JR Pass worth it - 3 main trips?

When working out whether to get a JR Pass, should I include seat reservation fees in my calculations?

We are travelling in late September and over a 6 day period will do the following trips:

Tokyo (Asakusa) to Kyoto - Fare: \ 8,620 ; Reservation::\ 5,390
Kyoto to Kanazawa - Fare: \ 4,000; Reservation:\ 2,700
Matsumoto to Tokyo (Asakusa) - Fare:\ 4,180; Reservation:\2,900

Including the reservation fees this comes to \ 27,790 which is close enough to the cost of the 7 day pass. Is that what I need to look at? Is the pass worthwhile because we would need to reserve seats?

We may also travel to Hakone the day before these 6 days, where we could use the pass for part of the journey.

Thanks for your advice!

With a JR Rail Pass, seat reservations are free. If the cost is that close you are much better off with the pass. You can reserve all the seats for all the trips at one time and you don't need to stand in line to reserve seats, find ticket machines for local trips, etc.

When you calculate long haul train fare like Limited Express or Shinkansen ones, you must always include the limited/super express surcharge, as it is mandatory. On the other hand reservation surcharge is optional on most trains (Narita Express and Hokuriku Shinkansen Kagayaki service being the most relevant exceptions)
Therefore your fare table looks actually like this:
Asakusa-Tokyo Station: 310 Y (170Subway + 140JR)
Tokyo-Kyoto: 13.080 Fare / 420 Hikari Reservation OR 920 Nozomi Reservation
Kyoto-Kanazawa: 6030 Fare/ 620 Reservation
Matsumoto-Asakusa: 6380 Fare/ 520 Reservation Matsumoto-Shinjuku + 340 (170 JR + 170 Subway) Shinjuku-Asakusa

The total amount of JR fare goes from 25800 without any reservation to 27360 using only reserved seats and the Hikari service, which would be included in the JRP. As both are pretty similar to a 7-day pass price I would get it, because reserved cars are usually more comfortable (less seats per row, more space) and using the JRP is really hassle-free.

If I may ask you, how do you intend to go from Kanazawa to Matsumoto?

Thanks Dick and Nikodarius, that's very helpful!

We will be going by bus from Kanazawa to Takayama, with a brief look at Shirakawa-go on the way although we won't spend time there. Then by bus to Matsumoto.

I'm assuming that there will be something of Shirakawa-go to be seen from the bus as we arrive from Kanazawa, and then catch the bus on to Matsumoto?

afaik seats in reserved and non-reserved are the same (contrary to what Nikodarius said).

Maybe he is talking about the Green car

Reserved ordinary cars of Sakura and Mizuho are in 2+2 configurations while non-reserved cars are in 2+3. As far as I know ordinary cars of other Shinkansens are in 2+3 regardless of reserved/non-reserved cars.

As far as I know ordinary cars of other Shinkansens are in 2+3 regardless of reserved/non-reserved cars.

That is generally true except for some funny exceptions. Such as the narrower train sets used on the Akita and Yamagata Shinkansen, which are all 2x2. Also, some non-reserved seats on the double decker trains on the Joetsu Shinkansen are non-reclining 3x3.

Since the train and the bus take a similar time to get from Kanazawa to Takayama, is it a good idea to take the bus to get a brief look at Shirakawa-go on the way, even though we could travel free by train using JR pass?