The position first
At noon across every year from 1930 to 2035, the Sun on 16 May has stood between about twenty four point seven and twenty six point one degrees of Taurus. Call it twenty five degrees. That is well past the twenty degree line where the last decan begins and well short of the crossing into Gemini, which happens around the twenty first of the month.
The tightness of the range comes from the leap year cycle, which keeps the calendar in step with the orbit. A date returns to nearly the same solar longitude every year, drifting forward and then being pulled back when February gains a day.
That places the Sun about five days short of Gemini and about five days past the twenty degree line where the third decan opens. Both margins are wide enough that nothing about the birth hour or the time zone can move the answer, so the layers described below apply to every 16 May birth in the sampled range.
Venus over the sign
Taurus is one of the two signs Venus rules in the traditional scheme, the other being Libra. Where Libra is cardinal air, Taurus is fixed earth, so the same planet is read very differently in the two. In Taurus the tradition takes Venus as attachment to the tangible: comfort, possession, the senses, and a strong preference for not being rushed.
Because Venus is the sign ruler, its own position in a chart is treated as carrying the Sun's affairs. That position depends on the year, since Venus does not keep step with the calendar the way the Sun does, and it is one more thing a date alone cannot supply.
Saturn over the decan
The last ten degrees of Taurus go to Saturn in the Chaldean order, which deals the visible planets around the zodiac slowest first. The triplicity scheme assigns the three decans of a sign to the three signs of its element in turn, giving Taurus, Virgo and Capricorn, and Capricorn is also ruled by Saturn. Both routes end in the same place.
Read together, the tradition takes this band as Venus material under Saturn's discipline: an appetite for the solid and the pleasant, held in by an instinct for economy and duration. That is a described reading rather than an observed fact, and a different chart context would shift it.
Where the two schemes for ruling decans disagree, and they often do, the honest approach is to name both rather than quietly pick one. In this band there is nothing to pick between, so the reading rests on whichever description of Saturn you find useful. Elsewhere in the zodiac the difference is real and worth flagging.
What the date leaves for later
The Sun and its decan are the whole of what 16 May settles. The Moon travels about thirteen degrees a day and can change sign inside the date, so two Moon signs remain possible. The rising sign changes every two hours or so and could be any of the twelve.
Venus itself, the ruler of this Sun, needs the year to place and does not depend on the hour much. The Moon and the horizon need the hour badly. Between them those three are where most of the individual detail in a chart lives, which is a fair reason to treat a sun sign description as a starting point rather than a summary.
Questions people ask about this
What rules a 16 May birthday?
Venus rules Taurus, the sign, and Saturn rules the last decan, where a 16 May Sun near twenty five degrees sits. The tradition reads both together rather than choosing between them.
Is 16 May ever Gemini?
No. The Sun does not reach Gemini until around 21 May, so this date is roughly five days clear of the boundary in every year and in every time zone.
Where exactly is the Sun on this date?
Between about twenty four point seven and twenty six point one degrees of Taurus, taken at noon across 1930 to 2035. Your own figure depends on your year, hour and birthplace.
Do both decan schemes agree here?
They do. The Chaldean order gives the last third of Taurus to Saturn, and the triplicity scheme reaches Capricorn for the same band, which returns Saturn as well.
Does Saturn in the decan conflict with Venus in the sign?
The tradition treats it as a combination rather than a conflict, reading Venus material held under Saturn's restraint. How it is weighted would depend on where Venus and Saturn themselves sit in the chart.
What do I need to place Venus in my own chart?
The date and year are usually enough for the sign, since Venus moves about a degree a day. The hour matters only when it is close to a boundary, and it matters for the house Venus falls in.