Duration of Rail Pass help

Hi

Arriving 7th September Haneda Airport

7th - 10th Hakone Yumoto
10th - 15th Kyoto
15th- 16th Takayama
16th - 19th Kanazawa
19th - 23rd Tokyo

is a 14 day rail pass cost effective, if yes when do I start it? The 10th to go to Kyoto and get the Hakone Free Pass at the start of the holiday?

My dates and destinations are set and accommodation is booked

any help appreciated