For the development of this topic, the recommendations of the UNE-EN ISO standard have been taken into account 5455:1996.

### Concept

Representation of objects at their natural size is not possible when they are very large or when they are very small. In the first case, because they would require formats of unwieldy dimensions and in the second, because there would be a lack of clarity in their definition.

This problem is resolved by SCALE, applying the necessary enlargement or reduction in each case so that the objects are clearly represented in the drawing plane.

The **SCALE** as the relation between the dimension drawn with respect to its real dimension, this is:

If the numerator of this fraction is greater than the denominator, it is an enlargement scale, and it will be reduction otherwise. The scale 1:1 corresponds to an object drawn at its actual size (natural scale).

### Standard scales

Though, in theory, it is possible to apply any scale value, in practice the use of certain standard values is recommended in order to facilitate the reading of dimensions through the use of rulers or scalemeters.

These values are:

However, in special cases (particularly under construction) certain intermediate scales such as:

1:25, 1:30, 1:40, etc…

### Practical examples

**EXAMPLE 1**

You want to represent in an A3 format the floor plan of a building 60 x 30 meters.

The most convenient scale for this case would be 1:200 which would provide dimensions of 30 x 15 cm, well suited to the size of the format.

**EXAMPLE 2:**

You want to represent in a A4 format a dimensional clock piece 2 x 1 mm.

The proper scale would be 10:1

**EXAMPLE 3:**

On a nautical chart to E 1:50000 a distance of 7,5 cm between two islets, What is the real distance between the two?

It is solved with a simple rule of three:

and 1 cm of the drawing are 50000 real cm

7,5 cm of the drawing will be real X cm

X = 7,5 x 50000 / 1 … And this results 375.000 cm, which are equivalent to 3,75 km.

### Graphic scale

Based on Thales' Theorem, a simple graphical method is used to apply a scale.

see, for example, the case for E 3:5

- With origin at an arbitrary point O two lines r and s are drawn forming any angle.
- On the line r is the denominator of the scale (5 in this case) and on the line s the numerator (3 in this case). The ends of these segments are A and B.
- Any real dimension located on r will be converted into that of the drawing by a simple parallel to AB.

### Universal triangle of scales

Through a triangle, we can build the simplest scales, both normalized and not. As we see in the figures, we can do it using an equilateral triangle of 10 cm sideways, or by means of an isosceles right triangle, whose legs measure 10 cm.

### Transverse decimal scale

With this type of scale you can get, more accurately, the measurements of a scale segment, since in the so-called contra-scale, from the left side, we can appreciate the tenths and hundredths of unity.

In the following image we can see how we have constructed the decimal scale of transversal 1:20, and in it we have indicated two examples of measurements on it, 2,77 m y 1,53 m.

### Using the scale

In the usual practice of drawing, when working with scales, ladders are used.

The most common form of the scale is that of a 30 cm length, with starry section of 6 facets the guys. Each of these facets is graduated with different scales, which are usually:

1:100, 1:200, 1:250, 1:300, 1:400, 1:500

These scales are equally valid for values that result from multiplying or dividing by 10, for example, the scale 1:300 is usable in scale drawings 1:30 from 1:3000, etc.

Another model, less usual of scale, is the fan scale, consisting of a series of rules on which the different graphic scales have been drawn.

**Examples of use:**

- For a plane to E 1:250, scale will be applied directly 1:250 of the scale and the numerical indications that are read on it are the actual meters that the drawing represents.
- In the case of a plane to E 1:5000; scale will be applied 1:500 and we will have to multiply by 10 scale reading. For example, if a dimension of the plane has 27 units on the scale, we're actually measuring 270 m.

Of course, the scale 1:100 is also the scale 1:1, normally used as a ruler in cm.