Catalysis of the transmembrane transfer of potassium by a channel with a unit conductance of 2 to 20 picoSiemens that opens in response to stimulus by internal calcium ions. Small conductance calcium-activated potassium channels are more sensitive to calcium than are large conductance calcium-activated potassium channels. Transport by a channel involves catalysis of facilitated diffusion of a solute (by an energy-independent process) involving passage through a transmembrane aqueous pore or channel, without evidence for a carrier-mediated mechanism.