Force definition

A force (F) is a physical vector quantity that describes any influence on a change in the shape and structure of a body, a change in the velocity of a body or particle, the interaction of physical systems, or the interaction of systems and fields.

The basic unit of force is Newton (N). The forces that act on a body from the outside can be; external forces and the forces that act in the body and resist the action of external forces (internal). External forces can be distributed on; the surface (e.g., hydrostatic pressure), by volume (gravitational, magnetic), or act concentrated in one point.

Meanwhile, make sure to see our Friction Calculator as well, since it is related to this subject.

3d-rendering-robot-hand-holding-newton-cradle | Force

How to calculate the force?

The term “force” appears in almost every area of daily life, from sports to weather to military engagements. However, force is ultimately a term established in physics, where it has a very precise and vital meaning. The newton (N) is the standard unit of force, equivalent to kg m/s2.

Force is one of two physical variables that impact an object’s motion, the other being mass. Kinematics is the study of the motion of things in space that considers position, velocity, and acceleration; adding force and mass in the study of motion introduces the idea of dynamics.

Force equation

According to the standard version of the force formula used throughout physics, the net external force on an item is the product of its mass and acceleration. Newton’s second law of motion defines the force formula: The force exerted by an item is equal to its mass multiplied by its acceleration:

 F = m * a

 You must use SI units to use this formula: Newtons for force, kilograms for mass, and meters per second squared for acceleration.

Force and acceleration are vector variables in this context, which means they have a value (magnitude, expressed by a number) and a direction in space associated with them. Mass is a scalar quantity, meaning it can only be defined in terms of its magnitude.

Newton’s laws

But what does the term “change of state of motion” mean? Basic the kinematic quantity that describes the state of motion is velocity. While it is constant. There is no impact. To change it, we have to apply it. Also, changing gear means accelerating. In this short story, Isaac Newton wrote in three short axioms (or laws):

1. If no force acts on the body, or if the sum of all, acting on the body is equal to 0, the body will rest or will move uniformly in the direction.

2. The F is equal to the product of the mass of the body and its acceleration. The acceleration of a body is proportional to the force acting on it and inversely proportional to its mass.

3. If one body acts on another by some force, then it will the second body act on the first of the same amount and direction, but opposite orientations.

All classical mechanics, with all its complicated equations, follow from these three axioms. It is clear that force, as a physical and mathematical quantity, must be vector; has direction, has amount, has an orientation. It is also clear that mass, as a measure of sluggishness, or resistance of the body to change his state of motion should be scalar, and it positive; the body itself equally resists the action of force on him regardless of the direction of the force. The mass should be positive. Can you imagine a situation in which push something? I.e., you want to push away from yourself, and what gets acceleration towards you instead of you?

Moment of force

Also, the static moment is the product of the force and the distance of the direction of its action from the axis or point towards which that moment acts. The magnitude and direction of action determine the moment of force, can be represented by a vector, and is most often described by a magnitude and a curved arrow around an axis or point in the direction of action of the moment.

The magnitude of the moment is

M = F * a

where a is the arm of the F concerning the axis or point of its action.

Also, the moment of a resultant concerning an axis or point is equal to the sum of the moments of its components concerning the same axis or point.

Coupling force

The coupling of forces (pair) consists of two F equal in magnitude with parallel directions of action and opposite directions. The distance between this F is the arm coupling force.

The magnitude of the coupling moment F is:

M = F * b

The unit for the moment of F and the moment of coupling of forces is the same, so it can simply say that the unit for the magnitude of the moment is – Nm (newton-meter) or Nmm (newton-millimeter). Nmm has a specific application in mechanical engineering.

External forces and moments that act on a body, or machine part, represent its load.


The forces acting on a body are in equilibrium if their joint action will not move the body from a state of rest or uniform rectilinear motion. Furthermore, the graphical equilibrium conditions are met if the force polygon and the chain polygon are closed. In a force polygon, all those must have the same sense of circumvention. When three forces are in balance, the triangle must be closed (with the same direction of travel), and in the position plan, all three must intersect at one point.

For each body in static equilibrium, can determine unknown quantities from the set static equilibrium conditions. If the number of unknown quantities does not exceed the number of equilibrium conditions, then we consider the observed system to be statically determined. Conversely, if the number of unknown quantities is greater than the possible number of set equilibrium conditions, the system is statically indeterminate.

