Nowruz falls at the vernal equinox, and it falls at the moment of the equinox, not on the day nearest it, not on a fixed date approximating it. Iranian families note the exact time, to the minute, and gather for it.
This is possible because the Solar Hijri calendar is astronomically determined rather than arithmetically approximated. Its year begins at the midnight nearest the instant the sun crosses the celestial equator, as observed for the meridian of Tehran. Whether a year has 365 or 366 days is a consequence of that observation, not of a leap rule. The result is a calendar that does not accumulate error against the tropical year at all, more accurate than the Gregorian, which requires its centurial correction and still drifts by a day in some three thousand years.
The month lengths are regular in a way the Gregorian's are not: the first six months have 31 days, the next five have 30, and the last has 29 or 30. The equinox anchoring means that Nowruz falls on 20, 21 or 22 March in the Gregorian calendar and never wanders further.
Afghanistan used the same calendar with different month names until 2022. A parallel arithmetic version, the Jalali reckoning associated with the reform of 1079 in which Omar Khayyam participated, is the historical ancestor.
Iran adopted the Solar Hijri as its official civil calendar in 1925, counting years from the Hijra but running them solar, which produces year numbers roughly 621 less than the Gregorian and about 40 less than the Islamic lunar year.