What is Dimensional Analysis? - Definition & Examples

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  • 0:00 What Is Dimensional Analysis?
  • 1:33 Dimensional Analysis Examples
  • 4:20 Lesson Summary
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Lesson Transcript
Instructor: Nissa Garcia

Nissa has a masters degree in chemistry and has taught high school science and college level chemistry.

When we measure an object's size or amount, we encounter different units. Sometimes, we need to convert one unit to another, and this is where dimensional analysis comes in. In this lesson, we will learn about dimensional analysis and practice it.

What Is Dimensional Analysis?

Comparing and converting between different units is a very useful and important skill. We do this every day without realizing it. For instance, when we follow a recipe, we may need to do simple conversions, like converting grams to ounces, or quarts to cups.

In science and math, we often convert a number or quantity with a dimensional unit to a different unit, like meters to kilometers. Dimensional analysis, also known as factor-label method or unit-factor method, is a method to convert one different type of unit to another. This way, we can convert to a different unit, but their values are the same. To convert from one unit to another, we make use of a conversion factor, which is a numerical quantity that we can multiply or divide to the number or quantity that we want to convert.

For example, if I want to know how many yards are there in 10 feet, we can recall that 3 feet is equivalent to 1 yard. Then, I can use dimensional analysis and convert feet into yards by using the conversion factor shown below in yellow. If I want to know how many minutes there are in two hours, I can use the conversion factor shown in blue.

Conversion Factors

Dimensional analysis is something that we have done without realizing it. We convert minutes to hours, or days to hours all the time. Also, if we travel to another country that normally measures distance by kilometers instead of miles, then we convert between the two units as well by using the dimensional analysis method.

Dimensional Analysis Examples

Let's go over a few examples of dimensional analysis. In this section, we can practice how to make use of conversion factors correctly to convert between units.

Example 1

Let's say we want to know how many kilograms there are in 55 pounds (lb). This means we need to convert pounds to kilograms (kg). In this case, our conversion factor is 1 kg = 2.2046 lb. This information can be written in two ways, one is shown in yellow in the image below and the other is shown in blue. You will notice that in (1), the kg unit is on top, and in (2), the lb unit is on top. Which one do we pick?

Conversion Factors for Example 1

We want to know how many kg there are, so we will pick (1) because kg is on top and lb is on the bottom. If we multiply this by 55 lb, the unit lb will cancel, and we will be left with kg. When we use conversion factor (1), let's see what happens:

Dimensional Analysis for Example 1

Now, we have successfully converted pounds to kilograms.

Example 2

How many feet (ft) are there in 140 centimeters (cm)?

First, we need to determine our conversion factors. We know that 1 ft = 12 inches (in) and that 1 in = 2.54 cm. In this case, we have two conversion factors. If we want to convert the units all the way to feet, we must convert cm to inches and then to feet:

Conversion Factors to Convert cm to ft

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