To analytically find unknown sizes of statically determined systems, it is necessary to apply the following sequence of procedures:

  • free the body of its connections with the environment;
  • select the coordinate system and plot the reactions of the connections;
  • select and write equations that express the equilibrium conditions in the simplest way;
  • solve the necessary geometric relationships;
  • calculate unknown quantities by solving equilibrium equations.

Types of forces

In nature, several types may differ in the mode of action of strength and nature. Furthermore, here are some types of it:

  • Electric and magnetic – attractive and repulsive.
  • Nuclear – range up to the distance between particles within the nucleus of an atom. They are strong and attractive.
  • Gravitational – one of the weakest in nature, acts at very long distances. The nature of gravity was first understood by Isaac Newton.

Concentrated force

The force acting at a point, we call it the concentrated force. Therefore, vectors represent concentrated forces – they have a numerical value called intensity, direction and direction of action, and grip. The mechanics of rigid bodies, in many cases, can be represented by a sliding vector – its influence does not change if the force moves in the direction of its action to some other grip, even outside the body.

Concentrated force, however, is idealization: each force acts distributed over a larger or smaller area or over the volume of the body, and the concentrated force is the result of such continuous action. In statics, the conditions of equilibrium of bodies affected are studied. They can divide into external and internal.

The appearance of internal forces is a consequence of the interaction of body particles at the atomic (and even more elementary) level – and interparticle forces resist changes in the distance between particles. Internal is the results of interparticle in a cross-section of a body.

External forces divide into active (results of various loads: snow, wind, vehicles …, but also their weight) and reactive (that occur in possible connections of the body with the ground or with other bodies). Reactions and internal forces are not only caused by external activity but can also be caused by actions such as temperature changes, shrinkage, creep…

What is not force?

Also, misconceptions of the concept of force appear very often. We will give some road examples of what force is not and how we sometimes misuse it.

  • It’s not a property of the body

Example: “A magnet has great force.”

A magnet near a piece of iron can attract a piece of iron with great force. At the same time, the iron attracts the magnet with equal F), but if the piece is iron far, the F is almost gone. Bodies cannot possess force, but they can possess energy or amount of motion.

  • It’s not a measure of body movement

Example: “A train is racing with great force.”

A running train has a large amount of motion and large kinetic energy. The F occurs only if the train collides with another body and depends on the mass of the other body. If a train hits another train, the F will be enormous. Also, it will be negligible if it hits a fly in flight.

  • Power is not energy. It cannot be stored or consumed

Example: “We push the body in the horizontal direction and it continues to move due to impact which acts on him even after we stopped pushing him.”

According to the Aristotelian view of dynamics, a very common misconception speaks that we have surrendered to the body, and it retains it as long as it moves. In doing so, the impact slowly “spends” until the body stops. It is obvious to replace the notion of impact with the notion of energy.


How to calculate net force?

The total of all forces exerted on an item is known as the net force. Newton’s second law, which says that F = ma, where F represents the net force, may be used to determine the net force. The object’s mass is denoted by m.

How to find acceleration with force and mass?

Newton’s second rule of motion states that an object’s acceleration equals the net force exerted on it divided by its mass or a = F * m. When the mass of an item and the net force acting on it are known, we use this acceleration equation to compute its acceleration.

Is weight a force?

Weight is a force that acts on matter. Any change in the motion of things is resisted by mass. The term weight has a specific meaning in physics: the force that operates on a mass owing to gravity.

What is the formula for force?

Force equals mass times acceleration for a constant mass, F = m x a.

What are the types of forces? 

The gravity force, electromagnetic force, weak nuclear force, and strong nuclear force are the four fundamental forces.

Is acceleration a force?

The acceleration is proportional to the net force; the net force equals mass times acceleration; the acceleration is directed in the same direction as the net force; a net force causes an acceleration.

Other calculators

Be sure to check out our Gravity Force Calculator and Free Fall Calculator, to find out something new about gravity and Newton’s laws also. You can find out how gravity was introduced and how it is represented through different research from different scientists. That calculator also contains an example on which you can actually see the calculation of the gravity F. For more calculators in math, physics, finance, health, and more, visit our CalCon Calculator official page.