When calculating the equilibrium constant, the equilibrium partial pressure p (in Pa) of gaseous substances is divided by the standard configuration pressure p? , the equilibrium concentration of solution components divided by the standard configuration concentration (C? ), the obtained equilibrium constant is called the standard equilibrium constant k? . So there is no dimension.
Kc is calculated from the equilibrium concentration of each substance (whether it is a solution or a gas, it is a calculated concentration); Kp is calculated from the equilibrium pressure of each substance (of course, it is mainly used for reactions involving gases).