From an older similar thread:
Modern aftermarket bass tuners come in two sizes: 1/2" post and 3/8" post. That's the diameter of the post that you wrap the string around. Most 1/2" post tuners have a separate bushing that presses into the headstock. It requires the headstock hole to be drilled/counterbored to 11/16" x 3/8" deep on the front side for the bushing. The back side of the hole going through is usually drilled 9/16".
Some 3/8" post tuners use a similar press-in bushing; others have a cylindrical sleeve nut that threads onto the tuner housing. Either way, a 3/8" post tuner requires a straight 9/16" dia hole.
Another:
To add to the general information:
The round part of the tuner that sticks up through the headstock, that the string winds around, is called the
Tuner Post. The ring/sleeve thing which is pressed into the headstock, which the post sticks up through, is called the
Bushing.
Most bass tuners come in two standard sizes, 3/8" or 1/2". This is the nominal (approximate) diameter of the posts. It's also the ID of the bushings.
On 3/8" tuners, the serrated OD of the bushing is made to lightly press into a 9/16" hole in the headstock. 9/16" is just a tiny bit over 14mm, so often the holes are drilled to 14mm instead. Most 3/8" bushings will work fine in either 9/16" or 14mm holes.
On 1/2" tuners, the serrated OD of the bushing is made to lightly press into a 11/16" hole. Likewise, 11/16" is just slightly larger than 17mm. Most American made 1/2" tuner bushings will fit nicely in 11/16" holes. However some imported 1/2" bushings are better sized for 17mm holes, and may be a little loose in 11/16" holes. Particularly if American made bushings had previously been pressed in.
But generally, basses with modern mini-tuners have nominally 9/16" holes in the headstock, and are made to fit 3/8" post tuners.
Basses with old-style big tuners have 11/16" holes and are made to fit 1/2" post tuners.
But there are small aftermarket tuners out there, like Hipshot's Ultralites, which are made in both 3/8" and 1/2" size post versions. Choose them to fit the size of the holes in your headstock.
Another useful thread:
Methods to increase tuner bore holes in headstock