Yes; standards are typically in fractional inches, or in whole millimeters (e g, 1/4", or 3mm, or whatever.)
Get a good set of calipers, and measure your output shaft diameter. Note that 1/4" will be 6.35mm, whereas 6mm will be 6.35mm.
Also note that holes are often "press fit" which means it will be very tight -- you may need an arbor press or similar to actually mount the gear.
Anything with a set screw in it will not have that problem; there will be slop (slip fit) but I don't know of a series of pinion gears that come with set screws.
The specifications for your servo should specify the output shaft dimensions, btw. Reading that would be safer than measuring yourself.