In architectural drawing, engineering graphics, urban planning, and design representation, scales are essential tools used to represent real-world dimensions on paper or digital drawings. Since actual objects such as buildings, roads, and cities are much larger than drawing sheets, they must be represented at a reduced or proportional size. Scales allow designers and planners to maintain accurate relationships between the drawing and the real object.

The concept of scale ensures that measurements taken from a drawing correspond correctly to the actual dimensions of the object. In technical drawing and graphic communication, several types of scales are used depending on the level of precision required. Among these, plain scales and diagonal scales are particularly important.

This tutorial explains the concept of scales, their types, and the specific use of plain and diagonal scales in graphical representation.

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1. Meaning of Scale

A scale is the ratio between the dimensions in the drawing and the actual dimensions of the object. It allows large objects to be represented on small sheets while maintaining proportional relationships.

The scale is usually expressed as:

Scale = Drawing Size / Actual Size

For example:

• If 1 cm on the drawing represents 100 cm in reality, the scale is 1:100.
• If 1 cm represents 1000 cm, the scale is 1:1000.

Scales are widely used in:

• Architecture and building design
• Urban and regional planning
• Engineering drawings
• Cartography and mapping
• Landscape design

They ensure that drawings are accurate, measurable, and understandable.

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2. Classification of Scales

Scales used in engineering graphics are generally classified into the following categories:

1. Plain Scale
2. Diagonal Scale
3. Vernier Scale
4. Comparative Scale
5. Scale of Chords

Among these, plain and diagonal scales are most commonly used in architectural and planning drawings.

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3. Plain Scale

Definition

A plain scale is a graphical scale used to measure two units or a unit and its subdivisions. It allows measurements to be read up to a certain level of accuracy, usually representing a unit and its immediate subdivisions.

Plain scales are commonly used when moderate precision is sufficient.

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Structure of Plain Scale

A plain scale consists of:

• A straight horizontal line divided into equal segments.
• The leftmost segment is further divided into smaller parts to represent subdivisions of the main unit.

The scale typically includes:

• Primary divisions representing major units
• Subdivisions representing smaller units

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Example

Suppose a scale represents meters and decimeters.

• Each large division represents 1 meter
• Each small division represents 0.1 meter

This allows measurements such as:

• 1.5 meters
• 2.3 meters
• 3.7 meters

Plain scales are commonly used in site plans, layout drawings, and simple engineering graphics.

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Steps for Constructing a Plain Scale

1. Determine the Representative Fraction (RF) of the scale.
2. Calculate the length of the scale line based on the maximum measurement required.
3. Draw a horizontal line equal to the calculated length.
4. Divide the line into equal parts representing the main units.
5. Subdivide the first division into smaller parts representing subdivisions.
6. Label the units clearly.

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Applications of Plain Scale

Plain scales are widely used in:

• Building drawings
• Simple site layouts
• Basic engineering drawings
• Map reading
• Planning diagrams

They are easy to construct and interpret, making them suitable for general graphical representation.

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4. Diagonal Scale

Definition

A diagonal scale is used to measure three units or units with greater precision than plain scales. It allows measurements to be read to smaller subdivisions such as tenths or hundredths of a unit.

Diagonal scales are particularly useful when higher accuracy is required.

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Principle of Diagonal Scale

The diagonal scale works based on the principle of similar triangles. By drawing diagonals within a grid structure, it becomes possible to divide a small length into even smaller parts.

This method allows the measurement of values such as:

• 1.23 meters
• 2.45 meters
• 3.78 meters

Thus, diagonal scales provide greater precision compared to plain scales.

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Structure of Diagonal Scale

A diagonal scale includes:

• A horizontal line representing the main scale
• Vertical lines forming rectangles
• Diagonal lines dividing these rectangles

These diagonals allow precise measurement of smaller subdivisions.

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Steps for Constructing a Diagonal Scale

1. Determine the Representative Fraction (RF).
2. Calculate the required length of the scale line.
3. Draw the main horizontal line and divide it into primary units.
4. Subdivide the first primary unit into smaller units.
5. Draw vertical lines above the subdivisions to form rectangles.
6. Divide the vertical height into equal parts.
7. Draw diagonal lines across the rectangles to create smaller measurement divisions.

Through these diagonals, extremely small measurements can be accurately read.

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Applications of Diagonal Scale

Diagonal scales are commonly used in:

• Architectural drawings
• Engineering drawings
• Detailed mapping
• Surveying work
• Technical design projects

They are particularly useful when precision is critical.

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5. Comparison Between Plain Scale and Diagonal Scale

Feature	Plain Scale	Diagonal Scale
Accuracy	Moderate	High
Units Measured	Two units or unit and subdivision	Three units or finer subdivisions
Construction	Simple	Slightly complex
Applications	General drawings	Precision drawings
Principle Used	Simple linear division	Similar triangles

Plain scales are suitable for basic graphical representation, while diagonal scales provide higher measurement accuracy.

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6. Importance of Scales in Planning and Design

In planning and architectural graphics, scales play a critical role in representing spatial information accurately.

For example:

• Site plans often use scales like 1:500 or 1:1000.
• Building plans may use 1:50 or 1:100 scales.
• Regional maps may use 1:10,000 or smaller scales.

Using appropriate scales ensures that drawings are consistent, measurable, and professionally standardized.

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7. Practical Exercise for Students

Students can practice constructing scales through the following exercises:

Exercise 1: Plain Scale

Construct a plain scale with RF 1:50 to measure meters and decimeters up to 5 meters.

Exercise 2: Diagonal Scale

Construct a diagonal scale with RF 1:100 capable of measuring meters, decimeters, and centimeters.

These exercises help students understand both the mathematical and graphical aspects of scales.

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Conclusion

Scales are fundamental components of engineering graphics, architectural drawing, and urban planning representation. They allow large real-world objects to be accurately represented on smaller surfaces while maintaining correct proportions.

Among the various types of scales, plain scales are used for general measurements involving units and subdivisions, while diagonal scales provide greater precision by allowing measurement of smaller units through geometric construction.

Understanding and constructing these scales is an essential skill for students and professionals in architecture, planning, engineering, and design, as it ensures accurate and effective graphical communication.