GeographyCBSE Class 11 · Map Scale

Constructing a Graphical (Bar) Scale (Class 11 Practical Work in Geography, Chapter 2)

Updated 17 October 2026 · Fact-checked

To construct a bar scale, take a line about 15 cm (metric) or 6 inches (English), find the ground distance it represents, pick a nearby round number, recompute the line length, divide it into primary divisions, and divide the first (left) division into secondary divisions, with zero at the end of the first division.

Zero sits at the right end of the first division; whole km are numbered rightwards and the left division is cut into 100 m secondary parts.

Illustration drawn for QuestionBuddy.

Understand Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems

Why this topic matters. Constructing a bar scale for a given R.F. is a certain practical-paper task; marks go for correct arithmetic, neat divisions and correct labelling.

1. Convention. A metric scale is drawn on a line of about 15 cm and an English scale on about 6 inches. Choose a round number of ground units close to what that length represents.

2. Method (R.F. 1:50,000 in km and m).
(i) Line of about 15 cm. (ii) Ground distance = 15 x 50,000 / 100,000 = 7.5 km. (iii) Take a round number near it, 5 km. (iv) Length of line for 5 km = 15 x 5 / 7.5 = 10 cm. (v) Draw 10 cm and divide it into 5 primary divisions each representing 1 km. Put 0 at the end of the first (left) division and number 1, 2, 3, 4 km to the right. (vi) 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.

3. English example. 1 inch represents 1 mile: 6 inches represent 6 miles; divide into 6 primary parts, then the left part into furlong divisions.

4. Awkward lengths. If the line for a round number comes out as, say, 6.34 inches (as in 1:50,000 for 5 miles), divide it into equal parts by drawing lines at about 40 or 45 degrees from both ends, marking equal steps on them, and joining corresponding marks with dotted lines whose crossings on the scale line give the divisions.

5. Reading a scale. Place a divider or paper edge on two points, then lay it along the bar to read the distance; whole kilometres are read on the primary divisions and the remainder on the secondary divisions to the left of zero.

6. Why the bar scale matters. It stays valid when the map is reduced or enlarged, which is its unique advantage.

Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems: key facts

Ground distance of a line: $G r o u n dd i s t an ce = l in e l e n g t h x d e n o mina t or /100, 000∣ I nk m w h e n t h e l e n g t hi s in c m$; e.g. 15 x 50,000 / 100,000 = 7.5 km.
Length for a round number: $L in e l e n g t h = 15 x r o u n dd i s t an ce / g r o u n dd i s t an ceo f 15 c m ∣ S am e u ni t s f or b o t h d i s t an ces$; e.g. 15 x 5 / 7.5 = 10 cm.
Division: Primary divisions: whole units
Secondary divisions: parts of the left division
Zero at end of first division; Labelling.
Convention: Metric about 15 cm | English about 6 inches; Starting length.

How to answer Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems questions

Bar scale construction has fixed steps.

1Start with 15 cm and compute the ground distance.
2Choose a round number and recompute the line length.
3Mark primary divisions and number from zero at the end of the first division.
4Divide the first division into secondary parts, label and write the R.F. beneath the scale.

Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems 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.

Trekking map

Suppose a trekker has a map of R.F. 1:25,000 and wants a bar scale to measure the trail with a string.

What ground distance would 15 cm represent?

Try it first, then show the solutionSolution

15 x 25,000 = 375,000 cm.
375,000 / 100,000 = 3.75 km.

Answer: 3.75 km, so a round 3 km scale is taken.

Memory hook: 15 cm becomes 3.75 km.

Shrunk printout

Suppose the same map is printed at 60 per cent size for a brochure.

What happens to a printed bar scale?

Try it first, then show the solutionSolution

It shrinks with the map.
It still reads the correct ground distance.

Answer: The bar scale remains valid; a statement of scale would not.

Memory hook: Bar shrinks with map.

Tricks to remember Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems

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

15 cm then round
Start 15 cm, find ground distance, pick round number
Use it when: Method.
Zero at the first division
Primary to the right, secondary to the left
Use it when: Labelling.
Dotted lines at 40 or 45
Equal parts of an awkward length
Use it when: Dividing.

Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems: solved examples

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

Example 1: Where is zero · 1 mark · MCQBoard level

On a graphical scale, the zero mark is placed at:
(A) the extreme left end
(B) the end of the first (left) division
(C) the extreme right end
(D) the middle of the line

Try it first, then show the solutionSolution

Zero is at the end of the first division (1 mark).

Answer: (B)

Example 2: Ground distance of 15 cm · 2 marks · Very short answerBoard level

For R.F. 1:100,000, what ground distance does a line of 15 cm represent? (2 marks)

Try it first, then show the solutionSolution

15 x 100,000 = 1,500,000 cm (1 mark).
= 15 km (1 mark).

Answer: 15 cm x 100,000 = 1,500,000 cm = 15 km.

Example 3: Construct scale 1:25,000 · 3 marks · Short answerHarder board level

Describe the construction of a bar scale for R.F. 1:25,000 reading kilometres and metres, with the arithmetic. (3 marks)

Try it first, then show the solutionSolution

15 cm represents 15 x 25,000 / 100,000 = 3.75 km (1 mark).
Round to 3 km; line length = 15 x 3 / 3.75 = 12 cm, divided into 3 primary divisions of 4 cm (1 km each) (1 mark).
Left division divided into 10 secondary parts of 100 m (0.4 cm each), zero at end of first division (1 mark).

