No calendar is the sky. Each is a political and sacred instrument that chooses a year-length, a month-length, and a story about when the world began. Egypt counted 365 days and a heliacal rising of Sirius. China kept a lunisolar year of officials and farmers. The Maya tracked interlocking cycles long enough to outlast cities.
The Islamic year follows the Moon and drifts through the seasons on purpose. The Hebrew year follows the Moon and is corrected by the Sun so that Passover stays in spring. The Gregorian year follows the Sun and pretends the Moon is a decoration.
To convert a date is to admit that several correct answers can occupy the same noon.