The two things the date does fix
The first is the sun sign, which is Aquarius. This date sits eleven days past the Capricorn boundary and eighteen short of the Pisces one, so no year, hour or birthplace can move it.
The second is the decan. At noon across 1930 to 2035 the Sun has been between 10.5 and 11.9 degrees of Aquarius, which places it in the second decan of the sign in every one of those years. That band runs from ten to twenty degrees and takes Mercury in the Chaldean order of rulers, and Gemini, and so Mercury again, under the triplicity scheme. The two schemes agreeing is not the usual case.
Why the degree stays put
The narrowness of that range surprises people. A century and more of birthdays, and the Sun never strays more than about a degree and a half from the same point.
The reason is arithmetic rather than anything mystical. The tropical year is roughly three hundred and sixty five and a quarter days, so each ordinary year the Sun ends up about six hours further along on a given date, and the leap day then pulls it back by a full day. Averaged over the cycle the calendar tracks the orbit closely, and only a slow residual drift remains.
There is a second effect worth naming, because it is often confused with this one. The equinox point itself drifts slowly against the fixed stars, a motion called precession, at about one degree every seventy two years. Tropical astrology measures from the equinox, so precession does not move these figures at all. It is why sidereal calculations give a different sign for the same birth.
What the date leaves entirely open
The Moon moves through a sign in about two and a half days, so on any 31 January it can begin the day in one sign and end it in another, and across different years it has occupied all twelve. Nobody can tell you your Moon sign from your birthday alone.
The rising sign is looser still. The whole zodiac rises over the horizon in roughly twenty four hours, so the Ascendant depends on the minute of birth and on the latitude of the place, and two babies born an hour apart in the same hospital can have different rising signs. The houses follow from the Ascendant, so they are unfixed as well, which means every statement about which area of life a planet falls in is unavailable from a date.
The widget above works from the year, hour and birthplace you give it, so it can report the exact solar degree and how far that sits from the nearest sign boundary.
Reading the sun sign for what it is
Aquarius is fixed air, given to Saturn in the traditional rulership and to Uranus in the modern one. Tradition reads it as principled, systematic and detached at the same time, and reads the Mercury decan as adding an interest in explanation and exchange. Those are interpretations carried by a long tradition, and they are offered here as that.
What they are not is a description of a person. A sun sign is shared with a twelfth of everybody alive, and the decan narrows that to a thirty sixth. The individual part of a chart begins where the birthday stops.
A reasonable way to use a page like this is as a starting position rather than a verdict. The degree and decan are checkable and worth writing down. The interpretive layer is a tradition to read against, not a result.
Questions people ask about this
What sign is a 31 January birthday?
Aquarius, in every year without exception. The date sits well inside the sign, more than a week clear of the Capricorn boundary and over two weeks short of Pisces.
What decan is 31 January?
The second decan of Aquarius, ten to twenty degrees. The noon solar degree runs from about 10.5 to 11.9 across the last century, so the decan never changes on this date.
Can a birthday tell me my Moon sign?
No. The Moon changes sign every two and a half days or so, and it can change partway through a given day, so two people born on the same date can differ. You need the year and usually the hour.
Can a birthday tell me my rising sign?
No, and it is not close. The Ascendant moves through all twelve signs in about a day, so it is set by your exact time and by the latitude of your birthplace.
Who rules the second decan of Aquarius?
Mercury in the Chaldean order. The triplicity scheme assigns the decan to Gemini, which is also ruled by Mercury, so both schemes point the same way here.
If I have no birth time, is anything still usable?
Yes. The Sun and the outer planets barely move in a day, so their signs are safe. The Moon is usually narrowed to two candidates, and the Ascendant and houses are not recoverable without the time.