GeographyCBSE Class 11 · Map Scale

Map Scale, Representative Fraction and Conversion (Class 11 Practical Work in Geography, Chapter 2)

Updated 17 October 2026 · Fact-checked

A map scale is the ratio of a distance on the map to the corresponding distance on the ground. It can be given as a statement of scale, a graphical (bar) scale or a representative fraction (R.F.), which has no units and is universal. To convert, bring both distances to the same unit; R.F. 1:253,440 equals 1 cm to 2.53 km.

Understand Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales

Why this topic matters. Conversion sums and the merits and limits of the three methods are standard practical-exam questions.

1. Meaning. A scale is the ratio of map distance to ground distance between the same two points. In 1:50,000 the numerator (1) is the map distance and the denominator (50,000) the ground distance in the same units. A drawing without a scale is only a sketch.

2. Units. Metric: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm (used in India and many countries). English: 12 inches = 1 foot, 3 feet = 1 yard, 220 yards = 1 furlong, 8 furlongs = 1 mile (used in the USA and UK and in India before 1957). Derived: 1 km = 100,000 cm; 1 mile = 63,360 inches; 1 furlong = 7,920 inches; 1 yard = 36 inches.

3. Statement of scale. For example 1 cm represents 10 km. Simplest, but unclear to users of the other system and wrong once the map is reduced or enlarged.

4. Graphical (bar) scale. A line with primary and secondary divisions. It can be read only in the units shown, but it stays valid when the map is reduced or enlarged.

5. Representative fraction. For example 1:24,000. It has no units, so it is universal: for 1:36,000 a metric user reads 1 cm = 360 m and an English user 1 inch = 1,000 yards (36,000 / 36). By convention it is read in cm or inches.

6. Statement to R.F. Convert the ground distance to the unit of the map distance, then drop the units. 1 inch represents 4 miles: 4 x 63,360 = 253,440 inches, so 1:253,440. If the map distance is not 1, divide: 2 cm represents 5 km, so 1 cm represents 2.5 km = 250,000 cm, giving 1:250,000.

7. R.F. to statement. Read the units as cm and convert. 1:253,440 means 1 cm represents 253,440 / 100,000 = 2.5344 km, about 2.53 km. Into miles divide by 63,360 (inches); into furlongs by 7,920; into yards by 36; into metres by 100.

8. Checklist. Same units on both sides; numerator is 1; round sensibly.

Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales: key facts

Metric units: $1 k m = 1, 000 m ∣1 m = 100 c m ∣1 c m = 10 mm ∣1 k m = 100, 000 c m$; Used in India.
English units: $1 mi l e = 8 f u r l o n g s ∣1 f u r l o n g = 220 y a r d s ∣1 y a r d = 3 f ee t ∣1 f oo t = 12 in c h es ∣1 mi l e = 63, 360 in c h es$; Used in USA and UK.
Statement to R.F.: $G r o u n dd i s t an ce inma p - d i s t an ce u ni t s d i v i d e d b y ma p d i s t an ce ∣ e . g .1 in c h t o 4 mi l es = 4 x 63, 360 = 1 : 253, 440$; Drop the units.
R.F. to statement: $D e n o mina t or in c m d i v i d e d b y 100, 000 g i v es k m p er c m ∣1 : 253, 440 = 2.53 k m p er c m$; Convert the ground units.

How to answer Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales questions

Conversion sums are solved by making the units equal.

1Write the given statement or R.F.
2Convert the ground distance to the same unit as the map distance.
3Make the map distance 1 by dividing both sides if needed.
4Write the answer as 1:n (no units) or as a statement with units, rounded sensibly.

Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Zoomed photocopy

Suppose a map with the statement "1 cm represents 10 km" is photocopied at half its linear size.

Why does the statement become wrong while a bar scale stays right?

Try it first, then show the solutionSolution

The 1 cm on the copy now stands for 20 km.
The bar scale is reduced along with the map, so it still gives the right ground distance.

Answer: The statement no longer fits; the bar scale remains valid.

Memory hook: Bar shrinks with the map.

Foreign tourist

Suppose a tourist who uses miles receives a map whose scale is given only as "1 cm to 36,000 cm".

Why is R.F. helpful here?

Try it first, then show the solutionSolution

R.F. has no units.
The tourist can read it in inches as well: 1 inch = 1,000 yards.

Answer: R.F. is universal and works in either system.

Memory hook: Fraction speaks every language.

Tricks to remember Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales

Short memory aids. Say each one aloud once, then use it on a question the same day.

63,360
Inches in a mile: 8 x 220 x 3 x 12
Use it when: English to inches.
100,000
Centimetres in a km
Use it when: Metric.
Same unit, then drop
Make units equal then remove them
Use it when: R.F.

Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: R.F. meaning · 1 mark · MCQBoard level

In the R.F. 1:50,000, the number 50,000 stands for:
(A) map distance in cm
(B) ground distance in the same units as the map distance
(C) the number of villages
(D) metres per inch

Try it first, then show the solutionSolution

Ground distance in the same units as the map distance (1 mark).

Answer: (B)

Example 2: Statement to R.F. · 2 marks · Very short answerBoard level

Convert "1 cm represents 2 km" into an R.F. (2 marks)

Try it first, then show the solutionSolution

2 km = 2 x 100,000 = 200,000 cm (1 mark).
R.F. = 1:200,000 (1 mark).

