Quick answer
For a #6 wood screw, use a 7/64 inch straight bit in hardwood or a 3/32 inch straight bit in softwood. With tapered bits, use 9/64 inch for hardwood or 1/8 inch for softwood.
Hardwood straight bit
7/64 in
Softwood straight bit
3/32 in
Hardwood tapered bit
9/64 in
Softwood tapered bit
1/8 in
How to choose the pilot hole
Hardwood needs more room so the screw does not split the board or snap during driving. Softwood can use a slightly smaller pilot hole because the fibers compress more easily.
Countersink size
A 5/16 inch countersink is a common match for a flat-head #6 wood screw.
Useful tools for this job
A countersink pilot bit set is the easiest buy because it drills the pilot hole and countersink in one step.
Frequently asked questions
Can I skip the pilot hole for a #6 screw?
Sometimes in softwood, but use a pilot hole near board ends, in hardwood, or when the finished surface matters.