Oh my.
Crusher numbers are a conversion of a physical change in the dimensions of a lead (for shotshells) cylinder into a pressure number using a Tarage Table
Scroll down just past 1/2 way here for an illustration and explanation.
https://docs.google.com/document/d/1F2sQuPm05IE4VWYYnCkvuXmYEzQoWd_SQgaAfUOZEFU/edit?tab=t.0 There is no formula for the conversion of lead crushers to modern piezoelectric transducer numbers -
+ 10 - 14% is close
From the CIP site: confirmation that 850 BAR = 12,328 PSI by crushers (LUP) is actually 960 BAR = 13,924 PSI by transducers (
13% higher)
“These cartridges, if they are to be fired from standard proof shotguns (ie those proved to 960 bar [13,924 psi transducer] or, previously, 850 bar [crusher]), or magnum proof shotguns (ie those proved to 1370 bar [19,870 psi transducer] or, previously, 1200 bar [crusher]) must not exceed the maximum admissible service pressure of 74 MPa (new units “megapascals”, in place of the old 740 bar) specified by the CIP and measured by means of a piezo-electric transducer.”
This is
Burrard's conversion for Long Tons/ Sq. Inch Lead Crusher Pressure (Cp) to transducer PSI (pound-force per square inch): (Cp x 1.5) - .5 = TSI, TSI X 2240 = PSI.
The 1954 Rules of Proof “Highest Mean Service Pressure” equivalent transducer values as converted from LUP by Burrard’s formula:
2 3/4 tons = 8,120 psi = 560 BAR
3 tons = 8,960 psi = 618 BAR
3 1/4 tons = 9,800 psi = 676 BAR
3 1/2 tons = 10,640 psi = 734 BAR
4 tons = 12,320 psi = 850 BAR
Conversion provided by the Birmingham Proof House 11-2001 courtesy of Larry Brown, is simply
Tons x 2240 x 1.33 Mr. Roger Hancox, Proof Master, Birmingham Proof House, 2008:
“A basic ‘Rule of Thumb’ conversion of tons to CIP transducer pressure (is) multiplying the tons per sq inch by 2240 to obtain psi, and then by a factor of 1.33 to obtain the approximate CIP pressure.”
(Apparently the Proof Master thought we Colonials aren't good with higher math

)
2” chamber / 2 3/4 tons = 8,193 psi
2 1/2” chamber / 3 tons = 8,938 psi
2 3/4” chamber / 3 1/4 tons = 9,682 psi
3” chamber / 3 1/2 tons = 10,427 psi
3” chamber “Magnum” / 4 tons = 11,917 psi