The boundary this date sits on
Capricorn splits into three bands of ten degrees. The first runs from zero to ten and takes Jupiter as its Chaldean ruler; the second runs from ten to twenty and takes Mars. Measured at noon across the years from 1930 to 2035, the Sun on 31 December lands between about eight point nine and ten point three degrees.
That range crosses the line. In most of those years the position is below ten degrees and the first decan applies, but in the years at the top of the range it is above and the second does. So this is one of the few dates where the honest answer is that the decan is year dependent and cannot be stated flatly for everyone born on it. The sign is settled and the band is not, which is an unusual combination and the reason this date needs its own treatment.
Which years fall which way
The pattern follows the leap year cycle rather than anything more exotic. Within each four year group the position creeps back by about a quarter of a degree a year and then jumps forward when February gains its extra day, so the years immediately before a leap year sit lowest and the leap years themselves sit highest.
Layered on top is the slow drift across the century, which is what pushes the upper end of the range past ten degrees at all. The practical upshot is that no rule of thumb will do here: to know which band applies to you, the position has to be calculated for your particular year, and the widget above does exactly that. It reports the longitude to a fraction of a degree, which is more than enough resolution to see which side of the line you sit on.
Why it matters which side you are on
The two bands carry different rulers, and a traditional reading of the Sun uses the decan ruler alongside the sign ruler. Saturn governs Capricorn either way. Whether Jupiter or Mars joins it changes what the older sources say about the position, and the descriptions attached to the two bands are not close variants of one another.
That is interpretation rather than measurement, and it should be held loosely. But it does mean the usual practice of naming a decan for a date without asking the birth year gives some readers the wrong band outright, which is a plain error rather than a shade of emphasis. The safe habit is to treat any band assignment near a ten degree mark as provisional until the position has been worked out.
The parts that are not in doubt
The sign is Capricorn in every year, with the solstice ingress ten days behind and the Aquarius boundary three weeks ahead. Nothing about being near a decan edge touches that, since decan boundaries sit inside a sign rather than between signs.
And the placements a date can never fix remain open as usual. The Moon changes sign every couple of days, so this date narrows it to two candidates that only an hour of birth can choose between. The rising sign stays entirely open, since the whole zodiac crosses the eastern horizon within a day and the birthplace latitude affects the timing as much as the clock does.
Questions people ask about this
What sign is 31 December?
Capricorn, in every year without exception. The solstice ingress was ten days earlier and the Aquarius boundary is three weeks away, so the sign carries no ambiguity at all.
Which decan is a 31 December birthday?
It depends on the birth year. The Sun sits between roughly eight point nine and ten point three degrees, straddling the line at ten degrees that separates the first decan from the second.
How do I find out which band applies to me?
Calculate the Sun's longitude for your own year, hour and birthplace. The widget above returns the figure, and anything below ten degrees is the first band while anything above it is the second.
What is the difference between the two bands?
The Chaldean ruler. The first decan of Capricorn takes Jupiter and the second takes Mars, and the traditional descriptions attached to them differ accordingly. Saturn rules the sign in both cases.
Why do other pages state one decan flatly?
Because they work from date ranges rather than positions, so they have no way to notice that a date sits on a band boundary. For most dates that shortcut is harmless, and for this one it is not.
Does a New Year's Eve birthday carry any astrological meaning?
Not in itself. The tradition works from the Sun's position rather than from what the calendar calls the day, and the position here is the tenth degree of Capricorn whatever the date is named.