 1:50,000. We measure the distance along a boundary line as 2.6 cm. What is the length this represents?

We multiply the distance measured on the map by the inverted Representative Fraction (RF).

Thus: 2.6 cm. * 50,000/1 = 130,000 cm.

Centimetres are not a very useful unit for real world measurements of this size so we can convert the result to Kilometres by dividing by 100,000 (number of centimetres in a kilometre) This gives us a real world measurement of 1.3 Km.

If the map scale is not expressed as an RF it would help to be able to convert the scale to an RF. To convert the verbal scale of (say) “One inch to a mile” to a representative fraction the working would be as follows:

1 mile = 1,760 yards = (1,760 * 36) inches = 63360 inches

So the RF would be 1:63360

Calculating Area from a map scale

This works in a similar way to calculating linear measurement but you have to square some of the numbers.

Suppose we have a rectangular plot that measures 3cm. by 4 cm. on a map with a scale of 1:25000

We could work like this: 3cm * 4cm = 12 cm² = area on map

12 cm² * (25,000/ 1)² / (100)² = area on the ground

Thus we have multiplied the area on the map by the square of the RF and (in this instance) divided the resulting area by the number of square centimetres in a square metre as this would be a better unit for real world use.

The calculation then proceeds:

12 * (625,000,000) / (10,000) = 750,000 square metres.

If you live in Europe you would probably divide that result again by 10,000 and express the result in hectares (75 ha).

Determining the area of rectangles from a map is a relatively straightforward task. More complex polygons may need to be simplified and broken down into triangles and rectangles. The area for each individual element could then be calculated and the sum totalled.

Our own AditSite program has the capacity to measure the area of a complex polygon on a map. The accuracy is dependent upon a number of factors such as scale and the range of normal distortions of cartography but the results are usually accurate enough to provide a useful guide to the program users.