The band your birthday falls in
Decans are the oldest subdivision in the western tradition, older than the aspects most people use daily. Each sign is cut into three parts of ten degrees, and each part carries a planet of its own. The Chaldean order assigns the third decan of Capricorn to the Sun.
On 14 January the Sun has been between about 23.2 and 24.6 degrees of Capricorn at noon in every year from 1930 to 2035. That places the birthday firmly in the final band, four degrees or so from its inner edge and five from the end of the sign.
What the tradition attaches to it
Saturn rules Capricorn throughout, so the whole sign is read as patient, structural and slow to spend itself. The decan ruler modifies rather than replaces that. Where the first decan is read as Saturn on Saturn, the third puts the Sun's interest in visibility and standing on top of Saturn's material.
Older texts describe this as work that eventually has to be shown to somebody. Whether that reads true is a question for the reader and not something a date can settle. The decan itself is a measured fact, the character attached to it is inherited interpretation, and the two are worth keeping apart.
The Egyptian decans and the Chaldean rulers are not the same system, and where a modern source gives a decan ruler it is usually the Chaldean one, drawn from the planetary order used for the hours of the day. Knowing which scheme is in front of you matters more than which reading you prefer, since the two assign different planets to the same band.
Why the position sits still
The degree range for this date is barely more than a degree wide across a century, which surprises people who expect drift. The tropical year is close to 365.2422 days, so a plain calendar year runs short and the Sun ends up about a quarter of a degree further along at the same clock time each year. The leap day then subtracts almost exactly the accumulated difference.
What is left is a small sawtooth. Your own year decides where in that sawtooth you fall, which the widget above works out precisely, along with how far the position sits from the nearest boundary.
The parts of the chart still open
A birthday fixes the Sun and very little else. The Moon covers roughly thirteen degrees a day and can be in either of two signs on a given 14 January, sometimes a third depending on the year. Nothing about the date narrows that down without an hour attached.
The rising sign is untouched by the date. It cycles through all twelve signs every day, so it is decided by the clock and the latitude of the birthplace. This is why the sun sign is the least individual thing in a chart rather than the most, despite being the only part most people are ever told.
Mercury and Venus are also worth a mention here. Both stay close to the Sun, so on this date Mercury is generally within a sign or so of Capricorn and Venus within two. That is a genuine constraint the date supplies, though it is a narrowing rather than an answer, and the exact positions still need a year.
Questions people ask about this
Is 14 January always Capricorn?
Yes. The date sits several days clear of both the Sagittarius and Aquarius boundaries in every year, so no combination of year, hour or place moves it.
Which decan does 14 January fall in?
The third decan of Capricorn, covering twenty to thirty degrees. The Chaldean scheme gives that band to the Sun while Saturn keeps the sign.
What is the Sun's degree on this date?
Roughly twenty three to twenty five degrees of Capricorn, depending on the year and hour. The widget above returns the exact value for your details.
Does the decan change my sun sign?
No. A decan is a subdivision inside the sign, not an alternative to it. You are Capricorn either way, and the decan only refines what the older texts read into the placement.
Can two Capricorns have different decans?
Yes, and most do. The sign spans thirty degrees and around thirty days, so birthdays roughly ten and twenty days apart sit in different bands with different rulers.
Why do most birthday pages ignore decans?
Because they work from a date table rather than a calculated position, and a date table stops at the sign. Once the actual longitude is computed, the decan follows from it immediately.