It depends on the kind of job and the possible "loss" of soil along the way, as well as compaction required.
Common highway shrinkage figures run from 10 to 30 percent, generally around 20 percent. It seems to be better practice to go on the high side with the plans, since running short of fill may be difficult to correct on the job.
If you really think the tests will be useful, then also get density of the cut material as a guide as to the difference. However, if much drying is required to achieve the percent compaction, that may not occur on the job.
In my experience, the loss (from volume of exc in the borrow area to volume of compacted fill) is generally much larger than the borrow-area and compacted densities would indicate. There is always some spilled from trucks, rejected, blown away, overbuilt and bladed off, lost under seat cushions, etc. If you are evaluating a borrow area's available volume, allow for quite a bit more than just the ~20% "shrinkage." Bedrock may be higher than expected in the borrow area, or you may need to reject more material for being too wet or having wrong gradation, or there may be an overrun so you need more than you plan on, etc. For dam construction, we have generally tried to prove out 150% of expected need on big jobs, and 200% on small jobs, although we have to be more finicky about materials than most people do.
ground compaction for compaction of subgrade, prior to placing the structural fill should also be estimated and can account for significant amount of material if the site is large.
