The number itself
Solar longitude is measured from zero degrees of Aries, the March equinox point, right round the ecliptic. Capricorn begins at two hundred and seventy degrees, and on 26 December, taken at noon, the Sun sits between about three point eight and five point two degrees past that line, in every year from 1930 to 2035.
The variation across that whole span is little more than a degree, which surprises people who expect the calendar and the sky to have drifted apart over so long. They have not, because the drift is corrected almost as fast as it accumulates. Anyone born on this date in the last hundred years shares that solar position to within about a degree, whatever else differs between their charts.
Why the position holds so still
The Earth takes about three hundred and sixty five days and a quarter to return to the same point relative to the Sun. A calendar of three hundred and sixty five whole days therefore runs fast, and each year the same date arrives a quarter of a day earlier in the orbit, which shows up as the Sun being a quarter of a degree further back.
The leap day added every fourth February pushes the date the other way by roughly three quarters of a degree in one step. Over the four year cycle the two effects nearly cancel. What is left over is the small excess that the century rule handles, and it moves the position by a fraction of a degree over a lifetime rather than by whole signs.
What the degree is used for
Aspects are measured in degrees, not signs. Whether your Sun makes a close square to a planet or a loose one depends on its exact longitude, and traditional practice cares a great deal about how close an aspect is. A sign name cannot answer that; a degree can.
The degree also fixes the decan. Four and a bit degrees of Capricorn falls in the first band, zero to ten, which the Chaldean order assigns to Jupiter. And in a full chart the degree decides which house the Sun lands in when a cusp falls nearby, which can move it from one part of the chart to the next on a difference of minutes.
None of that is available from a sign name, and none of it is contested technique. It is simply the level at which traditional practice works, and the level that date range lookups discard before they print anything.
Where the date runs out
What the degree cannot do is describe you. The Sun is one placement, and the ones that vary most between two people born on the same date are the fast ones. The Moon shifts sign every couple of days, so 26 December offers two candidates and the hour of birth chooses. The Ascendant offers all twelve, decided by the hour and the latitude together.
The widget above takes your year, your time if you have it, and your birthplace, and returns the Sun's exact longitude for that moment along with the distance to the nearest sign boundary. On this date that distance will be comfortable in both directions, which is the useful thing to have confirmed rather than assumed. With a birth time added it can go further and place the Sun in a house, which is where the position begins to say something particular.
Questions people ask about this
What sign is 26 December?
Capricorn, with no year to year variation. The Sun entered the sign at the solstice several days earlier, so this date has never fallen in Sagittarius in the modern calendar.
What is the solar degree on 26 December?
Between about three point eight and five point two degrees of Capricorn at noon, across the years from 1930 to 2035. Your own figure depends on the year, the hour and the birthplace.
Why does the degree hardly change over a century?
Because the leap year rule keeps the calendar tied to the orbit. The date slips a quarter of a degree each ordinary year and the leap day pushes it back, so the two nearly cancel and only a small residue accumulates.
Does an earlier or later degree make me more Capricorn?
No. Every degree from zero to thirty is fully inside the sign. The degree changes which decan applies and which aspects are close, not the strength of the sign.
What can I do with my exact degree?
Use it to find your decan, to check which planets your Sun aspects closely, and to see where the Sun sits relative to house cusps once a birth time is known.
Is a noon calculation good enough for this date?
For the sun sign and the decan, yes, since neither is near a boundary. For the Moon and the rising sign it is not, and those need an actual birth time.