Hydraulic press is based on

A hydraulic press operates based on Pascal's law, which states that any pressure applied to a confined fluid is transmitted undiminished throughout the fluid in all directions. The relationship is governed by the formula:
$$P=\frac{F_1}{A_1}=\frac{F_2}{A_2}$$

where $P$ is the pressure, $F$ represents the applied forces, and $A$ represents the cross-sectional areas of the pistons. This allows a small force applied over a small area to generate a much larger force over a larger area.