From AMS Glossary
(Abbreviated CIN.) The energy needed to lift an air parcel vertically and pseudoadiabatically from its originating level to its level of free convection (LFC).
For an air parcel possessing positive CAPE, the CIN represents the negative area on a thermodynamic diagram having coordinates linear in temperature and logarithmic in pressure. The negative area typically arises from the presence of a lid. Even though other factors may be favorable for development of convection, if convective inhibition is sufficiently large, deep convection will not form. The convective inhibition is expressed (analogously to CAPE) as follows:
where pi is the pressure at the level at which the parcel originates, pf is the pressure at the LFC, Rd is the specific gas constant for dry air, Tvp is the virtual temperature of the lifted parcel, and Tve is the virtual temperature of the environment. It is assumed that the environment is in hydrostatic balance and that the pressure of the parcel is the same as that of the environment.