What the date genuinely fixes
Two things follow from the date alone. The first is the sign: the Sun entered Aries at the March equinox and does not leave it until around 19 or 20 April, so a 3 April birth is Aries with no boundary in reach.
The second is the degree, within a narrow window. At noon between 1930 and 2035 the Sun on this date has sat between about twelve and three quarters and fourteen and a quarter degrees of Aries. That fixes the decan too, since the whole window lies inside the band from ten to twenty degrees, the one the Chaldean order hands to the Sun.
Those two facts are checkable against any ephemeris. They are also, on this date, the complete list of what the calendar decides on its own.
The Moon is decided by the hour
The Moon travels between twelve and fifteen degrees a day, roughly half a sign. On most dates it therefore starts the day in one sign and ends it in another, and 3 April is no different in that respect from any other date.
So a lunar sign cannot be read off a birthday. Someone born at six in the morning and someone born at eleven at night can hold different Moon signs while sharing every digit of the date. Since the Moon is the placement most closely tied in the tradition to habit and emotional response, that is not a small piece to leave blank.
The horizon is wide open
The rising sign is the point of the zodiac coming over the eastern horizon at the moment of birth. The Earth turns once a day, so that point passes through all twelve signs every twenty four hours and changes by about a degree every four minutes.
It also depends on latitude. The same clock time in Edinburgh and in Nairobi gives different Ascendants, because the angle at which the zodiac meets the horizon changes with distance from the equator. Every house cusp in a chart is anchored to that point, which means the date on its own leaves the entire house structure undetermined.
This is why an astrologer asks for a time of birth before saying anything specific. Without one the chart can still be cast for noon, but the houses in it are a placeholder rather than a reading.
Why the sun sign still gets all the attention
The Sun is the one placement a newspaper column can assume. It needs no birth time, no birthplace and no calculation, so it became the public face of astrology in the twentieth century for reasons of print logistics rather than of doctrine.
In the older texts the Sun is one significator among several, and the Ascendant often carries more weight for describing a person. Reading the tradition on its own terms means putting the sun sign back in proportion. The widget above computes the exact solar degree for a given year and place, works out the Moon and the Ascendant from the same details, and reports how far the birth fell from the nearest sign boundary.
Questions people ask about this
What sign is 3 April?
Aries, in every year of the modern calendar. The Sun is near thirteen degrees of the sign, which leaves several days of margin on either side and no scope for doubt.
Can I work out my Moon sign from my birthday alone?
No. The Moon covers about half a sign in a day, so it is frequently in one sign in the morning and the next by evening. The hour and the place are needed.
How much does the rising sign change during a day?
It moves through all twelve signs, about one sign every two hours on average, though the pace varies a good deal with latitude. Four minutes of clock time shifts it roughly a degree.
Does this mean the sun sign is unimportant?
Not unimportant, just partial. It is a measured position that the tradition reads as one significator among several, rather than a complete description of a chart.
Which decan does 3 April fall in?
The second decan of Aries, from ten to twenty degrees. The Chaldean order assigns that band to the Sun, so the reading is Mars as sign ruler with a solar qualification.
What if my birth time is only approximate?
An hour of uncertainty leaves the Sun and the decan untouched and usually leaves the Moon sign clear as well. The Ascendant is the placement that suffers most, since it can cross a sign boundary inside that hour.