Q:

Comparison of naval fleet strengths during the Napoleonic wars

Do we have knowledge on the number of vessels in the armadas of the various belligerents of the Napoleonic wars? Information on the types of boats, captured vessels, and sunk vessels will also be nice.

A:

A very raw comparison of the fleet strengths of the major players during the French Revolutionary & Napoleonic Wars is given below. In these tables a Ship of the Line is any vessel that would be considered to sit in the line of battle, generally these had their guns on 2 or 3 decks and had 50 or more cannon. Cruisers are smaller sea-going warships, encompassing the classic frigate and corvette designs (i.e. fifth and sixth rates in British service) and also including some of the larger sloops-of-war.
Ships of the line 

Year    GBR FRA NLD ESP DNK RUS 
1790    145 73  48  72  32  58 
1795    123 56  28  76  30  61 
1800    127 44  16  66  28  67 
1805    136 41  15  40  20  47 
1810    152 46  13  28  2   43 
1815    126 52  19  16  2   48 

Cruisers 

Year    GBR FRA NLD ESP DNK RUS
1790    131 64  36  46  16  52 
1795    160 65  30  51  13  40
1800    158 43  6   41  9   34
1805    160 35  10  26  11  16
1810    183 31  7   17  0   14
1815    151 31  14  15  3   21

Source: The Command of the Ocean, N.A.M Rodger (Allen Lane, 2004) derived from data by Prof. J.Glete
However, these raw figures should be treated with some caution when trying to establish the true strengths of the various national fleets. 
The following points should be considered;
1) The figures represent the notional numbers of ships available to each navy. In addition to the ships in active service, the figures also include ships in harbour service (e.g. guardships, hospital ships, etc), in 'ordinary' (what we'd now call 'mothballed') and even ships that were being built/re-built. So the number of ships immediately available for active service with each navy is probably between 50-75% of the given figures.
2) The figures also give no indication to the make up of each fleet in terms of age and quality. Older ships would generally be slower, harder to maintain and lacking in some of the technical innovations compared to their newer bretheren. They would also, generally, be smaller and have a weaker armament than their more modern counterparts. Consequently, a large fleet made up of older ships would be at a disadvantage to a smaller but more modern fleet.
3) While these tables give us the notional fleet strengths (and, by extension, an idea of the actual serviceable fleet strengths), in terms of vessels, they don't show how many ships were actually at sea in any given year or how many ships the respective navies were actually capable of manning and putting to sea. 
With regard to the last point, it was common for standing navies to be drastically reduced in manpower during times of peace. When a new war started, it often took time to re-employ these experienced sailors (and to train new replacements). So, for example, where the raw numbers show a moderate increase in the number of British cruisers (from 130 to 160) between 1790 and 1795, the actual increase in the number of those ships at sea would have been far greater as the Navy shifted from a peacetime to wartime footing.
In terms of losses, the following data was taken from the detailed lists in the "History of the Royal Navy" by William Laird Clowes, vol 4 and vol 5, covering 1793-1815;
  Ships of the line 
        Wrck    Sunk    Taken
  DNK   0       7       18
  ESP   0       10      12
  FRA   9       34      48
  GBR   23      8       6
  NLD   2       8       25

  Cruisers
        Wrck    Sunk    Taken
  DNK   0       10      18
  ESP   1       8       28
  FRA   11      49      203
  GBR   89      13      23
  NLD   1       10      39

  Unrated
        Wrck    Sunk    Taken
  DNK   0       8       36
  ESP   1       22      101
  FRA   0       48      383
  GBR   225     21      114
  NLD   3       12      79

Where "Wrck" is vessels that were wrecked or floundered without enemy action. "Sunk" is vessels that were sunk, burnt or otherwise destroyed. "Taken" is vessels that were captured by an enemy. Where vessels were retaken, I've counted a loss to each side (as some vessels were retaken months or years later).
In terms of ship types these follow the same classification as the fleet strengths tables for Ships of the Line and Cruisers, and I've added an extra section for small "unrated" ships of fewer than 20 guns.  
I've omitted Russia as the data in the source only included losses against the British and was therefore distorted compared to the others. I've also omitted the US Navy (although the British losses include actions in the War of 1812). 

A:

I can tell you two things, how many were under Nelson's fleet in the Mediterranean and how many were in commission throughout the world in May 1804.
Under Nelson's command were 13 Ships of the Line, 1 Fifty, 11 Frigates, 10 Sloops, 3 Bombs, 6 Gunboats and 2 Cutter and Schooners.
In total commission (throughout the world) were 88 Ships of the Line, 13 Fifties, 125 Frigates, 92 Sloops, 18 Bombs, 40 Gunbrigs, 6 Gunboats and 82 Cutter and Schooners and 41 Armed ships.
Source: The Command of the Ocean, A Naval History of Britain, 1649–1815, N.A.M Rodger.

A:

According to www.napolun.com the European fleet strengths, in terms of Ships of the Line (1st to 3rd rates), in 1808-1809 (shortly after Trafalgar) were:

Great Britain: 113
Spain: 45
France: 45
Russia: 34
Denmark: 21

Also according to that website, in 1805 the Great Britain (presumably including state owned trade ships etc) had a total fleet size of approaching 950 vessels.
The website has a list of sources at the bottom of the page for further reading.

