The degree, which is the figure nobody prints
A sun sign is a thirty degree band, and saying you are Capricorn only tells you which band. The Sun on 13 January has been between about 22.2 and 23.6 degrees of Capricorn at noon in every year from 1930 to 2035. That is a spread of under a degree and a half across more than a century.
The reason it holds still is that the calendar was built to track the orbit. A tropical year runs a little under 365.25 days, and the leap day corrects the drift almost exactly. The degree creeps forward through three ordinary years, then February gains a day and pulls it back. The result is a slow four year wobble around a fixed point rather than a steady march.
That is worth stating plainly because the usual claim runs the other way. People are often told the dates shift, or that a birthday can quietly change sign as the years pass. Precession does move the constellations against the tropical signs, but it does so over millennia and the tropical zodiac is defined against the equinox rather than the stars, so the calendar dates hold.
The decan, the layer under the sign
Each sign divides into three bands of ten degrees called decans. Twenty three degrees of Capricorn falls in the third, the band from twenty to thirty, and in the Chaldean scheme that band is assigned to the Sun.
Tradition reads the third decan of Capricorn as the point where Saturn's discipline is turned toward something visible. Saturn still governs the whole sign, so the material is the same, but the older writers attached the Sun's concern with standing and recognition to this final third. That is interpretation rather than measurement, and it is worth holding as interpretation. What is measurable is only that the position is in that band.
What the date leaves wide open
The Sun moves about one degree a day, which is why a date fixes it so tightly. The Moon moves roughly thirteen degrees a day and changes sign every two and a half days, so on any 13 January it can be in one of two or three different signs depending on the hour and the year. The date alone cannot narrow it.
The rising sign is looser still. It turns through all twelve signs in twenty four hours, so it depends almost entirely on the clock time and the latitude of the birthplace, and not at all on the calendar date. Two people who share this birthday can have nothing in common in a chart beyond the Sun.
The slower planets are a different case again. Jupiter takes about twelve years to circle the zodiac and Saturn about twenty nine, so those placements depend almost entirely on the birth year and hardly at all on the day. A date shared across a century covers every sign for both of them.
Using the widget above
The widget above takes your year, your birth time if you have it, and your birthplace, and returns the Sun's exact longitude rather than a range. It also reports how far you were born from the nearest sign boundary, which on this date will be a comfortable distance in both directions.
That distance is the useful output. It tells you the answer does not depend on whether your recorded birth time is right, and it gives you a figure you can carry into an aspect list or a house placement, where a degree genuinely changes what is being read.
Questions people ask about this
What sign is 13 January?
Capricorn, without qualification. The date sits well inside the sign in every year, so there is no year in which it falls in Sagittarius or Aquarius.
What degree is the Sun on 13 January?
Between roughly twenty two and twenty four degrees of Capricorn, depending on the year and the hour. The widget above will give you the exact figure for your own birth details.
Which decan is a 13 January birthday?
The third decan of Capricorn, the band from twenty to thirty degrees. In the Chaldean order that decan is assigned to the Sun, while Saturn continues to rule the sign as a whole.
Why does the degree hardly change between years?
Because the leap year cycle keeps the calendar in step with the orbit. The position drifts forward by about a quarter of a degree in each ordinary year and the leap day pulls it back, so it circles a fixed value.
Do I need my birth time for this date?
Not for the sun sign, which is settled either way. You need it for the Moon, which can be in more than one sign on this date, and for the rising sign, which depends on the hour above everything else.
Is a late Capricorn degree different from an early one?
In the tradition, yes, because the decans differ and the aspects a placement can make differ. As a sign membership it makes no difference at all: twenty three degrees is as much Capricorn as three.