# Scalar Quantity in Physics: Definition & Examples

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• 0:01 Definition of a Scalar
• 0:46 Examples of Scalars
• 2:10 Scalars vs. Non-Scalars
• 3:32 Numbers Alone Are Not Scalars
• 4:01 Lesson Summary

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Lesson Transcript
Instructor: Richard Cardenas

Richard Cardenas has taught Physics for 15 years. He has a Ph.D. in Physics with a focus on Biological Physics.

In this lesson, you will learn about what makes a number a scalar quantity. You will learn how to identify quantities that are scalars from those that are not scalar quantities. You will also learn about numbers that don't look like scalars but are actually scalars.

## Definition of a Scalar

How tall is that building? How long did your trip take? How hot is it outside? All of these questions have one thing in common. All of the answers to these questions are called scalar quantities. A scalar is any quantity that only requires a magnitude or size to describe it completely. A scalar is any number that gives you the size or magnitude of a quantity, so a unit of measure must be attached to the number, like degrees or meters. Any random number is not a scalar. For example, the number 42 is meaningless unless you tell us that 42 is a measurement of something like distance or time or temperature.

## Examples of Scalars

Another example of a scalar is distance. Before driving to the grocery store, you zero out the trip meter of your car. When you return home from the grocery store, your trip meter reads 34.5 miles. The trip meter reads the distance traveled by your car. It gives you an idea of how far you traveled during your trip to the grocery store.

Average speed (or just speed) is another example of a scalar quantity. Speed is defined as the distance traveled divided by the time it took to travel that distance. It is a measure of a rate of change of your distance and has units of meters/second (m/s) or miles/hour (mph), or kilometers per hour (kph). Speed depends on distance and time, which are also both scalar quantities, therefore, speed is also a scalar quantity. For example, a long road trip covered a distance of 338 miles. You drove that distance in 5 hours. Therefore, your average speed for the trip was 338 miles divided by 5 hours, or 67.6 mph. These are all scalar quantities.

## Scalars vs. Non-Scalars

Scalar quantities do not specify direction like north or south, up or down, left or right. In physics, direction is sometimes indicated by a plus (+) or minus (-) sign in front of a quantity or an angle, such as 30 degrees. For example, -10 meters is not a scalar quantity because the negative sign indicates direction relative to some reference point. This reference point is also called the origin. The statement 10 meters to the left of the oak tree is an example of a non-scalar quantity because both a magnitude (10 meters) and direction (left) is specified in the statement, and the tree is the reference point or origin.

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