A four-stroke rotary-piston engine has an outer disk, and inner disk, at least one cylinder, at least one piston, at least one piston rod, a fixed gear engaged with a planet gear and a rotary gate valve positioned at a head of the cylinder. The inner disk is rotatable with respect to the outer disk by a compression control device. The planet gear rotates a crank situated on a shaft thereof. The shaft passes upwardly through the inner disk. The crank reciprocates a lever via the piston rod. The lever has an end pivoted on the outer disk so as to push the piston into and out of the cylinder.