Answer: The ground distance for 15 cm is 15 x 25,000 / 100,000 = 3.75 km. Take the round number 3 km: the line is 15 x 3 / 3.75 = 12 cm. Divide it into 3 primary divisions of 4 cm, each 1 km, with zero at the end of the first division, and divide the left division into 10 secondary divisions of 0.4 cm, each 100 m.

Example 4: Assertion and reason: round numbers · 1 mark · Assertion-reasonHarder board level

Assertion (A): A round number of ground units is chosen before dividing the scale line.
Reason (R): Round numbers make primary and secondary divisions easy to mark and read.
(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

Round values make the divisions simple to draw and read (1 mark).

Answer: (A)

Example 5: HOTS: scale for 1:40,000 · 5 marks · Long answerHOTS / competency

Construct the arithmetic for a bar scale for R.F. 1:40,000 in km and m. Find the ground distance for 15 cm, choose a suitable round number, find the line length, state the primary and secondary divisions, and say how a 7.5 cm map distance is read. (5 marks)

Try it first, then show the solutionSolution

15 x 40,000 / 100,000 = 6 km (1 mark).
Round number 6 km already round; line 15 cm (1 mark).
Primary divisions: 6 of 2.5 cm each representing 1 km (1 mark).
Secondary: left division into 10 parts of 100 m (0.25 cm each) (1 mark).
7.5 cm x 40,000 = 300,000 cm = 3 km, read as 3 primary divisions (1 mark).

Answer: For 15 cm the ground distance is 15 x 40,000 / 100,000 = 6 km, which is already a round number, so the line stays 15 cm. Draw 6 primary divisions of 2.5 cm each representing 1 km, with zero at the end of the first division, and divide the left division into 10 secondary parts of 0.25 cm (100 m each). A map distance of 7.5 cm is 7.5 x 40,000 = 300,000 cm = 3 km, which is read as 3 primary divisions.

Where students lose marks in Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems

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

Mistake: Putting zero at the left end
Habit from rulers.
Wrong working
Zero at the extreme left.
Right working
Zero at the end of the first division, with secondary divisions to its left.
Do this: Mark zero after the first division.
Usually costs: 1 mark.
Mistake: Skipping the round number
Using 7.5 km directly.
Wrong working
Divide 15 cm into 7.5 parts.
Right working
Choose 5 km (round) and recompute 10 cm.
Do this: Round before drawing.
Usually costs: 1 mark.
Mistake: Forgetting the R.F. below the scale
Incomplete labelling.
Wrong working
Scale with no title or R.F.
Right working
Write the R.F. and units beneath the scale.
Do this: Label fully.
Usually costs: 1 mark.

Exam tips

Show all four arithmetic steps before drawing.
Write units (km, m) along the scale and the R.F. below it.
Use a sharp pencil and a ruler for the divisions.

Practice questions on Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems

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
The usual starting line for a metric graphical scale is:
(A) 5 cm
(B) 10 cm
(C) 15 cm
(D) 30 cm
Hint
Convention.
Answer
(C)
Q2 · 2 marks · Very short answerBoard level
Why is the left division of a bar scale subdivided? (2 marks)
Hint
Fractions of a unit.
Answer
The first division is subdivided into secondary divisions so that distances smaller than one primary unit can be read, for example in hundreds of metres.
Q3 · 3 marks · Short answerHarder board level
For R.F. 1:50,000, find the line length (cm) to represent exactly 4 km. (3 marks)
Hint
Ground over denominator.
Answer
4 km = 400,000 cm. Line length = 400,000 / 50,000 = 8 cm.
Q4 · 3 marks · Short answerHarder board level
For R.F. 1:200,000, find the ground distance represented by 15 cm and the line length for a round 25 km. (3 marks)
Hint
15 cm to 30 km.
Answer
15 cm x 200,000 = 3,000,000 cm = 30 km. For 25 km: 25 x 100,000 / 200,000 = 12.5 cm.
Q5 · 4 marks · Short answerHOTS / competency
A map has the R.F. 1:50,000. Describe how to divide a line of 6.34 inches into 5 equal parts without a calibrated ruler, using the method in the chapter, and state when the English scale is used. (4 marks)
Hint
Angle lines.
Answer
Draw lines at about 40 or 45 degrees from both ends of the line, mark 5 equal steps (for example of 1 inch) on each, join corresponding marks with dotted lines and mark where they cross the scale line. English scales (in miles and furlongs) are used for maps for users of the English system, such as in the USA and UK.

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.How long is the standard metric line?Show answer
About 15 cm.
2.Where is zero placed?Show answer
At the end of the first division.
3.Which divisions are to the left of zero?Show answer
Secondary divisions.
4.Why is the bar scale useful on enlargement?Show answer
It enlarges with the map.

Constructing a Graphical (Bar) Scale: Primary and Secondary Divisions and Worked Problems: frequently asked questions

Can I use any round number?

Use one close to the ground distance of the line, such as 5 km for 7.5 km.

What if the length is awkward?

Divide it by the angle-line method.

Is this chapter in the theory paper?

No, it is in the practical exam.