The measurable part
Taken at noon in each year from 1930 to 2035, the Sun on 29 September occupies between 5.4 and 6.8 degrees of Libra. It is past the halfway mark of the sign's first decan and a week clear of the equinox that opened the sign.
That figure comes from the same ephemeris calculations an astrologer would run, and it can be checked against any published table. It is the sort of statement this site prefers, in that it is either right or wrong and the reader can find out which.
The figure sits in the second half of the sign's opening decan and roughly twenty three degrees short of Scorpio, so no birth hour and no time zone brings the boundary within reach. Anyone told they are on a cusp because the date falls in late September can put the idea aside on the arithmetic alone.
Why the number holds steady
Calendar years and orbital years disagree by close to a quarter of a day. Left alone that gap would march the seasons through the calendar, which is what the leap day exists to prevent, and it does the job well enough that the Sun returns to nearly the same longitude on a given date for a century at a stretch.
Inside each four year cycle there is still a visible pattern. The position creeps later in each ordinary year and drops back when February gains a day, so a birth in a leap year finds the Sun a little short of where a birth three years later would find it. The total swing on this date, over the whole span, comes to 1.4 degrees.
The correction is not exact, which is why the range has width at all. A tropical year falls a little short of three hundred and sixty five and a quarter days, so the Gregorian rule withholds the leap day in three century years out of four, and the leftover shows up as a slow tilt across the span rather than as anything a reader would notice.
The decan, and the two ways of ruling it
Zero to ten degrees of Libra is the sign's first decan, and this date falls inside it in every year of the range. The Chaldean system, which cycles the visible planets in order of apparent speed through all thirty six decans, hands this band to the Moon while Venus keeps the sign.
The triplicity system divides the same band differently in name only, calling it the Libra decan of Libra and leaving Venus in charge of both layers. Tradition reads the first pairing as balance coloured by mood and the second as Venus undiluted. These are interpretations attached to a position, not consequences of it, and no observation distinguishes them.
What no birthday page can supply
A date fixes the Sun because the Sun is slow. It leaves the Moon at two possibilities, since a lunar sign lasts only a couple of days, and it leaves the Ascendant at twelve, since the whole zodiac rises each day. Those are the placements on which people born the same day actually differ.
The widget above takes the year, the hour and the birthplace and returns the exact solar longitude for that moment, together with the distance to the nearest sign boundary. On this date that distance runs to several days, which settles any suggestion of a cusp before it starts.
Questions people ask about this
What sign is a 29 September birthday?
Libra in every year covered by these calculations, with the Sun between 5.4 and 6.8 degrees of the sign at noon. The equinox that begins Libra falls a week earlier.
Why do birthday pages never give a degree?
Because the degree changes with the year and the hour, and a fixed date table has no column for it. Dropping the variable part is what makes the tables copyable.
Which decan is 29 September?
The first decan of Libra, from zero to ten degrees. Every year in the range lands inside it, and the Chaldean order assigns that band to the Moon.
Is a birth in a leap year different?
Only slightly, and only in the degree. Within each four year cycle the Sun's position on a given date creeps later and then resets after the extra day, a swing of about a degree in total.
Does this date make me a typical Libra?
Tradition associates the middle degrees of a decan with the band's character rather than with the sign boundaries either side of it. That is a reading rather than a measurement, and the sign applies in full at any degree.
How much does my birth hour move the Sun?
Around a degree across a full day, since the Sun advances about that much in twenty four hours. It refines the figure without changing the sign or the decan here.