*This article is about the concept of force in physics. For all other uses see Force (disambiguation).*

Force isn't really a fundamental quantity in physics, despite the inertia of physics education still introducing students to physics via the Newtonian concept of force. More fundamental are momenta, energy and stress. In fact, no one measures force directly. Instead, everytime one says one is measuring a force, a quick rethinking would make one realize that what one really measures is stress (or maybe its gradient). The "force" you feel on your skin, for example, is really your pressure nerve cells picking up a change in pressure. A spring meter measures the tension of the spring, which is really its stress, etc. etc.

In physics, a net **force** acting on a body causes that body to accelerate (i.e. to change its velocity). Force is a vector. The SI unit used to measure force is the newton.

See also engineering mechanics:

- Statics Where the sum of the forces acting on a body in static equilibrium (motionless, Acceleration=0) is zero. F=MA=0
- Dynamics The sum of the forces acting on a body or system over time is non zero with a resulting set of accelerations defined by detailed analysis of equations derived from F=MA.

*m*is the inertial mass of the particle,

*v*is its initial velocity,

_{o}*v*is its final velocity, and

*T*is the time from the initial state to the final state; the expression on the right of the equation being the limit as

*T*goes to zero.

Force was so defined in order that its reification would explain the effects of superimposing situations: If in one situation, a force is experienced by a particle, and if in another situation another force is experience by that particle, then in a third situation, which (according to standard physical practice) is taken to be a combination of the two individual situations, the force experienced by the particle will be the vector sum of the individual forces experienced in the first two situations. This superposition of forces, along with the definition of inertial frames and inertial mass, are the empirical content of Newton's laws of motion.

Since force is a vector it can be resolved into components. For example, a 2D force acting in the direction North-East can be split in to two forces along the North and East directions respectively. The vector-sum of these component forces is equal to the original force.

Table of contents |

2 Relationships between force units and mass units 3 Imperial units of force 4 Conversion between SI and imperial units of force 5 Combining Forces 6 External link |

## More depth

If**F**is not constant over Δt, then this is the definition of average force over the time interval. To apply it at an instant we apply an idea from Calculus. Graphing

**p**as a function of time, the average force will be the slope of the line connecting the momentum at two times. Taking the limit as the two times get closer together gives the slope at an instant, which is called the derivative:

In most expositions of mechanics, force is usually defined only implicitly, in terms of the equations that work with it. Some physicists, philosophers and mathematicians, such as Ernst Mach, Clifford Truesdell and Walter Noll, have found this problematic and sought a more explicit definition of force.

## Relationships between force units and mass units

which is derived from Newton’s second law of motion,*F*is the force in newtons,

*m*the mass in kilograms and

*a*the acceleration in meters per second squared. To a physicist, the kilogram is a unit of mass, but in common usage "kilogram" is a shorthand for "the weight of a one kilogram mass at sea level on earth". At sea level on earth, the acceleration due to gravity (

*a*in the above equation) is 9.807 meters per second squared, so the weight of one kilogram is 1 kg × 9.807 m/s² = 9.807 N.

To distinguish these two meanings of "kilogram", the abbreviations "kgm" for kilogram mass (i.e. 1 kg) and "kgf" for kilogram force, also called kilopond (kp), equal to 9.807 N, are sometimes used. These are only informal terms and are not recognized in the SI system of units.

## Imperial units of force

The relationship F = m×a mentioned above may also be used with non-metric units.

## Conversion between SI and imperial units of force

- 1 kgf = 9.807 newton
- 1 metric slug = 9.807 kgm
- 1 lbf = 32.174 imperial newtons
- 1 slug = 32.174 lbm
- 1 kgf = 2.2046 lbf

## Combining Forces

When forces combine, one of two things may happen:

- The forces are equal and result in equilibrium (they have canceled each other out).
- The more powerful force cancels out the less powerful; a resultant force is produced.