Your foot makes a few hundred pounds. The hydraulics turn that into thousands.
Brake fluid can't be compressed, so pressure you make at the master cylinder is felt equally everywhere in the system — that's Pascal's law. Push a small master-cylinder piston and that pressure acts on the much larger caliper pistons, multiplying your force. Force = pressure × area, so bigger caliper pistons clamp harder. The catch: the system only works because the fluid is solid and sealed. Let air in and the pedal goes spongy; spring a leak and the pedal drops to the floor.
Force = Pressure × Area
and pressure is equal everywhere
Where the force comes from
The pedal ratio (~4:1) multiplies your foot first; the master cylinder turns that force into pressure; the larger caliper pistons turn pressure back into a bigger force. Three stages of multiplication.
⚑ Spongy vs sinking
Feel the pedal: spongy (springy, comes back) = air in the lines — bleed it. Slowly sinking to the floor under steady pressure = fluid getting past a seal, usually a failing master cylinder (or an external leak). Different feel, different fix.
02 The Hydraulic Bench
Press harder, or change the bore sizes, and watch pressure and clamping force build — then break it with air or a leak.
509Line pressure · psi
2498Clamp force · lb
25×Force multiplication
Pedal feel
Firm
Pedal force100 lb
Master bore1.00 in
Caliper bore2.50 in
03 What If…
Reason first, then reveal.
?The pedal feels springy and low, but pumps up firmer on the second push. What's in there?
Air. Air compresses, so the first push squeezes the bubble instead of clamping; pumping stacks fluid and firms it up briefly. Bleed the system to get a solid pedal — a healthy circuit never needs pumping.
?Under steady foot pressure the pedal slowly sinks to the floor, but you see no fluid leaking anywhere. Cause?
A failing master cylinder — fluid is bypassing an internal seal, so pressure bleeds off internally with nothing dripping outside. A sinking pedal with no external leak is the classic bad-master symptom. Replace the master cylinder.
?You fit a caliper with bigger pistons but keep the same master cylinder and pedal effort. What changes?
More clamping force for the same pressure (force = pressure × area), so more braking — but the pedal travels farther, because the master must move more fluid to fill the bigger caliper. Hydraulics trade pedal travel for force; there's no free lunch.
04 Practice
ASE-style. Pick an answer to see why.
05 Recap
Brake fluid doesn't compress, so pressure is equal everywhere (Pascal's law).
Force = pressure × area — bigger caliper pistons clamp harder (but the pedal travels farther).
Force is multiplied three ways: pedal ratio → master cylinder → caliper pistons.
Spongy pedal = air (bleed it). Slowly sinking pedal, no leak = failing master cylinder.
A pedal that goes straight to the floor = lost fluid / no pressure — find the leak.