Here you go, Piston area and force.
Look, guys.
The nickel in the clay.... that's not showing how pressure moves a nickel into clay. It's show how the pressure applied by the nickel on the clay is higher if the force is applied edgewise (small area) vs side ways (large area).
Maybe a way of looking at this that is easier for some folks to grasp.... let's talk about braking systems.
Larger caliper pistons, and more caliper pistons, yield more rotor clamping force for a given fluid pressure.
Smaller master cylinder pistons give greater fluid pressure for a given amount of pedal force.
Pressure = Force/Area. This can be expressed as PSI (POUNDS PER SQUARE INCH, or stated another way, pounds (force)/square inch (area).
Let's play with some numbers.
Ex. 1: 10 PSI = 10 lbs/Area
Area=10lbs/10psi = 1 square inch
Ex. 2: 10 PSI = 100 lbs/Area
Area=100lbs/10psi = 10 square inches
Ex. 3: 10psi = force/10 square inches
Force = 10psi*10 square inches =100 pounds
Ex. 4: 10psi = force/100 square inches
Force= 10psi*100sq in = 1000lbs
In these examples....the area is the piston face area. The pressure is fluid pressure. The force is the Force the piston will exert on the rotor. Given constant pressure, if you increase piston size, force will increase. If pressure reduces, force decreases.
This is the most basic, fundamental physics guys. It's absolutely irrefutable.
It's not whatchamacallits or what have yous. Anyone who's talking like that just doesn't have good basic arithmetic skills.