The honest caveat comes first
The Hijri calendar is not a calculated calendar. A month begins when the new crescent is seen, and whether it is seen depends on where you are standing, on the weather, and on which authority your country follows. Two Muslims a thousand miles apart can begin Ramadan on different days and both be right.
What this page uses is the tabular scheme — an arithmetic calendar in which eleven years in thirty carry an extra day and months alternate between thirty and twenty-nine. It is exact, it is always available, and it has no way of knowing what anyone actually saw. Expect a day either way, and follow your local announcement for anything that turns on a single date.
For everything that does not — how old a lunar year is, when your zakat falls due, roughly when Ramadan is coming — the arithmetic is the right tool and a sighting is not available in advance anyway.
Why the year numbers keep closing
A Hijri year is twelve lunar months, about 354 days, against the Gregorian 365. It gains eleven days a year on the solar calendar, which is why Ramadan walks backwards through the seasons and arrives in midsummer once every three decades or so.
It is also why the two year numbers are not separated by a fixed 622. Every 33 solar years the calendars gain a whole year on one another, so the gap narrows continuously — a detail that surprises people who try to convert by subtraction.
The mistake this page exists to prevent
Zakat falls due once your wealth has stood above the nisab for a full lunar year, and the day it first crossed becomes your anniversary. A great many people write that date down in the Gregorian calendar — 1 April, say — and calculate on it every year after.
That loses a year. The lunar year is eleven days shorter, so a Gregorian anniversary drifts a whole zakat year late roughly every third decade, and the missed year is owed rather than forgiven. Convert the day it crossed, keep the Hijri date, and the problem does not arise.
The zakat calculator asks about the year for exactly this reason, and the Hajj savings plan counts days rather than months so that the extra zakat year appears where it actually falls.
The four sacred months
Dhu al-Qa’dah, Dhu al-Hijjah and Muharram fall together, and Rajab stands alone in the middle of the year. They are named at 9:36, where fighting in them is forbidden and wrongdoing in them is described as weightier than elsewhere.
Dhu al-Hijjah holds the Hajj, the Day of Arafah and Eid al-Adha; Muharram holds Ashura on its tenth day. Ramadan, though not among the four, is the month of the fast, and Shawwal opens with Eid al-Fitr.