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Scale: explanation and conversion

You can learn an explanation of the scale and how to convert it here. Let's look at this:

  • A Explanationwhat you need a yardstick for.
  • Examples for converting standards (including word problems).
  • Tasks / exercises so that you can practice this yourself.
  • A Video to units of measure as a basis.
  • A Question and answer area to this topic.

Tip: You should know what centimeters, meters and kilometers are. If you have no idea about this, please look into converting units of length.

Explanation of scale

If an architect draws a house on paper or electronically, the drawing is much smaller than in reality. This also applies to maps: Here, reality is shown much smaller. Just how much smaller is something displayed? This is indicated with the yardstick.

In some cases something is also enlarged. If you look at very small objects - for example under a microscope, it is possible to display them much larger on paper or on a screen. How much larger something is shown is also indicated with a scale.

Definition of scale:


The scale indicates how much something is enlarged or reduced. These are two numbers with a colon between them.

Example scale reduction:

On a map, the scale is 1: 50000. How many are 2 centimeters on the map in reality?


The scale 1: 50000 means that 1 cm on the map is in reality 50,000 centimeters. To go from 1 cm to 2 cm, we have to multiply by 2.

This means that 2 centimeters on the map correspond in reality to 100,000 cm (converted 1,000 meters or 1 kilometer).

Example scale enlargement:

On a plan, a computer chip is 18 centimeters wide. The plan is on a 40: 2 scale. How wide is the chip?


The scale 40: 2 means that 40 cm on the plan is 2 cm in reality. However, we don't want to know how much 40 cm is on the plan, but how much is only 18 cm. And what exactly this is in reality. So let's first write this down:

To get from 40 cm to 18 cm, we have to multiply by 18:40. We are doing this on both sides.

In reality, the chip is 0.9 cm wide.


Examples of scale

In this section we look at word problems (factual problems) on the yardstick.

example 1:

A scale of 1: 500,000 applies on an aircraft map. A distance of 5 cm must be measured between two airfields. What is the distance in kilometers in reality?


1 cm on the plan is 500,000 cm in reality. You can get from 1 cm to 5 cm by multiplying by 5.

That brings us to 2,500,000 cm. This is 25,000 m or 25 km.

Example 2:

In reality, two train stations are 10 kilometers apart. This distance should be entered on a map at a scale of 1: 25,000. How many centimeters is the distance between the stations on the map?


1 centimeter on the map is 25,000 centimeters in real terms. We first convert the 25,000 centimeters into 250 meters or 0.25 kilometers. We know that 1 cm on the map is in reality 0.25 km. Therefore, to calculate the length on the map, we need to multiply by 10: 0.25.

On the map, the two train stations are 40 cm apart.

Example 3:

An apartment was drawn on a scale of 1: 100. What is 100 times as big in reality? The lengths or the areas?


  • The scale refers to the lengths in a plan. 1 cm on the plan is 100 cm in reality.
  • An area is obtained by multiplying length by width.
  • For example, a square on the plan would be 1 cm x 1 cm = 1 cm2 large
  • In reality this is 100 cm x 100 cm = 10,000 cm2.

From 1 cm2 at 10,000 cm2 is a factor of 10,000 or 1: 10,000. If you don't believe it, take a square with 10 cm x 10 cm = 100 cm2 or in comparison, in reality 1000 cm x 1000 cm = 1,000,000 cm2.

Exercises / tasks scale


Video units of length

Basics of units of measurement

In order to be able to convert scales, it is very helpful to know different units of length. The units of length include, for example, centimeters, meters, kilometers, and a few others. You will learn how this works in the next video:

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Questions with answers about the yardstick

This section deals with typical questions with answers about the yardstick.

Q: What are the typical standards?

A: A small overview of very small scales (as a substitute for a table):

  • 1 : 5
  • 1 : 100
  • 1 : 20
  • 1 : 1000
  • 1 : 1
  • 1 : 50

Q: Is there a simple formula for measuring rods?

A: Many books simply multiply or divide by a number to do the math. A formula could be made out of this. However, this is of little use when you have to solve demanding word problems. Because this is exactly where an understanding of a topic is necessary and not just inserting it into a formula.

Q: When is this topic covered in school?

A: Sometimes this topic is covered a bit in elementary school. However, this topic only really comes into play in the 5th or 6th grade.