1/4" W and 5/16" BS is 0.525" or 13.33mm.
The W and BS (BSF) is the diameter of the shank of the bolt, and the 0.525 is the measurement across the flats of the head of the bolt. Correct me if I am wrong here
So a 13mm socket could be made to fit if persuaded with a hammer for example, and 14mm socket would slip on the bolt head if torqued up to tight.
I like to have the correct size on my beloved A7 head bolts.
Thanks
Keith