the ratio between map distance and ground distance is called
Map Scale: Ratio Between Map Distance and Ground Distance
1. What is Map Scale?
A map represents a part of the Earth’s surface on a much smaller size. Therefore, it is necessary to know how much the real distance has been reduced. This relationship between map distance and actual ground distance is called map scale.
Before calculating the scale, map distance and ground distance must normally be converted into the same unit.
2. Why is Scale Important?
Scale is an essential element of a map because it allows us to calculate the actual distance between places shown on the map.
- It helps calculate ground distance.
- It helps calculate map distance.
- It allows comparison between map distance and real distance.
- It helps in measuring distances between two places.
- It is useful in geographical and surveying work.
- It helps us understand the amount of reduction used to prepare a map.
3. Basic Relationship Between Map and Ground Distance
For example, if the scale is 1 : 100,000, then one unit on the map represents 100,000 of the same units on the ground.
Therefore:
- 1 cm on map = 100,000 cm on ground
- 2 cm on map = 200,000 cm on ground
- 5 cm on map = 500,000 cm on ground
Since 100,000 cm = 1 km:
4. Numerator and Denominator in Map Scale
In a Representative Fraction such as 1 : 50,000, the first number is the numerator and the second number is the denominator.
| Part | Meaning | Example |
|---|---|---|
| Numerator | Map distance | 1 |
| Denominator | Ground distance in the same unit | 50,000 |
5. Three Main Methods of Showing Scale
Scale can be expressed in three major ways:
- Statement of Scale
- Representative Fraction (R.F.)
- Graphical or Bar Scale
6. Statement of Scale
In the statement method, the relationship between map distance and ground distance is written in words.
1 cm represents 10 km.
This means that every 1 cm measured on the map represents 10 km on the actual ground.
Another Example
1 inch represents 10 miles
This means 1 inch on the map represents 10 miles on the ground.
7. Advantages and Limitation of Statement Scale
- It is simple to understand.
- It is easy for beginners.
- The relationship is directly written in words.
- It can be expressed in metric or English units.
- However, it can become inconvenient if the map is enlarged or reduced.
- People unfamiliar with the particular measurement system may find it difficult.
8. Representative Fraction (R.F.)
Representative Fraction is a numerical method of expressing map scale. It represents the relationship between map distance and corresponding ground distance using the same units.
For example:
This means 1 unit on the map represents 24,000 of the same units on the ground.
- 1 cm → 24,000 cm
- 1 mm → 24,000 mm
- 1 inch → 24,000 inches
9. Why is R.F. Called a Universal Method?
R.F. is considered a versatile or universal method because it does not depend on a particular named unit in the ratio.
For example:
1 : 36,000
This can be interpreted using centimetres, inches or another unit, provided the same unit is used on both sides.
10. Converting R.F. into Statement of Scale
Example 1: Convert 1 : 36,000 into a metric statement.
1 : 36,000 means:
1 unit on map = 36,000 units on ground
Take the unit as centimetre:
1 cm = 36,000 cm
Since:
100 cm = 1 metre
Therefore:
36,000 ÷ 100 = 360 metres
11. Example: Convert 1 : 100,000 into Statement Scale
Given:
R.F. = 1 : 100,000
Therefore:
1 cm = 100,000 cm
We know:
100,000 cm = 1 km
12. Converting Statement Scale into R.F.
Example: 1 cm represents 10 km
First convert 10 km into centimetres.
1 km = 100,000 cm
Therefore:
10 km = 1,000,000 cm
Thus:
1 cm : 1,000,000 cm
13. Important Unit Conversions
- 1 kilometre = 1,000 metres
- 1 metre = 100 centimetres
- 1 centimetre = 10 millimetres
- 1 kilometre = 100,000 centimetres
- 1 mile = 8 furlongs
- 1 furlong = 220 yards
- 1 yard = 3 feet
- 1 foot = 12 inches
14. Finding Ground Distance from Map Distance
Example
Map scale = 1 : 50,000
Map distance = 4 cm
Ground distance:
4 × 50,000 = 200,000 cm
Convert into kilometres:
200,000 ÷ 100,000 = 2 km
15. Finding Map Distance from Ground Distance
Example
Scale = 1 : 100,000
Ground distance = 8 km
Convert 8 km into cm:
8 × 100,000 = 800,000 cm
Map distance:
800,000 ÷ 100,000 = 8 cm
16. Finding Scale When Both Distances Are Given
Example
A road measures 5 cm on a map and its actual ground distance is 10 km. Find the R.F.
