GeographyCBSE Class 11 · Chapter 2

Map Scale, Class 11 Practical Work in Geography

Updated 15 October 2026 · Fact-checked

Not in the CBSE annual exam course structure. Assessed in the 30-mark practical exam (25-mark written test, practical file 3, viva 2), not in the theory paper.

Map Scale is Chapter 2 of NCERT Practical Work in Geography Part I for Class 11. It explains what a map scale is, the metric and English systems of measurement, the three methods of showing scale (statement, representative fraction and graphical or bar scale) with their merits and limits, and how to convert scales and construct bar scales.

What Map Scale is about

Assessment: this chapter carries 4 marks in the 30-mark practical exam (written test, practical file and viva); it is not in the theory paper.

What is scale? A map scale gives the relationship between the map and the earth's surface shown on it: the ratio of the distance between two points on the map to the distance between the same points on the ground. A drawing without a scale is only a sketch.

Two systems of measurement (Box 2.1): metric (1 km = 1,000 m; 1 m = 100 cm; 1 cm = 10 mm), used in India and many countries; English (12 inches to a foot, 3 feet to a yard, 220 yards to a furlong, 8 furlongs to a mile), used in the USA and UK, and in India before 1957.

Three methods:
1. Statement of scale (e.g. '1 cm represents 10 km'): simplest, but not understood by users of the other system, and becomes wrong if the map is reduced or enlarged.
2. Graphical (bar) scale: a line with primary and secondary divisions; read only in the units shown, but stays valid when the map is reduced or enlarged (its unique advantage).
3. Representative fraction (R.F.), e.g. 1:24,000: one unit on the map = 24,000 of the same units on the ground; it has no units, so it is universal and the most versatile.

Skills: converting statement to R.F. and R.F. to statement, and constructing bar scales (by convention about 15 cm for metric and about 6 inches for English scales, choosing a round number of ground units).

Key concepts

Meaning of scale; numerator and denominator

NCERT section Map Scale (introduction)

A scale bar with equal divisions marked in km or miles lets you find ground distances on a map.
A map scale gives the relationship between the map and the area it shows: 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) is the ground distance, in the same units.
Representative Fraction (glossary): a scale written as a fraction: one unit of map distance compared with the matching ground distance measured in that same unit.
The scale decides how much detail a map can show (Chapter 1).

Worked example

In the R.F. 1:20,000, what do the numerator and denominator represent? Express the scale as a statement in metres. (2 marks)

Try it first, then show the solutionSolution

Numerator 1 = map distance; denominator 20,000 = ground distance in the same units.
1 cm represents 20,000 cm = 20,000 ÷ 100 = 200 m.

Answer: 1 cm represents 200 m.

Systems of measurement

NCERT section Map Scale (introduction)

Metric system	English system
1 km = 1,000 m	1 mile = 8 furlongs
1 m = 100 cm	1 furlong = 220 yards
1 cm = 10 mm	1 yard = 3 feet
-	1 foot = 12 inches
Used in India and many other countries	Used in the USA and the UK; India used it before 1957

Useful derived values (from Box 2.1):

1 km = 100,000 cm
1 mile = 8 × 220 × 3 × 12 = 63,360 inches
1 furlong = 220 × 36 = 7,920 inches
1 yard = 36 inches

Worked example

Show that one mile contains 63,360 inches, using Box 2.1. (2 marks)

Try it first, then show the solutionSolution

1 mile = 8 furlongs = 8 × 220 = 1,760 yards.
1,760 yards × 3 feet × 12 inches = 1,760 × 36 = 63,360 inches.

Answer: 63,360 inches.

Three methods of scale: merits and limits

NCERT section Methods of Scale

Method	Example	Advantages	Limitations
Statement of scale	1 cm represents 10 km; 1 inch represents 10 miles	Simplest	Users of the other system may not understand it; becomes redundant if the map is reduced or enlarged
Graphical (bar) scale	A line with primary and secondary divisions read in km and m (or miles and furlongs)	Stays valid when the map is reduced or enlarged (unique advantage)	Read only in the units shown, so restricted to those who understand them
Representative fraction	1:24,000	Expressed in units, not a particular system, so universal and most versatile	Users must convert to their own units

Why R.F. is universal (NCERT example): take 1:36,000. A metric user reads 1 cm = 36,000 cm = 360 m; an English user reads 1 inch = 36,000 inches = 36,000 ÷ 36 = 1,000 yards. By convention, R.F. units are read as centimetres or inches.

