Conversion between SI and imperial units of force
At sea level on earth, the magnitude of lbm exactly equals the magnitude of lbf, and the magnitude of kgm exactly equals the magnitude of kgf. This equivalency is only true at the surface of the earth, and does not hold up when acceleration other than that of the standard acceleration of gravity (that at the sea level of Earth) is used.
In other words, your mass and force exerted on the ground equal the same number in pounds (that is, lbm and lbf) on Earth at sea level. Since kgf and lbf are units of force, they are invariant, and the equivalence 1 kgf = 2.2046 lbf is always true. However, the conversion 1 kgm = 2.2046 lbm is true only on Earth at sea level.
The concept of weight, unlike force and mass, depends on the environment in which the weighing is done. It can be assumed that this is at sea level on Earth, unless other conditions are stated. Thus one pound mass (lbm) weighs one pound (lbf), and one kilogram mass (kgm) weighs one kilogram force (kgf). Further, an item with a weight of 10 lbf has a mass of 10 lbm and also a mass of 0.3108 slugs (= 10 lbm divided by 31.174 lbm per slug).
By analogy with the slug, there is a rarely used unit of mass called the "metric slug". This is the mass that accelerates at one metre per second squared when pushed by a force of one kgf. An item with a weight (on Earth at sea level) of 10 kgf has a mass of 10 kgm and also a mass of 1.0197 metric slugs (= 10 kgm divided by 9.807 kgm per metric slug).
An even rarer unit of force called the "imperial newton" is defined as the force that accelerates 1 lbm at 1 foot per second squared. Given that 1 lbf = 32.174 lbm times one foot per square second, we have (1/32.174 =) 0.0311 lbf = 1 lbm times 1 foot per square second = 1 imperial newton. Thus 1 lbf = 32.174 imperial newtons.
In conclusion, we have the following conversions, with "metric slugs" used very infrequently, and "imperial newtons" virtually never used.
- 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
