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Force Definition, Formula and Units


In the subject of physics, force is any external agent which, when not opposed by a body, changes the state of motion of that body, that is, accelerating that body from rest to motion or bringing the body, which was already in motion, to a resting stop. In simpler terms, it is the mere push or pull influence experienced by an object that may or may not change its state of motion or position. It is denoted using the symbol F. A force can either move a body that was initially in rest (or even accelerate a body in motion) or can make a body in motion come to a position of equilibrium (rest). Force is a vector quantity in nature because it is measured in terms of both magnitude and the direction through which it is acting. The SI unit is newton (N), and the value of force is generally given by F = ma where

  • m is the mass of the object on which the force is applied
  • a is the acceleration of that object

The acceleration experienced by a body due to a force acting on it is directly proportional to the normal force and indirectly proportional to the mass of the object, as proven by Newton’s second law of motion. Force can be classified into two types as fundamental forces and non-fundamental forces, which are derived from the fundamental forces. In any material matter, two adjacent parts of a body constantly apply forces on each other. The distribution of these acting forces on the body is known as internal mechanical stress. This internal mechanical stress does not bring about any acceleration in the measured body because the internal forces cancel each other out, bringing the effective net force to zero.

Units of Force

  • Newton: Named after the English physicist Sir Isaac Newton, newton, denoted as N, is the SI unit of force. One newton is defined as the force acting on a body that has a mass of 1 kilogram producing an acceleration of 1 meter per second squared. The body is accelerated in the same direction that the force is applied. The SI base unit of newton is given as 1 kg⋅ m/ s 2 . In cases where there are forces of huge magnitude involved, the unit kilonewton is used, and 1 kN = 1000 N = 102 kg × 9.81 m/ s 2 . For example, the thrust produced by jet engines like the F100 and the load limit of safety equipment platforms can be expressed in terms of kilonewtons.
  • Dyne: The unit of force in the centimeter – gram – second system of units is dyne. It is denoted using the symbol dyn and is defined as the force acting on a body with a mass of one gram producing an acceleration of one centimeter per second squared. The dyne is also defined as the force that is acting for a time duration of one second on a body of mass one gram, producing a rate of change of velocity of one centimeter per second. One dyne is equal to 10 micronewtons, (10 −5 N), as shown below. 1 dyn = 1 g⋅ cm/s 2 = 10 −5 kg⋅ m/s 2 = 10 −5 N 1 N = 1 kg⋅ m/s 2 = 10 5 g⋅ cm/s 2 = 10 5 dyn
  • A pound of force: Otherwise referred to as pound-force, a pound of force is a unit of force part of the English Engineering units and the foot-pound–second system. A pound of force is simply defined as the force of gravitation acting on a body of mass one pound (0.45359237 kg) on the surface of the Earth. A pound of force is denoted using the symbol lbf. This unit of force is not very accurate because the force of gravitation acting on an object tends to differ from one place to another. That is, the force of gravitation acting on an object at the pole is different in magnitude from the force of attraction acting on an object near the equator.


The different units of force and their equivalent of each other are shown below.








1 N

1 kg. m/ s2

105 dyn

0.10197 kp

0.22481 lbf


1 dyn

10-5 N

1 g. cm/ s2

1.0197 x 10-6 kp

2.2481 x 10-6 lbf

7.2330 x 10-5 pdl

1 kp

9.80665 N

980665 dyn

gn x 1 kg

2.2046 lbf

70.932 pdl

1 lbf

4.448222 N

444822 dyn

0.45359 kp

gn x 1 lb

32.174 pdl

1 pdl

0.138255 N

13825 dyn

0.014098 kp


1 lb. ft./ s2



where gn = 9.8 m/s2


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