The reason the pages all match
Naming the sign for a date requires no computation at all. A table of ranges covers the whole year, and every site copies the same table, which is why the answers agree and why they also disagree by a day at the edges where the tables were rounded differently. Nothing beyond the sign follows from that table, so nothing beyond the sign gets published.
The next fact down is the solar longitude, and it takes an ephemeris rather than a lookup. For this date the Sun sat between roughly twenty two and twenty three and a half degrees of Libra at noon in every year from 1930 to 2035. That is a tighter and more useful statement than any date range, and it is absent from almost every page written about this birthday.
Why a fixed date keeps a fixed degree
The Earth's year is about a quarter of a day longer than a common calendar year, so the Sun arrives at any longitude roughly six hours later each year by the clock. Four years of that adds up to close to a day, and the leap day added to February cancels it in a single correction.
The two effects are not perfectly matched, which is why the figure swings by a little over a degree rather than staying at one exact value. The century rule that omits the leap day in 1900 and 2100 catches the remaining slippage, so the swing does not accumulate over long spans.
None of that is difficult to explain, and it is worth asking why the explanation is so rarely offered. The likely answer is that the sign is the only output most birthday pages were built to produce, so the mechanism behind it never comes up. Once the position itself is calculated the mechanism becomes obvious, because the calculation is where the leap year correction has to be applied.
The layer under the sign
Ten degree faces divide each sign into thirds, and this position falls in the last third of Libra, the band from twenty degrees to thirty. The Chaldean sequence of planets hands that band to Jupiter. The triplicity scheme instead associates it with Gemini, which points to Mercury. A source quoting one ruler without naming the scheme has made a choice on your behalf.
Traditional writing on Libra emphasises balance, judgement and the weighing of one thing against another, and reads the closing face as the sign's material settling into place. All of that is interpretation and should be read as interpretation. What is checkable is the position; what a tradition attaches to that position is a separate kind of claim.
What is still unknown after the date
A birthday fixes the Sun and leaves the rest of a chart untouched. The Moon takes under a month to circle the zodiac, so on this date it might be in any sign, and someone born in the morning and someone born late the same evening can have it in neighbouring signs. The ascendant changes sign roughly every couple of hours and depends on latitude as well as time.
Put plainly, the sun sign is the part of a chart shared with the greatest number of other people, which makes it the least distinguishing thing a birthday reveals. The widget above asks for the year, the hour and the birthplace and returns the exact degree together with the margin to the nearest sign boundary.
Questions people ask about this
What zodiac sign is 16 October?
Libra in every year checked at noon from 1930 to 2035. The date sits comfortably inside the sign with no boundary nearby, so no year in that span is ambiguous.
What is the solar degree for this birthday?
Roughly twenty two to twenty three and a half degrees of Libra at noon over that century. The exact value for one person depends on the year, the hour and the birthplace.
Which Libra decan is 16 October?
The third, covering twenty to thirty degrees. Chaldean attribution gives it to Jupiter and the triplicity route gives it to Mercury by way of Gemini.
Why do birthday pages disagree about the dates?
Because the boundary moves by up to a day and a half between years and the published tables round it differently. A calculated position removes the disagreement entirely.
Is a late Libra birthday different from an early one?
In the older material, yes, because they fall in different faces of the sign with different attributions. In terms of the sun sign itself they are identical.
Do I need my birth time for this date?
Not to establish the sign, which is settled. You need it for the exact degree, for the Moon, and for the rising sign, none of which the calendar date supplies.