What the date does fix
The Sun moves a little under a degree a day, so a calendar date pins it tightly. On 15 January it has been between about 24.2 and 25.6 degrees of Capricorn at noon in every year from 1930 to 2035, and that puts the birthday in the third decan of the sign, the band from twenty to thirty degrees, which the Chaldean order assigns to the Sun.
So the date gives you a sign with no argument, a degree to within a degree and a half, and a decan. That is a real amount of information and more than most sources offer. It is also where the date stops being useful.
It is also stable enough to be useful. Because the figure moves so little between years, someone born on this date in 1948 and someone born in 2012 sit within a degree and a half of each other, which is closer than most people assume a century apart could be.
What the Moon does on this date
The Moon covers around thirteen degrees a day and changes sign roughly every two and a half days. On a given 15 January it can be in either of two signs, and in some years the change falls within the day itself so both are possible depending on the hour of birth.
Across a run of years the same date will have produced a Moon in most of the twelve signs at one time or another. There is no lunar pattern tied to a calendar date, which is why nobody publishes a moon sign table by birthday. It has to be computed from the year and the time.
The rising sign owes nothing to the date
The ascendant is the point of the ecliptic coming over the eastern horizon, and the horizon turns through the entire zodiac once a day. Two births six hours apart on the same 15 January will normally have ascendants a quarter of the way around the wheel from each other.
Latitude matters as well. Signs rise unevenly, and the further from the equator the birthplace, the more the durations distort, so the same clock time yields different ascendants in Edinburgh and in Lagos. None of this can be inferred from the date, only from the hour and the place.
Whole sign, Placidus and equal house all read the ascendant differently once it is found, and they disagree most sharply about which house a planet sits in. That disagreement only starts after the hour is known. Without it there is nothing for the house systems to argue about.
Where that leaves the sun sign
Once you have seen how much the date leaves open, the sun sign starts to look like what it is: one placement out of a chart full of them, and the one shared by roughly a twelfth of everyone alive. It is the least personal element rather than the most.
The widget above computes the Sun's exact longitude from your own year and birthplace and reports the distance to the nearest sign boundary, which on this date is comfortable in both directions. From there a full chart is what adds anything individual.
Questions people ask about this
Is a 15 January birthday always Capricorn?
Yes. The date is well inside the sign and stays there across every year in the modern record, so there is no year, hour or time zone that changes it.
What is my moon sign if I was born on 15 January?
The date cannot tell you. The Moon changes sign every two and a half days, so it depends on your year and hour of birth and has to be calculated rather than looked up.
Does the date tell me my rising sign?
No. The ascendant depends on the clock time and the latitude of the birthplace, and it moves through all twelve signs in a day, so the calendar date contributes nothing to it.
What degree is the Sun on 15 January?
About twenty four to twenty six degrees of Capricorn, with the exact value set by the year and the hour. That places it in the third decan, the band ruled by the Sun in the Chaldean scheme.
If I do not know my birth time, what can I still get?
The Sun, and with it the decan, since neither is close to a boundary on this date. Planets that move slowly are also safe. The Moon may be uncertain and the ascendant cannot be found at all.
Why do birthday pages say so much about the sun sign?
Because the date is the only input they have. Every other placement needs a year, an hour and a place, which a page written for a calendar date does not know.