Why the usual answer is so short
A sign is a thirty degree band, and a calendar date maps onto it cleanly unless the date sits near a boundary. Twenty four December is two or three days past the solstice ingress, far enough that no year in the modern calendar has ever put it in Sagittarius. There is nothing to argue about, so the standard page states Capricorn, adds a few adjectives borrowed from the sign as a whole, and finishes.
The trouble is that those adjectives are identical for the whole month, from the solstice through to mid January. They describe a thirty degree slice of sky, so they cannot distinguish this birthday from any other Capricorn birthday. If a description would read the same with a different date at the top of it, it is not really about the date. The test is easy to apply and most birthday writing fails it.
The measurement that does distinguish it
The Sun's longitude on 24 December, measured at noon and taken across the years from 1930 to 2035, runs between about one point eight and three point one degrees of Capricorn. That is a genuinely narrow window for a span of over a century, and it holds because the leap year rule keeps the calendar and the orbit close to step with each other.
Ordinary sign tables never publish this because they work in date ranges rather than positions. But the degree is what traditional technique actually uses. It decides which aspects the Sun makes to other planets in a chart, which house cusp it falls near, and which of the three decans applies to it.
Second and third degrees of Capricorn
Those degrees put this date firmly in the first decan of Capricorn, the band from zero to ten degrees, whose Chaldean ruler is Jupiter. The tradition treats the decan as a modifier rather than a second sign: Saturn still governs, and Jupiter colours the opening third with something less severe and more outward looking than the rest.
Whether you find that persuasive is a separate question, and it should be marked as interpretation rather than measurement. The degree and the decan boundaries are arithmetic. What is read into them is a body of tradition with a long history and no particular claim on your character.
It is still worth knowing which band you are in, if only because the sources disagree about the three bands in ways they do not disagree about the sign. Reading the wrong decan description is a plain mistake rather than a matter of taste.
Two people, same date, different charts
Two babies born on 24 December in different hours share a sun sign, a degree to within a fraction, and a decan. They may hold different Moon signs, since the Moon changes sign every couple of days, and they will almost certainly hold different rising signs, since the whole zodiac rises within a single day.
That is the practical reason the sun sign is the least personal part of a chart rather than the most. Sharing it with roughly one person in twelve is what makes it easy to look up and weak as a description of anybody.
The widget above computes your own solar degree from your year, hour and birthplace, along with the distance to the nearest boundary. It is the starting point rather than the answer, and the next thing it wants from you is a birth time.
Questions people ask about this
What star sign is 24 December?
Capricorn. The Sun entered the sign at the solstice on the twenty first or twenty second, so by the twenty fourth it is a few degrees in and the date carries no ambiguity in any modern year.
What degree is the Sun on 24 December?
Roughly between one point eight and three point one degrees of Capricorn at noon, taking every year from 1930 to 2035. Your exact figure depends on your year, hour and birthplace.
Is 24 December a cusp birthday?
No. It is past the solstice boundary by two or three days, which is several degrees of movement. The Sun is unambiguously inside Capricorn on this date.
What is the decan for this birthday?
The first decan of Capricorn, zero to ten degrees, ruled by Jupiter in the Chaldean order. It applies to every 24 December with no year to year variation.
Why does my birthplace matter if the sign is certain?
It does not change the sign here, but it fixes the exact degree and the local time, and both are needed before the Moon and the rising sign can be worked out.
Does a Christmas Eve birthday mean anything astrologically?
Nothing in the tradition attaches to the calendar festival. What the tradition works with is the Sun's position, which happens to be the early degrees of Capricorn, and that would be true whatever the date was called.