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Introduction

QUICK LINKS


Introduction

INTRO
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A unit conversion takes the value of a physical property (time, length, mass/weight, volume, etc.) and expresses it using a different unit of measurement.

For example, we can convert to . Even though these two measurements look different, they actually have the same value.

This is similar to how we can express our thoughts and feelings using emojis in place of words.

Instead of typing, β€œbut that’s none of my business,” we can convert the words to emojis, β€œπŸΈβ˜•,” and call it a day. The expression changes, but the meaning (or value) stays the same.

To convert units, we use a process called dimensional analysis.

Dimensional analysis is the process of multiplying a given measurement by one (or more) conversion factors in order to express it using a different set of units.

A conversion factor is a ratio that compares two quantities that are equivalent. This means a conversion factor is always equal to 1.

In the example below, we use the conversion factor, 1 foot = 12 inches, to create a path that gets us from feet to inches.

We can cancel out ft (feet) because it shows up 1 time on the top and 1 time on the bottom ( is equal to 1).

In general, an unwanted unit needs to show up an equal number of times on the top and bottom to cancel out.

If we imagine the units as parts of an Easter egg, we need a matching bottom half for every top half to close the egg and cancel out. πŸ‡

What is a unit of measurement?

A unit tells us what type of measurement we’re dealing with and its relative size.

Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about unit conversion and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

CALCULATOR
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Unit Conversion Calculator

What type of measurement do you want to convert?

Convert to

Step 1. Identify the given unit (starting position) and the unknown unit (ending position).

The given unit is the unit that has a given number.
The unknown unit is the unit we need to find the unknown number of.

given input:

unknown unit:

Step 2. Identify the path from start to finish.

Select the set of conversion factors that can get us from the given unit to the unknown unit.

Step 3. Use the conversion factors to set up an equation that cancels out unwanted units and gets the unknown unit by itself.

To cancel out, we need a matching top half for every bottom half.

Step 4. Multiply across the top and bottom.

Step 5. Divide.

So, is equal to .

KEY STEPS
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How to Convert Units

Step 1. Identify the given unit (starting position) and the unknown unit (ending position).

The given unit is the unit that has a given number.
The unknown unit is the unit we need to find the unknown number of.

Step 2. Identify the path from start to finish.

Select the set of conversion factors that can get us from the given unit to the unknown unit.

Step 3. Use the conversion factors to set up an equation that cancels out unwanted units and gets the unknown unit by itself.

To cancel out, we need a matching top half for every bottom half.

Step 4. Multiply across the top and bottom.

Step 5. Divide.

LESSON
β€” Converting Units

Converting Units

When we convert a unit, we’re just finding another way to express the same value using a different unit of measurement.

To convert a unit, we use dimensional analysis, which involves multiplying the original measurement by a pathway of conversion factors that gets us from the given unit to the unknown unit.





We can cancel out unwanted units as long as they show up an equal number of times on the top and bottom.

Think of this as needing a matching bottom half for every top half to close an Easter egg and cancel out.

Let’s walk through some step-by-step examples of how to convert units!

EXAMPLE 1

Let's start with the following problem:
Convert to

Step 1. Identify the given unit (starting position) and the unknown unit (ending position).

The given unit is the unit that has a given number.
The unknown unit is the unit we need to find the unknown number of.

given input:

unknown unit:

Step 2. Identify the path from start to finish.

Select the set of conversion factors that can get us from the given unit to the unknown unit.

Step 3. Use the conversion factors to set up an equation that cancels out unwanted units and gets the unknown unit by itself.

To cancel out, we need a matching top half for every bottom half.

Step 4. Multiply across the top and bottom.

Step 5. Divide.

So, is equal to .

EXAMPLE 2

Nice work! Now, let's try the following problem:
Convert to

Step 1. Identify the given unit (starting position) and the unknown unit (ending position).

The given unit is the unit that has a given number.
The unknown unit is the unit we need to find the unknown number of.

given input:

unknown unit:

Step 2. Identify the path from start to finish.

Select the set of conversion factors that can get us from the given unit to the unknown unit.

Step 3. Use the conversion factors to set up an equation that cancels out unwanted units and gets the unknown unit by itself.

To cancel out, we need a matching top half for every bottom half.

Step 4. Multiply across the top and bottom.

Step 5. Divide.

So, is equal to .

EXAMPLE 3

Amazing! Last one - let's try the following problem:
Convert to

Step 1. Identify the given unit (starting position) and the unknown unit (ending position).

The given unit is the unit that has a given number.
The unknown unit is the unit we need to find the unknown number of.

given input:

unknown unit:

Step 2. Identify the path from start to finish.

Select the set of conversion factors that can get us from the given unit to the unknown unit.

Step 3. Use the conversion factors to set up an equation that cancels out unwanted units and gets the unknown unit by itself.

To cancel out, we need a matching top half for every bottom half.

Step 4. Multiply across the top and bottom.

Step 5. Divide.

So, is equal to .

Awesome! If you’d like to practice additional problems with unit conversion, expand the
Practice
below before closing out this lesson! ⚑
PRACTICE
β€” Converting Units

Practice: Converting Units

Question 1 of 10: Convert 1 hours to minutes.

Step 1. Identify the given unit (starting position) and the unknown unit (ending position).

The given unit is the unit that has a given number.
The unknown unit is the unit we need to find the unknown number of.
Given:
Unknown:

Step 2. Identify the path from start to finish.

Select the set of conversion factors that can get us from the given unit to the unknown unit.

Step 3. Use the conversion factors to set up an equation that cancels out unwanted units and gets the unknown unit by itself.

To cancel out, we need a matching top half for every bottom half.

Step 4. Multiply across the top and bottom.


Step 5. Divide.

Awesome job! 1 hours is equal to minutes.

CONCLUSION
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Sheesh, look at you go! Thanks for checking out this lesson β˜ΊοΈπŸ™. Where to next?
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