3" auger is really too big for any hand held drill though, in any but soft dirt.
3" auger will kill most cordless drill's in short order.
I just knocked first gear out of a porter cable. That was a new drill just for trapping. It was a 20v max red battery.
Brush less drill is my next drill.
In construction work for over 40 years and never saw a 3" hole drilled (except wells) large holes are usually cut by some means, in general a drill motor will work a drill twice the chuck size. So 1/2" chuck should not be used for over a 1" drill. The SDS Roto Hammers in concrete are OK up to 3/4"-1", but for lots of holes that big or larger holes I'd want a spline drive like this
https://www.gamut.com/c/power-tools...erm=4574724286467288&utm_content=AllFrozen dirt isn't much different than concrete, I've drilled bunches of holes in frozen dirt to drive form support stakes. Pick a tool that is capable of doing what you want to concrete. Obviously if we are still trapping, money is no object so don't cheap out. It is my feeling that battery tools are not designed for trapline work and using them on the line is likely to be a net loss.
To get a large hole, you could drill a few 3/4" holes and break out the rest, but, really what digs a 3" diameter hole? Mouse/vole holes are what 3/4" ? and chipmunk holes 1 1/4" ? Only ground squirrels make 3" holes that I'm familiar with and they don't occur on many of our lines.
Other animals make large holes and are also large enough that they aren't commonly part of dinner.
So why pick 3"?