7/8 diameter drill or .875
To accommodate a 3/8 bolt, drill a hole that is 3/8 inch in diameter.
by using a drill
A threaded hole with a minor diameter of approximately 2.61 inches and a thread pitch of 11 threads per inch (TPI) indicates it is likely a 2.5-inch nominal size with a coarse thread. The actual major diameter can be calculated based on the TPI and the thread profile. In this case, the major diameter would be around 2.75 inches, consistent with standard measurements for 11 TPI threads.
The recommended drill bit size for a 15/64 inch hole is a 15/64 inch drill bit.
The recommended size of the drill bit for a 7/16 inch hole is a 7/16 inch drill bit.
I drill a pilot hole the size of the 'barrel' of the screw. -I always use a combination drill bit for sinking screwheads. The first part of the bit is the diameter of the 'barrel' of the screw and the step, one inch higher is the size of that screw's head. (The barrel is the diameter inside threads) -I have a set of these drill bits for #6, #8, and #10 screws and they are great.
For all practical purposes an 8mm drill is equal to 5/16 inch.
A 3/16 inch pilot hole drill bit should be used for installing a 1/4 inch screw into hardwood.
Drill bits not only come in fractional number sizes they also come in letter sizes. The F size drill bit is .257 thousandths of an inch in diameter. A 1/4 inch drill bit is .250 thousandths of an inch in diameter, so size F is .007 thousandths of an inch bigger than a 1/4 inch drill bit.
A 10 cm hole is almost 4 inches ! ! - IF you meant 10mm, then that's a little over 3/8 of an inch, or 13/32 for a clearance hole.
For a clearance hole you need a 9/64 drill bit.
A # 30 drill bit is 0.1285 inch, or fractionally more than a 1/8 bit.