The calendar chases the orbit
The Earth completes an orbit in about three hundred and sixty five and a quarter days, and the calendar year is a whole number of days. That leftover quarter is the whole problem. Left alone it would push each date a day later against the Sun every four years, and the seasons would slide through the calendar within a lifetime.
The leap day is the correction. Three years of quarter day slippage accumulate to nearly a full day, and February gains that day back in the fourth. The result is that a given date does not drift through its sign, it oscillates around a fixed solar longitude with a four year rhythm.
What that means for this date
Taken at noon across every year from 1930 to 2035, the Sun on 4 August has stood between roughly eleven and a quarter and about twelve and a half degrees of Leo. The lowest values fall in leap years and the highest in the third year afterwards, and the pattern simply repeats.
The century long correction from skipping leap years in most century years does not touch this window, since 2000 was itself a leap year. Someone comparing a birth in the nineteenth century would see a slightly different figure, but nobody currently alive falls outside the band given here.
The practical upshot is that a published degree for a date is useful. It is not exact, but the error is small enough that it beats a sign name by a wide margin.
A position inside the second band
Twelve degrees puts the Sun in the second of Leo's three ten degree divisions, the stretch from ten to twenty, which the Chaldean order assigns to Jupiter. The whole of the century wide window sits inside that band, so the assignment holds for every year and every hour of this date.
What the tradition reads into Jupiter in a solar sign is generosity on top of warmth, a pull towards teaching, hosting and the wider gesture. That is inherited convention rather than measurement, and the honest way to hold it is as a description of what the texts say rather than of what the date does. The band itself follows from the degree and does not depend on the reading.
Precision has a limit
Knowing the Sun to within a degree still leaves most of a chart unwritten. The Moon covers about thirteen degrees a day, so it moves through half a sign between one 4 August midnight and the next, and the date cannot say which sign a given birth caught.
The Ascendant changes several times faster again and depends on the latitude of the birthplace, which means all twelve signs are possible. The widget above takes a year, a time and a place, returns the exact solar degree rather than the range, and reports the distance from the birth to the nearest sign boundary.
What a stable solar position does give is a reliable starting point. The degree is known before anything else is asked, and the remaining questions can be put to a birth record rather than to a table.
Questions people ask about this
What degree is the Sun on 4 August?
Between about eleven and a quarter and roughly twelve and a half degrees of Leo at noon, depending on the year. Adding a birth hour and a place narrows that to one figure.
Why does my birthday always fall at the same solar position?
Because the leap day cancels the quarter day the calendar loses each year. Without it the date would slide steadily through the sign instead of returning to nearly the same point.
Do leap years give the lowest or the highest degree?
The lowest. A leap year arrives with the accumulated slippage already corrected, so the Sun has advanced slightly less by that date. The third year after a leap year gives the highest value.
Is 4 August definitely Leo?
Yes. The Sun is around twelve degrees into the sign, comfortably clear of the ingress from Cancer and of the move into Virgo, so no year or hour changes it.
Which decan does this fall in?
The second decan of Leo, ten to twenty degrees, which the Chaldean order assigns to Jupiter. The entire noon range for this date sits inside that band.
Does the same stability apply to the Moon?
No. The lunar cycle has no whole number relationship to the calendar year, so the Moon can be in any sign on this date. Only the Sun keeps a fixed date to position relationship.