Convert 10 km into cm:
10 × 100,000 = 1,000,000 cm
Therefore:
R.F. = 5 / 1,000,000
Divide both terms by 5:
17. Graphical or Bar Scale
A graphical scale represents map distance and ground distance using a line divided into equal sections. Each section is assigned a particular ground distance.
The main advantage of a graphical scale is that it remains useful when the map is enlarged or reduced proportionally.
18. Example of a Graphical Scale
Suppose the map has an R.F. of:
1 : 50,000
This means:
1 cm = 50,000 cm
Since 100,000 cm = 1 km:
1 cm = 0.5 km
Therefore:
10 cm = 5 km
19. Large Scale and Small Scale Maps
| Large Scale | Small Scale |
|---|---|
| Shows a relatively small area | Shows a relatively large area |
| More detail | Less detail |
| Example: 1 : 10,000 | Example: 1 : 10,000,000 |
| Useful for local areas | Useful for large regions |
20. Important Rule to Remember
Always convert map distance and ground distance into the same unit before calculating R.F.
For example, do not directly write:
5 cm : 10 km
Instead convert 10 km into centimetres first.
21. Solved Question 1
Question: A map has a scale of 1 : 50,000. If the distance between two villages on the map is 6 cm, calculate their actual ground distance.
Solution:
Ground distance = 6 × 50,000
= 300,000 cm
= 3 km
22. Solved Question 2
Question: On a map with a scale of 1 : 100,000, the distance between two towns is 12 cm. Find the actual distance.
12 × 100,000 = 1,200,000 cm
1,200,000 ÷ 100,000 = 12 km
23. Solved Question 3
Question: The actual distance between two places is 15 km. If the map scale is 1 : 100,000, find the distance between them on the map.
15 km = 15 × 100,000 cm
= 1,500,000 cm
Map distance = 1,500,000 ÷ 100,000
24. Solved Question 4
Question: A distance of 4 cm on a map represents 8 km on the ground. Find the R.F.
8 km = 800,000 cm
R.F. = 4 : 800,000
Divide both sides by 4:
25. Solved Question 5
Question: Convert the statement scale “1 cm represents 5 km” into R.F.
5 km = 500,000 cm
Therefore:
1 cm : 500,000 cm
26. Solved Question 6
Question: Convert R.F. 1 : 200,000 into a statement of scale in kilometres.
1 cm = 200,000 cm
200,000 cm = 2 km
27. Practice Questions
28. Multiple Choice Questions
Q1. Which method of scale is expressed as a ratio?
A. Statement Scale
B. Representative Fraction
C. Graphical Scale
D. Verbal Scale
Q2. What does 1 : 100,000 mean?
A. 1 unit map distance = 100 units ground distance
B. 1 unit map distance = 1,000 units ground distance
C. 1 unit map distance = 100,000 units ground distance
D. 100,000 units map distance = 1 unit ground distance
Q3. Which method uses a line divided into sections?
A. Statement Scale
B. R.F.
C. Graphical Scale
D. Fraction Scale
Q4. 1 km is equal to how many metres?
A. 10
B. 100
C. 1,000
D. 10,000
Q5. 1 metre is equal to:
A. 10 cm
B. 100 cm
C. 1,000 cm
D. 10,000 cm
29. Important Formulas for Exams
30. Quick Revision
- Scale shows the relationship between map distance and ground distance.
- There are three major methods of expressing scale.
- Statement Scale expresses scale in words.
- R.F. expresses scale as a ratio.
- Graphical Scale uses a line or bar.
- In R.F., numerator represents map distance.
- The denominator represents corresponding ground distance in the same unit.
- Always convert units before calculating R.F.
- 1 km = 100,000 cm.
- Graphical scale remains useful when a map is enlarged or reduced proportionally.