The 4th Armada was composed of 20 ships and between 800 and 1800 men.
The Armada was originally envisaged as two squadrons - 15 ships under the admiral to head to India, 5 under the vice-admiral designated to patrol the mouth of the Red Sea.
As it turns out, not all ships were ready by the launch date, so the armada was re-arranged into three squadrons, the first two squadrons (10 under admiral Vasco da Gama, 5 under his uncle, vice-admiral Vicente Sodré) to head out at once, and the five remaining ships to go out a little while later as a third squadron under Gama's cousin, Estêvão da Gama, with instructions to catch up to the main fleet along the way. (
Whatever the mechanics behind the appointment, the 4th Armada certainly turned out to be a Gama family affair!)

The exact composition of the three squadrons differs in the various accounts.
The following list of ships should not be regarded as authoritative, but a tentative list compiled from various conflicting accounts.

This list of captains is principally based on João de Barros's Décadas, Damião de Gois's Chronica, Castanheda's História, the Relação das Náos, Couto's list, Faria e Sousa's Asia and Quintella's Annaes da Marinha.
The list of ship names is from Gaspar Correia's Lendas da Índia.
and should be suspected as unreliable.
As usual, Correia's list of captains differs significantly from the others.
 In Correia, neither of the Sodré brothers command their own ships - indeed Correia asserts Vicente Sodré was carried as a passenger aboard Vasco da Gama's flagship, with the result that the lead ship of the second squadron was captained by a certain Fernão d'Atouguia (of the Ataíde family?)
and the fifth ship by Pêro Rafael (a name that appears on several other lists).
The anonymous lists of the Memorias das Armadas  and Livro de Lisuarte de Abreu give their own variations.
Doubtless, the captain lists are complicated by the fact that there were some rearrangements of the fleet in Africa and India, and captains were shuffled around - at some point, both Vicente and Brás Sodré was definitely given command of a ship of his own.
 The chronicles report that the fleet also carried pre-fabricated lumber and fittings with instructions to assemble a new caravel upon arrival in East Africa.

The most famous ship in the 4th Armada was arguably the one commanded by Estevão da Gama, the Flor de la Mar (sometimes spelled as Frol de la Mar), a 400 tonne carrack (nau), the largest ship of that kind yet built.
The exact sizes of the other large carracks - the flagship São Jerónimo, Lionarda and the Leitoa/Esmeralda are unknown, but also presumed to be quite sizeable (that is, 250t or greater).
 These large ships were designated to return with spice cargo back to Lisbon.
The smaller naus(navetas, 80-120t) and caravels (40-80t), went out as armed fighting ships, to remain as naval patrol vessels in India if necessary.

The Gama clan dominated the fleet - Vasco da Gama, his cousin Estêvão da Gama and his uncles Vicente Sodré and Brás Sodré took the leadership positions.
We have assumed Pêro de Ataíde, to be the same person nicknamed 'o Inferno' ('Hell'), a notable veteran captain of Cabral's Second Armada.
But in some accounts, his name is given as 'Álvaro de Ataíde' a native of the Algarve, thus possibly Vasco da Gama's new brother-in-law (Gama had recently married Catarina de Ataíde in 1500 or 1501; she had a brother by that name).
Lopo Mendes de Vasconcellos was a soon-to-be brother-in-law (betrothed to Teresa da Gama, Vasco's sister).

Among the remaining captains, the most significant was probably Dom Luís Coutinho, son of the Count of Marialva, a high nobleman of considerable rank in the Portuguese court.
Diogo Fernandes Correia (archaically, Corrêa) was pre-designated by the Casa da India as the factor for Cochin (replacing the factor Gonçalo Gil Barbosa that Cabral had left there).