Worked example

A map with the statement '1 cm represents 10 km' is photocopied at half its size. What does 1 cm now represent, and which scale method would have avoided the problem? (2 marks)

Try it first, then show the solutionSolution

Every distance on the copy is halved, so 1 cm on the copy covers what 2 cm covered before: 1 cm now represents 20 km; the printed statement is wrong.
A graphical (bar) scale shrinks with the map, so it stays valid.

Answer: 1 cm represents 20 km; a bar scale would remain correct.

Conversion of scale

NCERT section Conversion of Scale

Statement → R.F.: convert the ground distance into the same unit as the map distance, then drop the units.

NCERT example: 1 inch represents 4 miles → 4 × 63,360 = 253,440 inches → R.F. 1:253,440.
If the map distance is not 1, divide: e.g. 2 cm represents 5 km → 1 cm represents 2.5 km = 250,000 cm → 1:250,000.

R.F. → statement: read the units as cm (or inches), then convert the ground units.

NCERT example: 1:253,440 → 1 cm represents 253,440 ÷ 100,000 = 2.5344 km ≈ 2.53 km.
Into miles: divide by 63,360; into furlongs: divide by 7,920; into yards: divide by 36; into metres: divide by 100.

Checklist: same units on both sides; numerator must be 1; round sensibly (two decimals).

Worked example

Convert 'one inch represents three miles' into an R.F. (2 marks)

Try it first, then show the solutionSolution

3 miles = 3 × 63,360 = 190,080 inches.
1 inch represents 190,080 inches, so R.F. = 1:190,080.

Answer: 1:190,080.

Constructing a graphical (bar) scale

NCERT section Conversion of Scale

Method (NCERT Problem 1: 1:50,000 in km and m):
1. By convention take a line of about 15 cm (metric) or 6 inches (English).
2. Find the ground distance it represents: 15 × 50,000 ÷ 100,000 = 7.5 km.
3. Choose a round number near it (5 or 10 km); NCERT takes 5 km.
4. Find the line for the round number: 15 × 5 ÷ 7.5 = 10 cm.
5. Draw 10 cm, divide into 5 primary divisions of 1 km; number 0 at the end of the first (left) division, then 1, 2, 3, 4 km to the right.
6. Divide the left division into 10 secondary divisions of 100 m each (or 2, 4 or 5 parts of 500, 250 or 200 m), numbered leftward from 0.

English example (NCERT Problem 2): 1 inch represents 1 mile → 6 inches = 6 miles; divide into 6 parts; the left part into 4 (or 8) for furlongs (as printed, labelled from 0).

Dividing an awkward length (NCERT Problem 3): for 1:50,000 in miles, 6 inches = 4.73 miles; for a round 5 miles the line is 6.34 inches. To divide such a line into 5 equal parts: draw lines at about 40° or 45° from both ends, mark 5 equal steps (1 or 1.5 inches) on them, join corresponding marks with dotted lines, and mark where they cross the scale line (Figure 2.4).

Worked example

Find the length of line needed for a bar scale of 1:40,000 reading in km, using the 15 cm convention. (2 marks)

Try it first, then show the solutionSolution

15 cm represents 15 × 40,000 ÷ 100,000 = 6 km, already a round number.
So draw a 15 cm line divided into 6 primary parts of 2.5 cm (1 km each), with the left part subdivided into 10 parts of 100 m.

Answer: 15 cm line for 6 km; 2.5 cm per km.

Map Scale in real life

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

Statement to R.F.

Suppose a trekking map says 'two centimetres represent five kilometres' and your friend from abroad wants the scale in a form any user can read.

Convert it to an R.F. and say why the R.F. is better for your friend. (2 marks)

Try it first, then show the solutionSolution

1 cm represents 2.5 km = 2.5 × 100,000 = 250,000 cm, so R.F. = 1:250,000.
An R.F. has no units, so anyone (metric or English) can read it in their own units: it is universal.

