• First get the area of the master cylinder pistons. The area of a circle is the amount of space the circle covers. ¹⁾
  • The formula for calculating the area of a circle is A = πr² where pi (π) equals 3.14 and the radius ® is half the diameter.
  • Or 3.14 x (r x r) = piston area (for one piston).
• The pressure is arrived at by Pascals law. ²⁾
  • F (force) = P (pressure) X A (area) or P (pressure) = F (force) ÷ A (area).
  • So with a 10 lbs force at the 5/8“ break lever, we get P = 10 ÷ 0.306640625 where P = 32.6 PSI.
    You would then multiply 32.6 by the area of the piston in the brake caliper to find the actual pressure applied to the disc by each brake piston.

• General rule of thumb when swapping master cylinders is: ³⁾
  • Bigger M/C = More pressure required to compress brake lever, less lever travel.
    The MoCo reduced pressure at the caliper in dual discs systems with a larger master cylinder piston.
  • Smaller M/C = Less pressure required, more lever travel.
    If the area of the master cylinder piston is reduced, the pressure at the caliper increases.
    A smaller master cylinder piston used in a dual disc system would make it too easy to lock up the brakes and make for an unsafe system.

Below is a reprint from vintagebrake.com.
⁴⁾

While attending Vintage Days West, and thoroughly enjoying it, I was reminded that many of the people I had occasion to talk to, lacked an understanding of the importance of master cylinder to wheel cylinder ratios. This critical ratio is of paramount importance in determining “feel”. It has been my experience that there is a “sweet spot” in the range. I like ratios in the 27:1 range-2 finger power brakes, feeling some line and/or caliper flex. 23:1 is at the other end of the spectrum-firm. Ratios lower than 20:1 can result a feel so “wooden” as to have a toggle switch effect: nothing happens until the wheel locks. Disc and wheel diameters must be taken into consideration. A 10 inch disc working against a 19” wheel just doesn't have the leverage ratio that a 13 inch disc working a 17“ wheel does. The hand lever ratio counts too: witness the adjustable master cylinders from Lockheed and Brembo.

A case in point: I had a complaint from a racer about Ferodo CP901- a compound renown for its great feel. His comment was that they worked poorly until the wheel locked. He had been thrown on the ground twice. Intrigued, I inquired as to the application. “Yamaha RD350” he replied. A red flag went up. CP901 was not available for the 48mm Yamaha caliper. I asked “How that could that be?” He had up-graded his braking system with the 41mm Lockheed unit, but was unaware that a master cylinder change was in order. A stock RD 350 has an already poor ratio of 18.3 :1, and with Lockheed, became an unhealthy 13.3 :1. The “sweet spot” formula said a change to a 11 or 12mm master cylinder was in order: my personal preference and recommendation would have been an 11mm. He was able to switch to a 1/2” , and although not ideal, he was keeping the rubber side down.

For 2 piston opposed calipers, I like ratios in the 27:1 range, feeling some line and caliper flex. For a firmer lever, use 23:1. I think ratios lower than 23:1 produce a lever feel so “wooden” as to have little, if any feel. Combine “low” leverage ratios with sticky pads, and unpredictable lockup is the result. The high effort required at the lever also results in undesired input to the bars. Single piston calipers are much happier in the 14:1 to 12:1 range. Disc and wheel diameters, as well as hand lever ratios, must be considered.

Example for the table below;
Area of a 10mm bore M/C = 78.54 mm² (3.14 x r² (5 x 5, or 25mm) = 78.54).
Area of a 28mm dia. caliper piston = 615.44 mm² (3.14 x r² (14 x 14, or 196mm) = 615.44).
The ratio between the caliper piston and the master cylinder is 7.84 to 1, (615.44 / 78.54 = 7.84).

( ) = Number of active pistons. ⁵⁾