There was significant private participation in the fleet.
 Two ships went out under Italian captains -  Tomásio da Cremona ('Thomas de Carmona') and Giovanni Buonagrazia ('João da Bonagracia') of Flore
The 4th Armada was composed of 20 ships and between 800 and 1800 men. The Armada was originally envisaged as two squadrons - 15 ships under the admiral to head to India, 5 under the vice-admiral designated to patrol the mouth of the Red Sea. As it turns out, not all ships were ready by the launch date, so the armada was re-arranged into three squadrons, the first two squadrons (10 under admiral Vasco da Gama, 5 under his uncle, vice-admiral Vicente Sodré) to head out at once, and the five remaining ships to go out a little while later as a third squadron under Gama's cousin, Estêvão da Gama, with instructions to catch up to the main fleet along the way. (Whatever the mechanics behind the appointment, the 4th Armada certainly turned out to be a Gama family affair!)
The exact composition of the three squadrons differs in the various accounts. The following list of ships should not be regarded as authoritative, but a tentative list compiled from various conflicting accounts.
This list of captains is principally based on João de Barros's Décadas, Damião de Gois's Chronica, Castanheda's História, the Relação das Náos, Couto's list, Faria e Sousa's Asia and Quintella's Annaes da Marinha. The list of ship names is from Gaspar Correia's Lendas da Índia. and should be suspected as unreliable. As usual, Correia's list of captains differs significantly from the others.  In Correia, neither of the Sodré brothers command their own ships - indeed Correia asserts Vicente Sodré was carried as a passenger aboard Vasco da Gama's flagship, with the result that the lead ship of the second squadron was captained by a certain Fernão d'Atouguia (of the Ataíde family?) and the fifth ship by Pêro Rafael (a name that appears on several other lists). The anonymous lists of the Memorias das Armadas  and Livro de Lisuarte de Abreu give their own variations. Doubtless, the captain lists are complicated by the fact that there were some rearrangements of the fleet in Africa and India, and captains were shuffled around - at some point, both Vicente and Brás Sodré was definitely given command of a ship of his own.  The chronicles report that the fleet also carried pre-fabricated lumber and fittings with instructions to assemble a new caravel upon arrival in East Africa.
The most famous ship in the 4th Armada was arguably the one commanded by Estevão da Gama, the Flor de la Mar (sometimes spelled as Frol de la Mar), a 400 tonne carrack (nau), the largest ship of that kind yet built. The exact sizes of the other large carracks - the flagship São Jerónimo, Lionarda and the Leitoa/Esmeralda are unknown, but also presumed to be quite sizeable (that is, 250t or greater).  These large ships were designated to return with spice cargo back to Lisbon. The smaller naus(navetas, 80-120t) and caravels (40-80t), went out as armed fighting ships, to remain as naval patrol vessels in India if necessary.
The Gama clan dominated the fleet - Vasco da Gama, his cousin Estêvão da Gama and his uncles Vicente Sodré and Brás Sodré took the leadership positions. We have assumed Pêro de Ataíde, to be the same person nicknamed 'o Inferno' ('Hell'), a notable veteran captain of Cabral's Second Armada. But in some accounts, his name is given as 'Álvaro de Ataíde' a native of the Algarve, thus possibly Vasco da Gama's new brother-in-law (Gama had recently married Catarina de Ataíde in 1500 or 1501; she had a brother by that name). Lopo Mendes de Vasconcellos was a soon-to-be brother-in-law (betrothed to Teresa da Gama, Vasco's sister).
Among the remaining captains, the most significant was probably Dom Luís Coutinho, son of the Count of Marialva, a high nobleman of considerable rank in the Portuguese court. Diogo Fernandes Correia (archaically, Corrêa) was pre-designated by the Casa da India as the factor for Cochin (replacing the factor Gonçalo Gil Barbosa that Cabral had left there).
There was significant private participation in the fleet.  Two ships went out under Italian captains -  Tomásio da Cremona ('Thomas de Carmona') and Giovanni Buonagrazia ('João da Bonagracia') of Flore
4th Portuguese India Armada (Gama, 1502)