Answer: 1:250,000; it is unit-free and universal.

Memory hook: No units, no confusion.

R.F. to statement in English units

Imagine an old British-era map of your district printed at 1:63,360.

Express its scale in miles per inch and in km per cm. (2 marks)

Try it first, then show the solutionSolution

1 inch represents 63,360 inches = 63,360 ÷ 63,360 = 1 mile: 'one inch to a mile'.
1 cm represents 63,360 cm = 63,360 ÷ 100,000 ≈ 0.63 km.

Answer: 1 inch represents 1 mile; 1 cm represents about 0.63 km.

Memory hook: 63,360: the inch-to-a-mile number.

Constructing a bar scale

Suppose you must add a bar scale in km to a 1:25,000 map for your practical file.

Work out the length of line and divisions. (3 marks)

Try it first, then show the solutionSolution

15 cm represents 15 × 25,000 ÷ 100,000 = 3.75 km, not a round number.
Choose 3 km: line = 15 × 3 ÷ 3.75 = 12 cm, so 1 km = 4 cm.
Draw 12 cm, 3 primary divisions of 4 cm (1 km each, 0 after the first), and divide the left one into 10 parts of 100 m.

Answer: A 12 cm bar: 3 divisions of 1 km (4 cm each), left one in 100 m steps.

Memory hook: Fifteen first, then round, then rescale.

Topics in this chapter

Map Scale: key facts

Scale: $S c a l e = ma p d i s t an ce : g r o u n dd i s t an ce (s am e u ni t s)$; Numerator = map distance; denominator = ground distance.
Metric conversions: $1 k m = 1, 000 m = 100, 000 c m; 1 m = 100 c m; 1 c m = 10 mm$; Divide the denominator by 100,000 to get km per cm.
English conversions: $1 mi l e = 8 f u r l o n g s = 1, 760 y a r d s = 63, 360 in c h es; 1 f u r l o n g = 7, 920 in c h es; 1 y a r d = 36 in c h es$; Divide by 63,360 for miles per inch.
Statement to R.F.: $R . F . = 1 : (g r o u n dd i s t an ce inma p u ni t s \div ma p d i s t an ce)$; 1 inch = 4 miles → 1:253,440.
R.F. to statement: $G r o u n d p er ma p u ni t = d e n o mina t or \div u ni t f a c t or$; 1:253,440 → 1 cm = 2.53 km.
Bar scale length: $L in e = (r o u n d g r o u n dd i s t an ce \div g r o u n dd i s t an ceo f 15 c m) \times 15 c m$; 1:50,000: 7.5 km per 15 cm → 5 km = 10 cm.
Map reduction: $N e w k m p er c m = o l d k m p er c m \div r e d u c t i o n f a c t or$; Halving a map doubles the ground distance per cm; bar scale stays valid.

Map Scale: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

Graphical (bar) scale for 1:50,000 (Figure 2.2)

Practical exam construction question.

Draw

A straight line 10 cm long with a thin parallel line above to make a bar.
Five primary divisions of 2 cm.
The leftmost division split into 10 secondary divisions of 2 mm.
Numbers: 0 at the end of the first division; 1, 2, 3, 4 km to the right; 100 to 1,000 m to the left.

Label

R.F. 1:50,000
Kilometres (primary)
Metres (secondary)
0
1 km
4 km

Watch out: Write the R.F. and the units above the bar; the zero is not at the left end.

Dividing a line into equal parts (Figure 2.4)

When the bar length is not a whole number (e.g. 6.34 inches).

Draw

The scale line AB.
A line from A at about 45° above, and a parallel line from B below.
Equal steps marked on both slanting lines.
Dotted lines joining matching steps, crossing AB.

Label

A
B
Equal steps
Intersection points = equal divisions

Watch out: Use a set square to keep the joining lines parallel.

