Why the pages all agree
The reason is structural. Most birthday pages are generated from a table of sign date ranges, and a table like that contains exactly one fact per date. Once the sign has been looked up there is nothing else in the source to report, so the remaining space is filled with descriptions of the sign, which are identical for every date inside it.
An ephemeris contains rather more. It gives the Sun's longitude for a given instant, and that number is different for every date, and slightly different for the same date in different years. Starting from a position rather than a range changes what a page can say.
The position on this date
At noon across the last century the Sun on the fifteenth of August has stood between roughly twenty one point seven and twenty three point one degrees of Leo. The whole window sits in the sign's closing band, which runs from twenty degrees to the Virgo boundary and answers to Mars in both of the rulership schemes that survived into modern practice.
The window is narrow because the leap day keeps the calendar in step with the orbit. Three years of drift forward, one correction back, and the position on a fixed date stays inside a band little wider than a single day of solar motion for a century at a time.
That narrowness is worth stating precisely, because it is what makes the degree usable. If the position on a fixed date wandered across half a sign over a century, quoting a figure would be misleading. It does not, so the figure holds for anyone with this birthday, and the small residual variation is exactly what the year and the hour resolve.
What the tradition attaches to those degrees
Leo is fixed fire and takes the Sun as its ruler, which the older texts read as a settled, visible, self referring quality. The final band is read as the sharper end of that, more willing to contest and less inclined to smooth things over, on account of Mars.
These are inherited interpretations. They come from a written tradition rather than from anything that was measured, and the honest way to use them is to say so and let the reader decide what weight to give them. What is not interpretation is the longitude, which any ephemeris will confirm and which does not vary between authors.
The larger part of the answer is missing from the date
Whatever a birthday page says about the sun sign, it is describing a category that includes a twelfth of the population. The placements that vary between people born on the same day are the ones a date cannot reach: the Moon, which shifts up to fifteen degrees a day and can change sign inside this one, and the Ascendant, which runs the full circle every twenty four hours and depends on the latitude of the birthplace.
The widget above takes those inputs and computes the position directly. It returns the exact solar degree rather than a range, reports how far the Sun sat from the nearest sign boundary, and supplies the placements that make one chart different from another chart with the same birthday.
Questions people ask about this
What sign is 15 August?
Leo. The date sits about a week before the Virgo boundary, which is far enough that no year, hour or time zone has moved it in modern times.
What decan is 15 August?
The third decan of Leo, twenty to thirty degrees, ruled by Mars. Every noon position for this date across the last century falls inside that band.
What is the exact solar degree?
Between about twenty one point seven and twenty three point one degrees of Leo at noon, depending on the year. The widget above narrows that to a single figure from your own details.
Why do most birthday pages say so little?
Because they are built from a table of date ranges, which holds one fact per date. An ephemeris gives a position instead, and a position differs from day to day and from year to year.
Are the decan meanings reliable?
They are traditional rather than empirical. Both surviving schemes agree that Mars rules this band, but agreement between conventions is not the same as evidence, and the readings should be treated as inherited interpretation.
Does the date tell me anything about my Moon sign?
Very little. The Moon can be in either of two signs on any given date, so the hour and the birthplace are needed before it can be named.