For the reaction,
$A + B rightleftharpoons C+ D$, we can write the equilibrium constant in terms of concentration, $mol*L^-1$:
$K_c$ $=$ $([C][D])/([A][B])$
Note that $K_c$ is dimensionless. Should the reaction be in the gas phase, then we can utilize the Ideal Gas Law: $PV=nRT$, or $n/v = P/(RT)$. Dalton's Law of partial pressures holds that the pressure exerted by a component in a gaseous mixtures is the same as the pressure it would exert if it alone occupied the container, thus,
$n_A/v = P_A/(RT)$; $n_B/v = P_B/(RT)$ etc.
And $K_P$ $=$ $([P_C][P_D])/([P_A][P_b])$ $=$ $K_c/(RT)$
Reasonably, ideal gas behavious is assumed. So, the units can be in $mol*L^-1$.