Tricks to remember Map Scale

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

Three methods
'Say, Read, Draw': Statement (say it), R.F. (read the ratio), Graphical (draw it).
Use it when: Methods of scale.
Which survives resizing?
'Bar bends with the map': only the bar scale stays valid when the map is reduced or enlarged.
Use it when: Merits question.
English chain
'8-220-3-12': miles to furlongs to yards to feet to inches.
Use it when: Box 2.1 conversions.
Key numbers
'100,000 cm in a km; 63,360 inches in a mile'.
Use it when: All conversions.

Where students lose marks in Map Scale

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

Mistake: Mixing units in the R.F.
Students leave km on one side and cm on the other.
Wrong working
1 cm represents 5 km → R.F. 1:5.
Right working
5 km = 500,000 cm → R.F. 1:500,000.
Do this: Convert to the same unit before dropping units.
Usually costs: Full marks for the conversion.
Mistake: Forgetting to make the numerator 1
Statements like '3 cm represents 12 km'.
Wrong working
R.F. 3:1,200,000.
Right working
1 cm represents 4 km = 400,000 cm → 1:400,000.
Do this: Divide both sides by the map distance first.
Usually costs: Half the marks.
Mistake: Starting the bar scale's zero at the left end
Copying a ruler.
Wrong working
0 written at the far left of the bar.
Right working
0 is at the end of the first (left) primary division; secondary divisions are numbered leftward from it.
Do this: Zero after the first block.
Usually costs: Marks in construction.
Mistake: Using the wrong number of inches in a mile
Memory slip.
Wrong working
1 mile = 63,630 inches.
Right working
1 mile = 63,360 inches (1,760 yards × 36).
Do this: Rebuild it from Box 2.1 if unsure.
Usually costs: Marks in English-system conversions.

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.Which method of scale can a metric user and an English user both read directly in their own units?Show answer
The representative fraction (it has no units, so it is universal).
2.In 1:50,000, which number stands for the ground distance?Show answer
The denominator, 50,000 (the numerator 1 is the map distance).
3.What is the unique advantage of the graphical scale?Show answer
It stays valid when the map is reduced or enlarged.
4.Until when did India use the English system?Show answer
Before 1957.
5.How many yards are in a furlong?Show answer
220.
6.What length of line is conventionally taken for a metric bar scale?Show answer
About 15 cm.
7.Convert 1:36,000 into yards per inch.Show answer
1 inch represents 1,000 yards.

Best order to study it

Learn the meaning of scale, numerator and denominator.
Learn Box 2.1 and derive 100,000 cm per km and 63,360 inches per mile.
Learn the three methods with their advantages and limitations.
Practise statement-R.F. conversions both ways in both systems.
Construct metric and English bar scales, including dividing an awkward line.

Quick revision checklist

The night before the exam: can you do each of these without looking?

Practical exam chapter: 4 marks.
Scale = ratio of map distance to ground distance; numerator = map, denominator = ground.
Metric: 1 km = 100,000 cm. English: 1 mile = 63,360 in; 1 furlong = 7,920 in; 1 yard = 36 in.
Statement: simplest; fails on resizing and across systems.
Bar scale: survives resizing; unit-specific.
R.F.: unit-free, universal (1:36,000 = 360 m per cm = 1,000 yards per inch).
1 inch = 4 miles → 1:253,440 → 1 cm = 2.53 km.
Bar scale: 15 cm (or 6 in) → ground value → round number → rescale line → primary and secondary divisions.

Map Scale: frequently asked questions

Is Map Scale in the Class 11 theory paper?

No. It is part of Practical Work in Geography Part I, assessed in the 30-mark practical exam, where this chapter carries 4 marks.

Why is R.F. called a universal method?

Because it expresses the ratio in units, not in a particular system, so a metric user reads it in cm and an English user in inches, each converting to their own statement of scale.

Why choose a round number when drawing a bar scale?

So the divisions read easily (e.g. 1 km or 1 mile each); NCERT finds the ground distance for about 15 cm, picks a nearby round value, and recalculates the line length.

What happens to a statement of scale if a map is enlarged?

It becomes wrong: every distance grows, so a new scale must be worked out; a bar scale enlarges with the map and stays correct.

Based on: CBSE Geography (029) syllabus 2026-27 (Classes XI-XII); NCERT Practical Work in Geography Part I, Class XI, Chapter 2 (Reprint 2026-27)