Force, here in the terms of physics, is an influence that makes objects be affected in terms of movement or geometrical composition. More precise, a force causes a an object with mass to change its velocity (which has both magnitude and direction) from a state of rest or if already moving to accelerate.
The derived SI unit of force is the newton (N). The newton can be dervied from Isaac Newton's second law of motion F=ma, which also could be written as 1 N=1 kg×m/s2.
The gravitational metric system (GMS) takes a different approach to force. In the SI system the unit of force, the newton, is normalised with the kilogram, metre and second so that 1 N=1 kg×m/s2.
In GMS, the base unit of force is not normalised against these quantities but it depends on a selected or locally measured gravitational constant g. Often g is set to of 9.80665 m/s2, the acceleration of gravity on the surface of the Earth.
The British gravitational system is based on the foot, the second, and the slug mass. One slug weighs 32.174 pounds at sea level and 45° latitude: The equivalent in terms of mass is 14.594 kilograms. This system is also known as the British engineering system of units.
The Foot-Pound-Second System (FPS) is based on the fundamental units foot, (avoirdupois) pound and second for the quantities of length, mass (or weight) and time. In this table the pound should be interpreted as a unit of mass (often abbreviated as lbm to make this obvious).
In FPS the unit of force is called the poundal (pdl) and is defined as 1 pdl = 1 lbm × ft/s2.
The metre-tonne-second (MTS) system of units was invented in France and became the legal system between 1919 and 1961. The Soviet Union also adopted the system between 1933 and 1955. It is coherent much like the SI or CGS systems but larger units are chosen for industrial purposes. Compared to SI the MTS uses tonne instead of kilogram as base unit of mass.
Yet another variant of the metric system is the Centimetre-Gram-Second System (CGS). Instead of the SI unit metre for length, CGS uses centimetre and instead of using kilogram as base unit of mass, CGS uses grams. It was proposed by the German mathematician Carl Friedrich Gauss in 1832 and extended with electromagentic units by James Clerk Maxwell and William Thomson. However, since the adoption of the MKS system since the 1940s CGS has gone much out of use.
The unit of force is called dyne (dyn) and is defined as g·cm/s2.
The atomic units (au) is a system of natural units adjusted for calculations on the level atomic physics. There are two variations of atomic units, the Hartree and Rydberg atomic units. This conversion is based on the Hartree standard. The difference is which unit of mass and charge to normalise against. See the article on natural units for more information on how this system is defined compared to the SI units and what benefits this may have.
The planck force (LMT-2) is part of the planck units. See the article for more information about the benefits of using planck units when calculating on the scale of quantum physics.