Several here have been using push cutting thread on a scale and measuring the load in grams. This is highly dependent on the type of thread used, and so it's difficult to compare from one tester to another. There is a BESS scale that is used by EdgeOnUp sharpness testing equipment, but it is basically grams as well. The advantage of the BESS scale and EdgeOnUp is that is uses a purpose made thread, so users with the same thread and apparatus can compare results.
The other way to test sharpness is by slicing light cord with a weight under tension. I have not tried this myself, as I have been mainly interested in push cutting sharpness (thread on a scale). However, the principle is to place a light cord under tension and make a slicing cut. The sharpness is measured by the length of edge required to make the cut, measured in inches or mm or whatever is appropriate. The shorter the edge needed and the lower the tension the cord is under, the higher the sharpness. For example, using a tension of 1 oz. and measuring a length of 0.25" to cut the cord.