What is the Formula for Force? - Definition & Explanation

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  • 0:00 What Is Force?
  • 1:01 Force Formula
  • 2:00 Solving for Other Variables
  • 3:34 Net Force
  • 6:14 Lesson Summary
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Lesson Transcript
Instructor: Amanda Robb

Amanda holds a Masters in Science from Tufts Medical School in Cellular and Molecular Physiology. She has taught high school Biology and Physics for 8 years.

In this lesson, we'll explain what forces are in science. We'll review how to construct free body diagrams and calculate net force in order to use the force equation to solve for force, mass, and acceleration.

What is Force?

When you get to school, you open your locker door and lift your books into your arms. You are late, so you have to run to class, slowing down when you get closer to the door. A typical scene in the day of a student, right? Although you might not know about force yet, in all the actions mentioned here, force is letting you complete them!

Force is an interaction between objects that causes them to change motion. So, when you opened your locker door, your hand applied a force to the door, causing it to change its motion. We measure force in newtons (N), the scientific unit for measuring weight. One newton is equal to about 0.22 pounds. So, a girl weighing only 100 lbs. would be equal to approximately 445 newtons, or her force due to gravity (Fg). Now that we know some basics, let's look at how we use the formula for force.

Force Formula

The formula for force states that force is equal to mass multiplied by acceleration. So, if you know mass and acceleration, just multiply them together and now you know the force! The units for acceleration are meters per second squared ( m/s2), and the units for mass are kilograms (kg).

Let's take a look at an example:

Mary is trying to lift a box from the floor to the shelf. She accelerates the 2 kg box with 2 m/s2. What force does Mary exert on the box?

To solve this problem, just multiply the mass (2 kg) by the acceleration (2 m/s2) to get the final answer: 4 N of force was exerted on the box. Remember, in physics, always include all units, both in your problem when you show your math and when you write your final answer.

Solving for Other Variables

You can also calculate any other variable in the equation if you have two of the three. For example, if you have mass and force, you can calculate acceleration.

If you're a little shaky with algebraic equations, here's a shortcut!


Using a circle, draw a horizontal line through the middle. Then, separate the bottom half of the circle into two sections. On the top, write F for force and on the bottom put m for mass in one section and a for acceleration in the other. The horizontal line will be used for division and the vertical lines indicate multiplication. Next, cover up whatever variable you want to solve for with your finger. For example, let's say we want to solve for acceleration. Cover the a on the circle. Now, you're left with F divided by m. This will be the math you use to solve for force! Pretty easy, huh?

Let's take a look at an example:

Jordan is trying to push a big chair across the room for his aunt. She wants it in the sun so she can read in the afternoon. Jordan uses 300 N of force on the 300 kg chair. How fast does Jordan have to accelerate to move the chair?

Let's use the circle again. Cover up the variable you want to solve for, a. Now, we're left with F divided by m. Now, we can plug in our numbers. The force (300 N) divided by the mass (300 kg) is equal to 1 m/s2, the acceleration Jordan needs to use to move the chair.

Net Force

Usually, there are lots of forces acting on objects all at once, not just one like we've seen so far. To calculate the other variables, we need to add the forces together to see what the net force is, or the sum of forces acting on an object. Force is considered a vector, meaning it has magnitude and direction. Usually we label forces that are directed down as negative and forces directed upwards as positive. Similarly, forces going left are negative and forces going right are positive.

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