Answer: 2 km = 200,000 cm, so the R.F. is 1:200,000.

Example 3: English to R.F. · 3 marks · Short answerHarder board level

Convert "1 inch represents 5 miles" to an R.F. (3 marks)

Try it first, then show the solutionSolution

1 mile = 63,360 inches (1 mark).
5 miles = 5 x 63,360 = 316,800 inches (1 mark).
R.F. = 1:316,800 (1 mark).

Answer: 5 miles = 5 x 63,360 = 316,800 inches, so 1 inch on the map represents 316,800 inches on the ground and the R.F. is 1:316,800.

Example 4: Assertion and reason: bar scale · 1 mark · Assertion-reasonHarder board level

Assertion (A): A bar scale remains correct when a map is photocopied at a smaller size.
Reason (R): The bar scale is reduced in the same proportion as the map.
(A) Both true, R explains A
(B) Both true, R does not explain A
(C) A true, R false
(D) A false, R true

Try it first, then show the solutionSolution

The bar shrinks with the map, so distances read from it stay right (1 mark).

Answer: (A)

Example 5: HOTS: R.F. to ground distance · 5 marks · Long answerHOTS / competency

On a map of R.F. 1:125,000 the distance between two towns measures 7.2 cm. Find the ground distance in km, express the scale as a statement in km per cm and in miles per inch (to two decimals), and say what happens to the R.F. if the map is reduced to half its linear size. (5 marks)

Try it first, then show the solutionSolution

1 cm = 125,000 cm = 1.25 km, so 1 cm represents 1.25 km (1 mark).
7.2 x 1.25 = 9 km (1 mark).
1 inch = 125,000 inches = 125,000 / 63,360 = 1.97 miles (1 mark).
Half-size map: 1 cm now stands for twice the distance (1 mark).
So R.F. becomes 1:250,000 (1 mark).

Answer: 1 cm represents 125,000 cm = 1.25 km. The ground distance is 7.2 x 1.25 = 9 km. In English units, 1 inch represents 125,000 inches = 125,000 / 63,360 = about 1.97 miles. If the map is reduced to half its linear size, each centimetre stands for twice the ground distance, so the R.F. becomes 1:250,000.

Where students lose marks in Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales

The slips examiners see most often, and what to write instead.

Mistake: Not converting to the same units
Writing 1 cm to 5 km as 1:5.
Wrong working
R.F. = 1:5.
Right working
5 km = 500,000 cm, so R.F. = 1:500,000.
Do this: Make units equal first.
Usually costs: 1 mark.
Mistake: Leaving units in the R.F.
Habit of writing units.
Wrong working
R.F. = 1:50,000 cm.
Right working
R.F. has no units: 1:50,000.
Do this: Drop the units.
Usually costs: 1 mark.
Mistake: Using 1 mile = 5,280 inches
Feet confused with inches.
Wrong working
1 mile = 5,280 inches.
Right working
1 mile = 63,360 inches (5,280 feet).
Do this: Multiply by 12.
Usually costs: 1 mark.

Exam tips

Write the units on both sides before cancelling.
Show the conversion chain (e.g. miles to inches).
Round to two decimals when asked.

Practice questions on Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
How many inches are there in one mile?
(A) 12,000
(B) 36,000
(C) 63,360
(D) 100,000
Hint
8 x 220 x 3 x 12.
Answer
(C)
Q2 · 2 marks · Very short answerBoard level
Convert R.F. 1:100,000 into a statement of scale in km per cm. (2 marks)
Hint
100,000 cm in 1 km.
Answer
100,000 cm = 1 km, so 1 cm represents 1 km.
Q3 · 3 marks · Short answerHarder board level
State two advantages of the R.F. over a statement of scale. (3 marks)
Hint
Units, universality.
Answer
The R.F. has no units, so it can be read in any system of measurement and is universal; it also does not depend on the language or the unit system of the user. A statement of scale in miles is not understood by metric users and becomes redundant when the map is reduced or enlarged.
Q4 · 3 marks · Short answerHarder board level
Convert "2.5 cm represents 4 km" into an R.F. (3 marks)
Hint
Make the map distance 1.
Answer
4 km = 400,000 cm. 400,000 / 2.5 = 160,000 cm for 1 cm. So the R.F. is 1:160,000.
Q5 · 4 marks · Short answerHOTS / competency
A map shows two towns 9 cm apart and the ground distance is 13.5 km. Find the R.F. and the statement of scale in km per cm, and the distance for 5.6 cm on the same map. (4 marks)
Hint
Ground over map.
Answer
13.5 km = 1,350,000 cm. 1,350,000 / 9 = 150,000, so R.F. = 1:150,000 and 1 cm represents 1.5 km. For 5.6 cm the ground distance is 5.6 x 1.5 = 8.4 km.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.What are the three methods of showing scale?Show answer
Statement, bar scale and R.F.
2.Which method is universal?Show answer
Representative fraction.
3.Inches in a yard?Show answer
36.
4.When did India stop using the English system?Show answer
After 1957 (used before 1957).

Map Scale: Meaning, Systems of Measurement, Three Methods and Converting Between Scales: frequently asked questions

Does the R.F. change when a map is enlarged?

Yes; the numerator stays 1 but the denominator becomes smaller.

Is 1:50,000 a large or small scale?

Larger than 1:250,000, so it is a large-scale topographical scale.

What is the denominator called?

The ground distance in the same units as the map distance.