When to activate JR Pass

Hi, am spending twelve days in Japan but have only bought a 7 day jr pass. Will be in Kyoto from 10th-14th July and plan on taking the bullet train to Tokyo for 4 nights then back to Nagoya . The last day I intend to use my pass is the 18th for the bullet train from Tokyo to Nagoya. Do I activate the pass on the 11th or 12th July? Activating on the 11th as I calculate means the pass runs out on the 17th. Is this correct? Need to know as I want to use while in Kyoto to get to Nara and Arashiyama. And does the pass run until 12 midnight of that final night? Thanks