The slow one
The Sun advances a little under a degree a day, which is why a calendar date corresponds so neatly to a solar position. The only reason the figure varies at all between years is the quarter day left over from each orbit, and the leap day cancels most of that every four years.
What remains is a spread of under one and a half degrees across the whole period, with leap years at the low end. On this date the entire range sits in the closing band of Leo, which runs from twenty degrees to the Virgo boundary and is ruled by Mars in the Chaldean order and in the triplicity scheme alike. Neither the sign nor the band is in question.
Because of that, the useful question about the Sun on a birthday is never which sign but which degree, and after that, how far from the nearest line. On the twentieth of August the answer to the second question is two or three degrees short of Virgo, which is close enough to be worth stating and far enough that nothing about the birth hour can change the sign.
The fast one
The Moon completes a circuit of the zodiac in about twenty seven and a third days, which works out at twelve to fifteen degrees a day depending on where it is in its orbit. It therefore spends a little over two days in each sign, and a change of sign falls on a given calendar date fairly often.
The practical effect is that a birth at two in the morning and a birth at eleven at night on the same twentieth of August can differ by half a sign, and can straddle a sign boundary. No date based description can name a Moon sign, which is why pages that try tend to leave the Moon out altogether.
The one that is not on the ecliptic clock at all
The rising sign is set by the Earth's rotation rather than by any orbit. A full twelve signs come over the eastern horizon every twenty four hours, so the Ascendant changes roughly every two hours and can be any sign whatsoever on any date.
It is also the placement that most depends on where the birth happened. Away from the equator, signs rise at very uneven rates, so the same clock time in two cities at different latitudes can yield different Ascendants. That is why a birthplace is asked for and not just a time zone.
What follows for a birthday page
The only placement a date determines is the one shared by everyone born within about a month. The tradition reads Leo as fixed fire under the Sun, and reads its final band as the more assertive stretch, but both statements describe a large category and are inherited interpretation rather than measurement.
The widget above uses the year, hour and place to compute the solar longitude exactly, to report how far it stood from the nearest sign boundary, and to work out the Moon and the Ascendant. That is where a chart stops being a description of a date and starts being a description of a moment.
Questions people ask about this
What sign is 20 August?
Leo. The Sun is near twenty seven degrees of the sign, and Virgo does not open until thirty, so the boundary is still two or three days off.
How much does the Moon move in a day?
Between twelve and fifteen degrees, which is about half a sign. That is why the Moon sign can change during a single calendar date.
Can I work out my Moon sign from my birthday?
Not reliably. On many dates the Moon changes sign partway through, so the hour and the birthplace are needed to settle it.
What decan is 20 August in?
The third decan of Leo, twenty to thirty degrees, under Mars. The date's noon range for the last century sits entirely inside that band.
Why is the Sun so much more predictable?
Because it moves slowly and because the calendar was built around its cycle. The leap day keeps a fixed date fastened to nearly the same solar longitude.
How often does the rising sign change?
About every two hours, though the rate varies with latitude. All twelve signs rise in the course of a day, so the date constrains the Ascendant not at all.