In a hydraulic system, applying a small force to a small piston can produce a large force on a large piston. Why?

In a hydraulic system, pressure (force per unit area) is transmitted equally through the fluid (Pascal's principle). Since pressure equals force divided by area, the same pressure acting on a larger piston area produces a larger force: F = pressure × area. So a small force on a small-area piston creates a pressure that, when applied to a large-area piston, yields a much greater force. The tradeoff is distance — the large piston moves a smaller distance than the small piston travels, conserving work/energy. This force-multiplication principle underlies hydraulic jacks, presses, and brakes.