How to determine a proving ring constant

Assuming you have a chart showing load versus a deflection, perhaps in decimals of an inch, The slope of that line is the calibration constant. The constant usually is the dial reading (above a zero reading) multiplied by that constant to get load applied. If you have a number in that "certificate" and multiply that by the dial reading, to get a calculated load, then verify that by using a testing machine to see if it is correct. Lacking a testing machine, take any known load and apply it to the ring and seehow it compares with the computed load. Even a simple bathroom scale should give an idea if that certificate number is approximately usable.

So if I understand you olestguy then the proving ring is similar to a spring constant eventho. we are not dealing with springs?

You are right, it is like a spring using the elastic part of the stress strain curve of the material.