I've never found a piece of braided hose (or fitting) that actually met that criteria even though that is what's published. The -6 hose I have is just almost 5/16" ID and a little over 1/2" OD.
And...I've never seen the odd numbered hose, only even numbered (-4,-6,-8, 10, ...)
I'm guessing you've got a -12 if the ID of the hardware (end fitting that is inserted into the hose) is 9/16" (the OD being close to 5/8" at the barb portion where nut/clamp screws over the hose. That is the measurement of all of my fittings. The -10 fittings I have are 1/2" and 9/16" respectively.