365

A tropical year is 365 days. The fraction is about 0.2422, not 0.25, which is why the Julian calendar drifted and the Gregorian reform skips three leap years every four centuries.

'A year' names at least three distinct measurements. The tropical year — equinox to equinox, and the one the calendar tracks — is about 365.2422 days. The sidereal year, one full orbit against the fixed stars, is about 365.256 days and is roughly twenty minutes longer. The anomalistic year, perihelion to perihelion, is longer still. The differences arise from the slow precession of the Earth's axis and the drift of its orbit, and they are why 'the length of a year' has to be qualified before it can be stated.

Earth completes one orbit of the Sun in approximately 365.24 days (the tropical year). The 365-day calendar year is a whole-number approximation of that figure, and the leap-year rule exists precisely to absorb the leftover quarter-day.

The 365-day year with a leap day every fourth year was fixed for the Roman world by the Julian reform of 46 BCE. That slightly overcorrected — the Julian year runs about 11 minutes long — and by the 16th century the calendar had drifted roughly ten days from the solar year. The Gregorian reform of 1582 removed the surplus by dropping three leap years in every four centuries.

The tropical year is about 365.2422 days, so a 365-day calendar drifts by roughly a day every four years. Every calendar reform in recorded history has been an attempt to manage that remainder rather than to change the count.

Attaching 365 to a product name to claim continuous availability became a recognisable convention in software and services. It is a marketing use of a calendar fact rather than a technical one.

365 is the number of days in a common Gregorian calendar year (366 in a leap year), a civil convention adopted, with local variation, across nearly all of the modern world.

Rabbinic tradition counts 613 commandments in the Torah, divided into 248 positive obligations and 365 prohibitions. The figure is attributed in the Talmud (Makkot 23b) to Rabbi Simlai, who connects the 365 with the days of the solar year and the 248 with a traditional count of the parts of the body. Which specific commandments make up the 613 was never fixed by the Talmud itself and different medieval enumerations, Maimonides' being the best known, disagree on the contents while agreeing on the total.

365 = 10² + 11² + 12² and also 13² + 14², so it is the smallest number that is a sum of consecutive squares in two different ways. The two decompositions meet at the point where 100 + 121 + 144 and 169 + 196 both reach the same total. It is an arithmetical curiosity with no connection whatever to the calendar — the year is 365 days because of the Earth's orbit, and the coincidence of the two facts landing on the same integer is exactly that.