In engineering and physics, g<sub>c</sub> is a unit conversion factor used to convert mass to force or vice versa. It is defined as
In unit systems where force is a derived unit, like in SI units, g<sub>c</sub> is equal to 1. In unit systems where force is a primary unit, like in imperial and US customary measurement systems, g<sub>c</sub> may or may not equal 1 depending on the units used, and value other than 1 may be required to obtain correct results. For example, in the kinetic energy (KE) formula, if g<sub>c</sub> = 1 is used, then KE is expressed in foot-poundals; but if g<sub>c</sub> = 32.174 is used, then KE is expressed in foot-pounds.
According to Newton's second law, the force F is proportional to the product of mass m and acceleration a:
or
If F = 1 lbf, m = 1 lb, and a = , then
Leading to
g<sub>c</sub> is defined as the reciprocal of the constant K
or equivalently, as