Net Force Definition: Formula, Calculation Steps, and Examples

Net force is the vector sum of all forces acting on an object. The net force formula is F_net = ma, and the SI unit is the newton. A net force of zero means balanced forces and constant velocity. This guide covers the definition, 5 calculation steps, 4 examples, and 3 misconceptions.

For a related explanation, see Newton Laws of Motion.

What Is Net Force?

Net force is the vector sum of all external forces acting on an object. It is also called resultant force or total force. The symbols are F_net and ΣF. Forces that combine into a net force include applied force, friction, gravity, normal force, tension, and air resistance. According to the OpenStax University Physics textbook, a net external force causes nonzero acceleration.

What Is the Simple Definition of Net Force?

Net force is the overall force on an object after adding every push and pull, including direction. Net force is a vector quantity, so it has magnitude and direction.

What Is the Net Force Formula?

The net force formula is F_net = ma, where net force equals mass times acceleration. The table below defines each symbol with its quantity and SI unit.

Newton's second law is known for relating net force, mass, and acceleration. Acceleration points in the same direction as the net force. In 2 dimensions, the formula splits into ΣF_x = ma_x and ΣF_y = ma_y.

According to NIST, the newton is the force required to give a 1 kilogram mass an acceleration of 1 meter per second squared. Therefore, 1 N equals 1 kg·m/s².

How Do You Calculate Net Force?

Calculate net force by adding all forces as vectors, or by multiplying mass and acceleration when both are known. Adding forces takes 5 steps:

• Draw a free-body diagram that shows every force on the object.

• Choose a positive direction, such as right or up.

• Assign positive values to forces in that direction and negative values to forces in the opposite direction.

• Add the values along each axis to get ΣF_x and ΣF_y.

• Combine the sums with the Pythagorean theorem for forces in 2 dimensions: F_net = √(ΣF_x² + ΣF_y²), with direction θ = tan⁻¹(ΣF_y/ΣF_x).

OpenStax gives a 2-dimensional example. A 0.400 kg soccer ball with acceleration components of 3.00 m/s² in x and 7.00 m/s² in y has net force components of 1.20 N and 2.80 N. The magnitude is 3.05 N at 66.8° from the x-axis.

How Do You Add Forces in the Same, Opposite, and Perpendicular Directions?

Add forces by direction: sum the magnitudes for the same direction, subtract for opposite directions, and use the Pythagorean theorem for perpendicular directions. The table below lists 4 cases with the rule, an example, and the resulting net force.

What Is the Difference Between Balanced and Unbalanced Forces?

Balanced forces produce a net force of zero, and unbalanced forces produce a nonzero net force. According to NASA Glenn Research Center, an object keeps a constant velocity when no net force acts on it, and an additional external force changes that velocity. The table below compares balanced and unbalanced forces across 5 features.

What Are Examples of Net Force?

Net force examples include a book on a table, a tug of war, an accelerating car, and a skydiver at terminal velocity. The table below lists the forces, the net force, and the result for each of the 4 examples.

How Are Net Force and Newton's Laws Related?

Net force connects to all 3 of Newton's laws:

• First law: an object keeps its velocity when the net force is zero.

• Second law: net force equals mass times acceleration.

• Third law: the 2 forces in a pair act on different objects, so they do not cancel in the net force on a single object.

What Misconceptions Do Students Have About Net Force?

Students hold 3 main misconceptions about net force. Hestenes, Wells, and Swackhamer reported these beliefs in the 1992 Force Concept Inventory study in The Physics Teacher. The authors gave the inventory to more than 1,500 high school students and more than 500 university students. The study found that conventional instruction produced little change in these beliefs.

The 3 misconceptions and their corrections are:

• Belief: motion requires a net force. Correction: a net force of zero allows constant velocity.

• Belief: the largest force determines motion. Correction: net force is the sum of all forces on the object.

• Belief: velocity is proportional to applied force. Correction: acceleration is proportional to net force.

What Are People Also Asking About Net Force?

Is net force a vector or a scalar?

Net force is a vector quantity with magnitude and direction.

What is the SI unit of net force?

The SI unit of net force is the newton (N).

Can net force be negative?

Yes, a negative net force points opposite to the chosen positive direction.

Is net force the same as resultant force?

Yes, net force and resultant force both name the vector sum of all forces on an object.

What is the difference between force and net force?

A force is a single push or pull, and net force is the vector sum of all forces on an object.

What is the net force of balanced forces?

The net force of balanced forces is zero.

Does a net force always cause motion?

No, a net force causes acceleration, which changes velocity, while an object with zero net force stays at rest or keeps constant velocity.

Why Does the Net Force Definition Matter in Physics?

The net force definition matters because net force determines the acceleration of an object through F_net = ma. Balanced forces give a net force of 0 N, and unbalanced forces change velocity. The newton measures net force in the SI system. The 1992 Force Concept Inventory study found that students confuse net force with motion, so the vector sum definition is the basis for correct force analysis.

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For the official reference, consult OpenStax University Physics Second Law.

Maurice Cotterell

MEd., BSc. QTS/OCT – Physics Teacher at Davenant Foundation School
The University of the West Indies

My passion as a teacher and leader in education is to contribute to students’ enhanced learning by creation of a positive teaching/learning environment, where they are motivated to develop strong critical thinking, analytical and problem-solving skills.
As acting Vice-Principal and head of Physics, I have amassed five years of experience in leading meetings, implementing strategies to maintain discipline and school ethos, liaise with stakeholders in planning for future development of the institution; successfully negotiated the implementation of various projects for student development as well as supervising effective execution of such. For the past 19 years, I have incorporated discovery learning within the classroom through practical activities, problem solving and cooperative learning and have realized that students retention in Physics and Mathematics have increased significantly.

I am always cognizant that students have different learning styles, and as such teaching strategies during planning and delivery must take this crucial factor into consideration and be tailored to meet such differences.