Clear of the boundary
The Sun enters Virgo when it reaches one hundred and fifty degrees of ecliptic longitude, and the moment falls somewhere across 22 and 23 August depending on the year. That ingress drifts about six hours later each common year and jumps back roughly eighteen hours when February gains a day, which is why dates in the low twenties of August are genuinely contested.
By the thirty first, that drift is irrelevant. The Sun has moved on by more than eight degrees, and a swing of a day and a half in the ingress could not carry the boundary anywhere near this date. Anyone born on 31 August is Virgo in every year and every time zone.
Ingress drift is also why printed date ranges disagree with each other. A table that ends Leo on the twenty second and one that ends it on the twenty third are both approximating a moving boundary, and neither is wrong about this date.
The degree on the last day of August
Taken at noon, the solar longitude on this date has run between about 7.1 and 8.5 degrees of Virgo across 1930 to 2035. The eighth degree is the practical answer, and the whole spread is small because the leap year cycle keeps the calendar in step with the orbit rather than letting a fixed date slide.
Your own value inside that band depends on the year, the hour and the meridian of your birthplace, since a local clock time has to be converted to a universal instant before the position can be worked out. The widget above does that and also reports how far the result stands from the nearest sign boundary, which on this date will be a comfortable distance.
Still in the first face
Eight degrees keeps the Sun inside Virgo's opening decan, which covers the first ten degrees of the sign. It is near the end of the band, and the next face begins at ten degrees, so a birthday a few days later crosses over.
The Chaldean order assigns this first face to the Sun, counting the loop of Mars, Sun, Venus, Mercury, Moon, Saturn and Jupiter forward from the start of Aries. The triplicity order assigns it to Virgo and so to Mercury. Tradition reads the face as a modifier on the sign rather than a replacement for it, and marks nothing about it as fortunate or otherwise.
Where the real uncertainty sits
Because the sign is beyond argument, it is worth being clear about what is not. The Moon crosses roughly thirteen degrees a day, so on 31 August it is in one of two signs and the hour decides which. The Ascendant runs through all twelve signs in a day, changing about every two hours.
House placements follow the Ascendant, so without a birth time the chart has planets but no framework to place them in. People often arrive at a date page hoping to resolve their sign and leave believing the chart is settled. On this date the sign was never in doubt and the rest still is.
The practical advice for this date is therefore short. Take the sign as given and spend the effort on finding a birth time.
Questions people ask about this
Is 31 August Leo or Virgo?
Virgo, with no ambiguity. The Sun crossed the boundary between 22 and 23 August depending on the year, and by the end of the month it is more than eight degrees past it.
Am I on the Leo Virgo cusp?
No, and in any case no such thing exists. The Sun holds one longitude at any moment and that longitude lies inside a single sign. On this date it is nowhere near an edge.
How far into Virgo is the Sun on this date?
About eight degrees. Noon figures from 1930 to 2035 fall between roughly 7.1 and 8.5, so the eighth degree covers almost every birth on 31 August.
Which decan is it?
Still the first, since that face runs to ten degrees. The Sun is near its end, and birthdays in early September start crossing into the second face.
Does the time zone of my birth matter?
Not for the sign here. It matters for converting your local clock time into the universal instant used for the calculation, which affects the exact degree, and it matters greatly for the Ascendant.
What should I look up next?
The Moon and the Ascendant, since those are the placements the date leaves open. Both need the hour of birth, and the Ascendant needs the birthplace as well.