Barbette: 5x 32 pdr, 16x 24 pdr
Casemate: 18x 32 pdr, 11x 24 pdr
Bastions: 9x 24 pdr flank howitzers
Other: 1x 8" mortar, 2x 12 pdr field howitzers and 2x 6 pdrs
Unmounted guns: 77x 32 pdrs, 15x 24 pdrs, 48x 24 pdr flank howitzers
The 92 unmounted 32 and 24 pdrs don't have carriages, but 48 old and broken down carriages are available for probably the flank howitzers.
These unmounted guns represent a very large chunk of the ca. 600 seacoast guns in inventories that weren't mounted. Between the fortification of Washington, the Act to arm Fort Adams and issuing of guns to other forts this reserve of guns was used or committed to use in early 1862.
Fort Adams is still there (see Google Earth) and sits on an interior spit of Rhode Island (the big island the whole state is named after) inside Narragansett Bay, defending the East Passage, one of the two channels into the bay - the deeper one that can easily admit ships-of-the-line with more the 50 feet of water in the channel. There are two other inlets of importance, the West Passage to the west of James Island with Dutch Island in it and the Sakonnet River to the east of Rhode Island. The West Passage is navigable to frigates at all tides, but only to ships-of-the-line at high tide. The Sakonnet is navigable for ships-of-the-line only upto Church Point, frigates upto Sapowet Point (with a tricky bit at Fogland Point) 2 miles south of the bridge joining the island to the mainland, but sloops and gunboats can steam literally right upto the bridge.
The geography makes the entire bay undefendable unless all three inlets are heavily defended. If the Sakonnet isn't blocked then a single enemy gunboat can steam up the river the drop the bridge (a simple wooden affair, the stone bridge was built in the 1890's) and cut the island of Rhode Island off from New Hampshire. The Western Passage means that (a) the fort can be bypassed and the cities of Providence etc. put under the gun without any intervention and (b) landings of James Island can be affected and the Fort reduced by a land battery. Historically in 1863-4 the state built an earthwork battery of 8 guns (7x 8" shell and 1x 32 pdr) on Dutch Island to defend the West Passage, but that's in the future.
The fort is a pretty standard single tier fort of the period. The casemates prettymuch all point northwest and north to fire into the shipping channel, thus those 19 guns all play on any force coming through the channel.
Fort Adams Plan, showing that the casemates all point NW and N
The barbette had 21 guns in early 1862, but we don't know what arcs they were in. Probably the majority were on the bastions.
The field pieces were probably in the redoubt, an infantry defence to the south of the fort proper.
Redoubt of Fort Adams
Attacking Fort Adams
Any enemy (probably the RN) will have a surprisingly easy time in 1862. The fort can be isolated easily with a few shells at the bridge and one can land a few guns on James Island and reduce the fortification. Being on a spit any attacking squadron can run down the shipping channel and get behind Fort Adams in Brenton Cove, which is very lightly defended. Once there they can basically reduce the fort without danger.
Given the geographical problems the fort had, and the fact that it's pointless and doesn't defend Providence at all due to an alternate channel, despite being one of the strongest and best armed forts in the US in 1861 it would not hugely worry the RN.