How far the boundary really is
The Sun leaves Virgo when it reaches one hundred and eighty degrees of ecliptic longitude, which happens around 22 or 23 September. On 16 September the noon longitude has ranged from about twenty two and seven tenths degrees of Virgo to roughly twenty four and a tenth over the years from 1930 to 2035.
That leaves between six and seven degrees of Virgo still to run, which is six or seven days of solar motion. The ingress moves by a few hours from year to year and jumps back by roughly eighteen hours at a leap day, a variation measured in hours against a gap measured in days. No combination of year, hour and time zone brings this date anywhere near the line.
Why the degree stays put
A tropical year runs about three hundred and sixty five and a quarter days, so the calendar loses a quarter day against the Sun each ordinary year and the same date arrives slightly earlier in the cycle, with the Sun a little further along. Three of those add up to about three quarters of a degree, and the leap day takes it back.
The upshot is that the solar position on a fixed date oscillates rather than drifts. On this birthday the whole set of noon values from the 1930s to the 2030s spans not much more than a degree. Someone born on 16 September in 1934 and someone born on the same date in 2034 have Suns within a degree and a half of each other, which is a small fraction of the ten degree band they both sit in.
The last third of the sign
Twenty two degrees puts this birthday in Virgo's final decan, the stretch from twenty to thirty. The Chaldean order gives that band to Mercury, which already rules Virgo, and traditional writers treat it as the sign in its least diluted form, weighted towards method, discrimination and the checking of work.
The triplicity scheme instead assigns it to Saturn, since Capricorn is the third of the earth signs, and the resulting description leans on patience and structure rather than analysis. The two schemes come from different traditions and there is nothing observable that decides between them, so the sensible thing is to know that the band is measured and the ruler is conventional.
The parts the date does not reach
The Moon will be in one of two signs on any 16 September, sometimes three, and the hour decides. The rising sign is fully open, since the whole zodiac passes the eastern horizon in a day, and the birthplace matters as much as the clock because latitude changes how long each sign takes to rise.
Those placements, and the houses that follow from the rising sign, are what make two charts with the same Sun read differently. The sun sign is what you share with everyone born in the same fortnight. The widget above will compute your own solar longitude and its distance from the Libra boundary, which on this date will come back as a comfortable margin rather than a close call. That margin is the reason the sign can be stated without any hedging at all.
Questions people ask about this
Is 16 September Virgo or Libra?
Virgo. The Sun still has six or seven degrees of the sign left to travel, which is nearly a week, and the boundary only moves by hours between years.
What degree of Virgo is 16 September?
Between roughly twenty two and seven tenths and twenty four and a tenth degrees at noon across the last century. Your own figure depends on the year, hour and place.
Which decan applies to this birthday?
The third decan of Virgo, twenty to thirty degrees. Mercury rules it in the Chaldean scheme and Saturn in the triplicity scheme.
Does the birth year change the sun sign here?
No. The variation between years is a little over a degree, and the nearest boundary is six or seven degrees away. The sign is the same in every year.
Why does the same date give almost the same position every year?
Because the leap day cancels the drift caused by the quarter day the year runs long. The position oscillates within a narrow band instead of moving steadily.
What else should I calculate?
The Moon sign and the rising sign, both of which need a birth time, and the house placements that follow from the rising sign. None of them can be read off a date.