solar year
The solar year is calculated based on the Earth's rotation around the Sun. The Earth's completion of this orbit is defined as a full year. This orbit takes about 365 days and six hours, or more precisely 365.2435 days.
On the other hand, the lunar year is shorter compared to the solar year as the difference between them is about 11 days, with an exact difference of 10.875444 days.

lunar year
The lunar year is defined as the period during which the Moon completes twelve revolutions around the Earth, with each of these revolutions taking an amount of time that makes their total amount to about 354 days, or more precisely, 354.367056 days.
The Hijri calendar, which is mainly used to arrange the months and organize school work in the Kingdom, is based on these lunar calculations. This method helps organize religious and scientific affairs in a manner consistent with the natural cycles of the moon.
Arithmetic relations between the solar year and the lunar year
The Holy Qur’an explains that the solar year, also known as the solstice year, continues from when the sun crosses the equinox twice in a row, marking a complete cycle that leads to the succession of the four seasons starting with summer, followed by autumn, then winter, and finally spring.
In contrast, the lunar year is calculated by the period between two successive eclipses, and it is divided based on the number of circular movements made by the moon.
Studies indicate that there is a time difference of ten eight hundred and seventy-five thousand one hundred and thirty-seven days between the solar and lunar year, which means a difference of about 358 days over the passage of thirty-three years, or the equivalent of almost a full year.
Astronomical calculations confirm that every hundred solar years are equivalent to three years more than lunar years, and thus every three hundred solar years contains three hundred and nine lunar years. These results are reliable astronomical investigations and have been recognized and accepted in the modern scientific community as established and accurate facts.
The scientific miracle in the Holy Qur’an regarding the solar year and the lunar year
Verses of the Holy Qur’an make it clear that the people of the cave stayed there for a very long time. There is a text in the Holy Qur’an that says that they remained in the cave for three hundred years, and this is calculated according to the solar calendar. Additionally, nine additional years are added, which are calculated according to the lunar calendar.
Modern scientific research, which relies on advanced astronomical observatories, confirms this fact that three hundred solar years are actually equivalent to three hundred and nine lunar years.
Ibn Kathir, in his interpretation of the noble verse, indicates that this period of time, in which the Companions of the Cave remained, is a divine statement of the length of time these people spent in their cave before the people of that era discovered them. The disparity between lunar and solar time periods is fixed by the nine-year difference indicated by the Qur’anic text.