The sign is settled, so start with the degree
The Sun enters Capricorn around 21 or 22 December and leaves it around 19 or 20 January. The first of January sits comfortably inside that span, roughly a fortnight clear of either end, so no year, hour or birthplace can move it out.
That leaves the degree. Measured at noon across births from 1930 to 2035, the Sun on this date falls between about 9.9 and 11.3 degrees of Capricorn. The whole spread is under a degree and a half, which is far tighter than most people expect once they hear that sign dates move at all.
Anyone whose birthday falls here has probably been told the sign a hundred times and the degree never once. It is the one figure that separates a 1 January Capricorn from a 15 January one, and it is not hard to compute.
Why the degree barely moves
The tropical year runs about a quarter of a day longer than a calendar year of 365 days, so the Sun arrives at any given longitude roughly six hours later each year. Left alone that drift would carry this date across whole signs within a few centuries.
The leap day pulls it back. Every fourth February adds a day and the accumulated six hour steps are cancelled almost exactly, which is the point of the rule. The result is a sawtooth: the degree creeps forward for three years, drops back in the fourth, and the pattern repeats without wandering. That sawtooth is the whole of the one and a half degree range on this date.
A useful consequence follows. Because a day of solar motion is only about one degree, a shift of several hours in the ingress moment changes nothing in the middle of a sign and everything at its edges. That is why sign dates are quoted as ranges with a day of slack at each end while dates like this one never move at all.
The middle decan of Capricorn
Ten to twenty degrees of Capricorn is the second decan, and a Sun near ten degrees is just inside it. In the Chaldean order of decan rulers that band belongs to Mars. In the triplicity scheme, which walks through the signs of the same element, it belongs to Taurus and so to Venus.
The two schemes disagree here, and both are in current use, which is why a decan ruler quoted elsewhere may not match. Traditionally the Mars attribution is read as effort applied to a Saturn framework, ambition with something abrasive in it. The Taurus attribution reads the same band as steadier and more comfort seeking. Neither is a measurement, and this page marks both as interpretation.
What the band is not is a second sign. A decan sits inside Capricorn and refines it, so a Sun at eleven degrees is entirely Capricorn and additionally in a Mars ruled face. Nothing is diluted and nothing is shared with another sign.
What 1 January does not tell you
The date fixes the Sun and almost nothing else. Over twenty four hours the Moon moves between twelve and fifteen degrees, so a 1 January birth can have the Moon in two signs, occasionally three, depending only on the hour. The rising sign turns through all twelve in a day, so without a birth time it is entirely unknown.
Put plainly, the sun sign is the part of a chart least specific to the individual, because it is shared with everyone born in the same month. The widget above takes your year and birthplace, computes your actual solar degree rather than the noon figure, and reports how far you were born from the nearest sign boundary.
Questions people ask about this
What sign is 1 January?
Capricorn, in every year. The date sits about two weeks inside the sign, so neither the year nor the birth hour can change the answer.
What degree of Capricorn is 1 January?
Between roughly 9.9 and 11.3 degrees at noon, taking the years 1930 to 2035 together. The widget above gives the figure for your own year and place rather than the noon average.
Which decan is a 1 January birthday?
The second decan of Capricorn, covering ten to twenty degrees. Births at the low end of the range can land a fraction under ten degrees, which would place them in the first decan instead, so the exact figure is worth checking.
Who rules the second decan of Capricorn?
Mars in the Chaldean order and Venus, by way of Taurus, in the triplicity scheme. Both attributions are traditional and they simply answer different questions about the same ten degrees.
Does a New Year's Day birthday mean anything astrologically?
No. The first of January is a calendar convention with no standing in the zodiac, which is measured from the March equinox. The date is unremarkable to the tradition and only notable to the diary.
Is my whole chart Capricorn then?
Not at all. Only the Sun is fixed by the date. The Moon depends on the hour and the rising sign depends on the hour and the birthplace together, so two people born on the same 1 January can share very little beyond the Sun.