How near the line this date gets
Sampled at noon in every year from 1930 to 2035, a 30 May Sun has stood between roughly eight and nine and a half degrees of Gemini. The boundary between the first and second decans sits at ten. So the date stays in the first face throughout the sampled span, but with less than a degree to spare at the top of the range.
A birth late in the day in one of the higher years narrows that further, since the Sun advances a little under a degree between one midnight and the next. This is not a sign boundary and nothing dramatic turns on it, but it is the one figure on this date that a range based table cannot get right.
What sits on either side
The first decan of Gemini is Jupiter's under the Chaldean count and Gemini's own, and so Mercury's, under the triplicity scheme. The second decan is Mars under the Chaldean count and Libra, and so Venus, under the triplicity one.
Those are wide gaps in tone, and they are wide on both sides. Tradition reads the first face as the sign broadened or the sign at its plainest, depending on the scheme, and the second as the sign sharpened or the sign socialised. Since the schemes disagree with each other more than the two faces disagree, the sensible reading of any decan description is to ask which sequence produced it before taking anything from it.
None of it changes the sun sign. All three faces sit inside Gemini, so crossing from one to the next alters the second layer of description and leaves the first untouched.
The stability behind the number
A degree and a half of movement across more than a century is the whole of the variation here, and it comes from the leap year cycle. The Sun arrives at a given longitude about six hours later each common year and a day earlier after each leap day, and those two cancel out.
That is why the position on a given date is a fact rather than an estimate. It also explains why sign start dates move between the twentieth and twenty first of a month while ordinary dates look fixed. The same wobble is present everywhere, and it only becomes visible where a boundary happens to fall inside it.
On this date the boundary that falls closest is a decan line rather than a sign line, which is why the decan is the number worth calculating and the sign is not.
Everything the date still leaves open
The Moon on this date occupies one sign or crosses into a second, depending on the hour, and across different years it has been in every sign. The Ascendant depends on the time and the place and can be any of the twelve.
The widget above resolves both the questions worth asking here. It returns the Sun's degree and minute for your own year, hour and birthplace, along with the decan that position actually falls in and the distance to the nearest sign boundary. On a date this close to a face boundary, a computed answer is worth more than a table.
Questions people ask about this
Which decan is a 30 May birthday in?
The first decan of Gemini in every year sampled at noon, though the position runs as high as about nine and a half degrees and the band ends at ten. A late birth in a high year is worth checking rather than assuming.
Could a 30 May birth land in the second decan?
Not at noon in the sampled span, but the margin is under a degree at the top of the range. The widget above settles it from a real birth time rather than from a noon default.
Does crossing a decan boundary change the sign?
No. All three decans lie inside the same sign, so a Gemini Sun stays Gemini whichever face it occupies. Only the second layer of description changes.
What degree is the Sun on 30 May?
Between about eight and nine and a half degrees of Gemini across the last century, with the year and the hour deciding where in that band a particular birth falls.
Is this date near a sign boundary too?
No, and that is the difference. Taurus ended around nine days earlier and Cancer does not begin for about three weeks, so the sign is settled while the decan is the tighter call.
Why do most pages not mention the decan at all?
Because they are generated from date ranges, and a date range cannot resolve a ten degree band the way it resolves a thirty degree one. Reporting the decan requires calculating the position.