# Scalar: Definition & Function

Instructor: Catherine Hagandora

Catherine has a doctorate in bioengineering.

In this lesson, we will explore the definition and function of scalar quantities as well as different examples of scalar quantities. You'll learn about the difference between scalar and vector quantities before testing your knowledge with a quiz.

## What is a Scalar?

Imagine you are lost in the woods. You have been walking around for hours trying to find your way, but it seems as though you've found yourself right where you started. How do you describe your efforts? Let's take a closer look at how we describe distances traveled in physics and how this relates to scalar quantities.

A scalar is a physical quantity that can be completely described by a real number or magnitude. You can think of scalars as having only one dimension.

## Examples of Scalar Quantities

There are many ways in which scalars are used in physics to describe different quantities. Among the most common are:

• Mass: The property of an object pertaining to the strength of its gravitational attraction toward other bodies. For example, we can describe the mass of an elephant as 5000 kg.
• Temperature: A measurement of hot and cold. We can describe the lowest air temperature ever recorded in Antarctica as -128.6 degrees Fahrenheit.
• Time: A point in time measured by hours, minutes and seconds. For example, we can say that Neil Armstrong took the first step on the moon at 10:56 P.M. Eastern Daylight Time.
• Speed: Average speed can be defined as the total distance traveled divided by the total travel time. When you are driving on the interstate, you are likely going at a speed of around 65 miles per hour.

All of the above quantities can be described by a single magnitude (with units) and are therefore scalar quantities. Let's take a closer look at the scalar quantity of speed in the following section to better understand the significance of scalar quantities.

## Scalars and Vectors

Even though scalars just provide information about magnitude, they are very important and used all the time in physics. In contrast, vectors are used to describe quantities with both magnitude and direction.

As we mentioned earlier, the average speed of an object is its total distance traveled divided by the total travel time. The direction is not taken into account, so speed is a scalar quantity.

The average velocity of an object is its total displacement (how far the object moved in relation to its starting point) divided by the total travel time. The direction is an important part of velocity, so it is a vector quantity.

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