Net Force Calculator

Use our net force calculator to find the net force and direction given a number of individual forces on an object.


Net Force:
Net Direction:
Learn how we calculated this below

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How to Calculate Net Force

Force is a vector quantity that refers to any interaction that, when unopposed, changes the motion of an object. Force can cause an object to accelerate.

Force can be represented as a push or a pull and is measured in Newtons (N). Net force is the total force acting on an object when all individual forces are combined.

The equation to calculate an individual force is given by Newton’s second law, which states F = m a, where F is the force applied to the object, m is the mass of the object, and a is the acceleration.

How Forces Interact

Forces can interact in different ways:

  • Additive Interaction: When two or more forces act in the same direction, they add together to produce a greater overall force.
  • Subtractive Interaction: When forces act in opposite directions, they subtract from each other, reducing the overall force.
  • Perpendicular Interaction: When forces act at right angles to each other, their effects are independent of each other, and they must be combined using vector addition.

The interaction of forces determines how they influence the motion and direction of an object, considering both the magnitude and direction of each force involved.

Understanding Force Vectors

A force vector represents the magnitude and direction of a force. Vectors are usually depicted as arrows, where the length represents the magnitude and the arrow points in the direction of the force.

The components of force vectors can be analyzed using trigonometric methods if they are not aligned along the same axis.

Steps to Calculate Net Force and Direction

The net force is the vector sum of all forces acting on an object. It determines the overall effect of multiple forces, influencing both the acceleration and direction of motion.

The formula to calculate the net force is:

Fnet = ∑ Fi

You’ll need to use trigonometry to apply this formula to calculate the net force and direction.

Step One: Calculate the Horizontal Forces

The first step is to calculate the total horizontal forces, denoted Fx.

Recall from the unit circle that to calculate the length of the base of a right triangle, you need to use the cosine of the angle. Thus, to calculate the horizontal force for each individual force, you need to multiply the amount of force by the cosine of the direction of the force.

Fix = Fi · cos θi

The horizontal force for a force Fi is equal to the force multiplied by the cosine of the angle of its direction.

After doing this for each force, you can find the sum of the horizontal forces Fx.

Fx = ∑ Fix

Step Two: Calculate the Vertical Forces

The next step is to calculate the vertical force. The process to calculate this is nearly identical to calculating the horizontal force, but using the sine of the force’s angle instead of cosine.

Fiy = Fi · sin θi

The vertical force for a force Fi is equal to the force multiplied by the sine of the angle of its direction.

You can find the sum of the vertical forces Fy after doing this for each force.

Fy = ∑ Fiy

Step Three: Calculate the Net Force

Now, you can calculate the net force by using the Pythagorean theorem.

Fnet = √(Fx² + Fy²)

Thus, the net force Fnet is equal to the square root of the sum of horizontal forces Fx squared plus the sum of vertical forces Fy squared.

Step Four: Calculate the Net Direction

The angle of the direction of net force can be calculated using the inverse tangent of the rise over the run.

θ = tan-1(Fy / Fx)

The angle of net force θ is equal to the inverse tangent of the sum of vertical force Fy divided by the sum of horizontal force Fx.

For example, let’s consider an object on which three forces are acting: a 10 N force to the right (0°), a 3 N force to the left (180°), and a 4 N force upward (90°).

Let’s start by finding the horizontal forces:

10 N · cos(0°) = 10 N
3 N · cos(180°) = -3 N
4 N · cos(90°) = 0 N
Fx = 10 N + -3 N + 0 N = 7 N

Next, let’s find the vertical forces:

10 N · sin(0°) = 0 N
3 N · sin(180°) = 0 N
4 N · sin(90°) = 4 N
Fy = 0 N + 0 N + 4 N = 4 N

Now, let’s calculate the net force:

Fnet = √(7² + 4²)
Fnet = √(49 + 16)
Fnet = √65
Fnet = 8.06 N

And finally, let’s calculate the direction of force:

θ = tan-1(4 N / 7 N)
θ = tan-1(0.5714)
θ = 29.74°

Thus, the net force of these individual forces is equal to 8.06 Newtons, and the direction of force is 29.74°.

Frequently Asked Questions

What happens if the net force on an object is zero?

If the net force is zero, the object will either remain at rest or continue moving at a constant velocity. This is a state of equilibrium.

Does the net force include all types of forces?

Yes, the net force calculation includes all types of forces acting on an object, whether they are gravitational, frictional, applied forces, or others.

How do you handle forces that are not aligned?

Forces that are not aligned must be broken down into their horizontal and vertical components and summed separately. The resulting components are then used to find the magnitude and direction of the net force.