Understanding Map Scale: The Case of 40 Kilometres Represented by 10 Centimetres

Maps are essential tools used in various fields such as geography, navigation, and urban planning. One of the fundamental concepts in map-making is scale, which is the relationship between distances on the map and actual distances on the ground. In this article, we will explore a specific example of how to determine the scale of a map when a known distance on the ground is represented by a specific distance on the map. Specifically, we will calculate the scale of a map where 40 kilometres on the ground is represented by 10 centimetres on the map.

What is Map Scale?

Map scale can be defined as the ratio between a unit of length on the map and the corresponding unit of length on the ground. This ratio can be expressed as a fraction (1:n), a word statement (1 inch to 1 mile), or as a graphic scale bar (e.g., 1 cm on the map equals 1 kilometer on the ground).

Calculating the Scale

Let us begin by understanding the formula used to calculate the scale:

Scale Distance on map / Distance on ground

In this particular scenario, the distance on the map is 10 centimetres, and the distance on the ground is 40 kilometres.

Stepwise Calculation

Convert the distance on the ground from kilometres to centimetres:

40 km 40,000 meters (since 1 km 1000 meters)

40,000 meters * 100 centimetres/meter 4,000,000 centimetres

Substitute the values into the scale formula:

Scale 10 cm / 4,000,000 cm 1 / 400,000

Express the scale in a more readable format:

The scale is 1:400,000, which means that 1 centimetre on the map represents 400,000 centimetres (or 4 kilometres) on the ground.

Interpreting the Scale

The scale of 1:400,000 can also be interpreted in different ways:

Option 1: 40 km / 10 cm on the map

If you rearrange the relationship, it becomes:

40 km on the ground is represented by 10 centimetres on the map. Therefore, the scale is:

40 km / 10 cm 4 km / 1 cm

This means that 4 kilometres on the ground are represented by 1 centimetre on the map.

Option 2: Keeping the same units for simplicity

Using the same units, the scale can be expressed as:

1 cm on the map: 400,000 cm on the ground, which is equivalent to 4 km on the ground.

Conclusion

Understanding map scale is crucial for accurate representation and interpretation of geographical data. The example of 40 kilometres on the ground being represented by 10 centimetres on a map leads to a scale of 1:400,000. This scale indicates that every 1 centimetre on the map corresponds to 4 kilometres on the ground, providing a reliable reference for geographical and navigational purposes.