Scalar Addition: Definition, Uses & Example

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

There are some quantities in physics that can be easily added via scalar addition without having to worry about the direction of the quantity. Learn about this along with how the addition works in this lesson.

Definition of Scalar Addition

Remember when you first learned math? You learned that 1 + 1 = 2 and 2 + 3 = 5 and so on. Well, this straight addition of your numbers is referred to as scalar addition. A scalar value is simply a value that only has one component to it, the magnitude. For example, your speed is a scalar value because it only has one component, how fast you are going. Your height is also a scalar value because the only component is how tall you are. The same goes for your mass. Directions, on the other hand, are not scalar values because they have more than one component: distance and one or more directional components.

Speed is a scalar quantity
scalar addition

In this lesson, you'll learn about scalar addition, where the values you are working with only have one component.

Scalar Addition How-To

Scalar addition is very straightforward, just like basic addition: all you need to do is add the values together. You don't have to worry about anything else.

For example, say you are given these two scalar quantities: 20 and 54. You can add these two quantities just as you would regular numbers.

  • 20 + 54 = 74

And you are done.


In physics, two scalar quantities that you'll work with often are mass and charge. The mass of an object measures how much matter the object is made of. When you step on a scale that uses a balancing arm, the result you get is your mass. The charge of an object is how much voltage it is emitting.

Because both of these quantities are scalar, you can add them using scalar addition.


Let's look at some examples using mass and charge.

You need to use an elevator to help you lift some heavy boxes up to the third floor of a building. The elevator has a capacity of 600 pounds, which means that the elevator can only lift 600 pounds. You need to figure out the mass of your boxes to see if the elevator will be able to handle it. The total mass of all the objects must be less than 600 pounds. What do you do? Here is a list of your boxes and their masses.

Box 1 45 pounds
Box 2 20 pounds
Box 3 95 pounds
Box 4 70 pounds
Box 5 80 pounds

You recognize that mass is a scalar quantity, so to solve this problem, you can go ahead and use scalar addition to find your answer. You can add your masses together as follows:

  • 45 + 20 + 95 + 70 + 80 = 310 pounds

All your boxes add up to 310 pounds. This is well below the capacity of 600 pounds, so you can safely use this elevator to help you transport your boxes to the third floor.

Here's another example.

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