Those estimates for Economus would assume that all 330 of the Roman ships present were the largest class of ships Rome had, ie their Quinqueremes (420 men roughly, and dividing 140000 by 330 gives 425 men per ship), and much the same for Carthage, with no smaller ships whatsoever being present.
I don't know how likely that would be. Xen, would an all-Quinquereme fleet of 330 be in line with Roman military thinking?
(Of course, if you start cutting the 120 soldiers each Quinquereme had - which have about as much place being counted as the planes) - then the number of men on the Roman side drops by about a third anyway).
Just to address this earlier question: Also depends whether the invasion force was on board, because after this the fleet sailed to Africa, and Regulus' defeat at Tunis. Those 'marines' were a big part of Rome's naval victories. The numbers of ships are reasonably accurate, Rome concentrated almost her entire building program on quinqueremes after the first battle, and I believe lost 500 in the war, with about 200,000 attendant deaths. So Ecnomus has probably over 250,000 men involved on both sides, does any modern naval battle compare to that ?
The Carthaginian expedition to Sicily in 480 BC was enormous with losses of maybe 100,000 by land and sea. Artemesium was also huge, with hundreds of Persian ships lost in storms and battle, along with about 100 Greek ships. So was the battle of Mycale 479 BC when 600 Persian ships were destrpoyed or captured by 300 Greek ships. The Delian League lost 200 ships in Egypt. The Athenian expedition to Syracuse was largely a naval one, with the loss of 200 triremes and more transports, with 40,000 men. Their final defeat at Aegospotamai was almost a repeat of that disaster.
The largest viking battle in history pitted the Norwegian King Olaf Trygvasson against Denmarks King Swein and Swedens King Erik. The Norwegian fleet of 100 ships fell to the numerically Danish/Swedish/Germanic superior fleet of some 400 ships. Like Horatio Nelson, the Norwegian King died, but with an arrow through his eye. The battle included some 15-20000 men, all midsized and larger longships, and the Norwegian defeat made Norway a part of Denmark, which already had made England a colony.
This is the largest naval battle in Scandinavian history.
Battle of Svolder , 1000 AD.
Thanks - we don't get to hear about those very much.
Ah yes I forgot to mention.

Chinese history in the era of the Three Kingdoms, the Battle of Chi Bi or Red Cliffs. I guess you can say it's a river battle but that still count's as naval right?
Anyhow estimates of 200 000 to 250 000 men under Cao Cao vs the combined force of Liu Bei and Sun Quan I forgot if it was 50 000 total of 50 000 each or total 100 000.
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300,000 might make that the biggest naval battle in personnel.
I wish people would stop calling Tsushima "decisive." Russia lost every naval battle of the war. They had no chance of winning that one, nor would it have changed anything had by some miracle they had.
But to be completely annihilated as they were, and the corresponding rise in prestige of the Japanese Empire and IJN makes it pretty significant. Prior to this, had the Russian Pacific fleets been able to gather at sea instead of being bottled up in harbours and losing their best admiral, the outcome would not have been so lopsided.
There is no doubt Salamis was decisive, but if you are measuring by personnel involved, modern battles still have higher totals (estimates were put together earlier in the thread). I think somebody suggested weighting battles by % of GDP or some other economic figure to show the relative importance of manpower and material for that time, although reliable figures would be hard to come by or simply impossible to obtain for battles in BCE times or even up towards Lepanto. (Can anyone tell me exactly what Venice owned, their GDP, etc. in the mid-16th century? What about Spain and the Ottomans?)
As far as manpower, there must have been 70,000 Greeks and 120-150,000 Persians at Salamis. The triremes had deckloads of hoplites too.
Yeah GDP is hopeless to estimate, and for Athens the %GDP would be very high, almost every able bodied man at Artemesium and Salamis.