Converting degrees into days
The Sun covers close to one degree of ecliptic longitude a day, a little less in early July when the Earth is furthest out and a little more in January. Four or five degrees of remaining sign therefore translates to four or five days of calendar time.
That is a wide margin by the standards of boundary questions, where the argument turns on hours. A birth anywhere on 16 June, at any hour and in any time zone, is Gemini, and no year in the sampled century comes close to changing that.
The Earth's orbit is slightly elliptical, which is why the daily figure is not exactly one degree. Around early July the Earth is at its furthest from the Sun and moves most slowly, so late Gemini and early Cancer pass a shade more slowly than the average.
Why the boundary here is the solstice
Cancer begins at ninety degrees of ecliptic longitude, which is the same instant as the June solstice. That is why the end of Gemini is reported in the news each year while the other sign changes pass unremarked.
The solstice moves between the twentieth and the twenty first of the month, drifting later by about six hours a year and jumping back when February gains a day. Those few days of movement are why dates in the last week of Gemini attract confusion, and why this one does not.
The northern solstice and the southern one are the same instant, of course, and the sign change is defined by longitude rather than by season. That is worth stating because the seasonal names attached to the signs describe one hemisphere and not the other.
The position itself
Twenty five degrees sits in the closing face of Gemini, which begins at twenty. In the Chaldean order that face belongs to the Sun; in the triplicity count it belongs to Aquarius and therefore to Saturn, with Uranus added by modern writers.
Mercury rules the sign as a whole in either scheme, and the face is read as a tint over that rather than a replacement for it. Both attributions come from tables rather than from measurement, and they are set down here as tradition.
The margin that is not comfortable
While the Sun sits five days from its boundary, the Moon may be within minutes of one. It crosses a sign roughly every two and a half days, so a 16 June birth places it in either of two signs and only the hour decides which.
The ascendant changes every two hours or so and needs a birthplace as well as a time. The widget above computes the exact solar degree from your year, hour and location and reports the distance to the nearest boundary, which on this date will be a wide one.
The same goes for the houses, which are drawn from the horizon at the moment of birth. A wide margin on the sun sign says nothing about them, and two people born on 16 June at different hours can have almost identical Suns in quite different parts of the chart.
Questions people ask about this
How close is 16 June to Cancer?
About four to five degrees, which is four or five days. The crossing happens at the June solstice, on the twentieth or twenty first.
Could a late birth hour make this date Cancer?
No. A full day of solar motion is roughly one degree, so even a birth at midnight leaves several degrees of Gemini to run.
What degree is a 16 June Sun?
Between roughly twenty four point four and twenty five point eight degrees of Gemini at noon, depending on the year.
Does being late in a sign weaken it?
Not in any technical sense. A Sun at twenty five degrees is as fully in Gemini as one at five. The degree matters for aspects and for the face, not for whether the sign counts.
Which decan applies?
The third, from twenty degrees on. The Chaldean order assigns it to the Sun and the triplicity count to Aquarius, and so to Saturn.
Why does the solstice get confused with the sign change?
Because they are the same event. Cancer begins at ninety degrees of longitude, which is the solstice by definition, so the two are reported as though they were separate facts about the same few days.