How far past the line
Taking noon in each year from 1930 to 2035, the Sun on 24 July has stood between roughly three quarters of a degree and two degrees of Leo. The narrowest of those margins is about seventeen hours of solar motion, and a birth near midnight moves the position by under half a degree either way, so the answer stays Leo at every hour in every year sampled.
That is a stronger claim than a date range can make, because a range is a rounded version of an instant that moves by up to a day and a half between years. Here the instant has already passed. What remains is a small question about exactly how far past it you were born, which the widget above answers. That is a different kind of uncertainty from the one on 22 and 23 July, where the sign itself is still open.
What the first degrees of a sign are
Nothing in the tradition treats early degrees as tentative. A Sun at one degree of Leo is in Leo in the same sense as a Sun at fifteen, and the older writers who did grade degrees were concerned with other schemes entirely rather than with a fade in or fade out at the edges.
Leo is fixed fire, ruled by the Sun, which makes this one of the two signs whose ruler is also the light that defines a sun sign. Practically the low degree matters for chart geometry. It sits near a sign boundary, which is where house cusps and aspects to other early degree planets tend to cluster, and a progressed Sun starting here will spend most of a normal lifetime inside Leo.
The face and its two rulers
The first ten degrees of Leo form its opening face, and the schemes part company over it more sharply here than almost anywhere. The Chaldean order, counting the visible planets by apparent speed across all thirty six faces, arrives at Saturn. The triplicity scheme keeps the first face with its own sign and therefore with the Sun.
Saturn and the Sun are close to opposites in the older symbolism, one cold and restrictive, the other hot and expansive, and the tradition made no attempt to reconcile them. Writers who follow the Chaldean count describe these degrees as Leo with a weight on it. Writers following the triplicity scheme describe them as Leo at full strength. Both are interpretation, and the disagreement is the honest part. A source that reports only one of the two has made a choice on your behalf without telling you.
What the date cannot settle
The sign is fixed, the degree is fixed to within a degree and a half, and everything else in a chart is untouched. The Moon crosses about thirteen degrees a day and can change sign inside your birthday, so the date narrows it to two candidates at best. The ascendant turns through all twelve signs in a day and depends on latitude as well as clock time.
Give the widget above your year, your hour and your birthplace and it returns the exact solar degree along with your distance from the Cancer boundary just behind you. If anyone has ever told you that being born the day after a sign change makes you partly the previous sign, that number is the answer to it.
Questions people ask about this
Is 24 July Leo or Cancer?
Leo. Every year from 1930 to 2035 checked at noon puts the Sun past the boundary, by between about three quarters of a degree and two degrees.
Am I partly Cancer if I was born just after the change?
No. The Sun occupies one longitude at any moment and that longitude lies inside one sign. Being recently across a boundary is a position, not a blend.
Does the birth hour matter on this date?
Not for the sign. Twelve hours shifts the Sun by under half a degree, which does not reach back into Cancer in any year sampled. It matters for everything else in the chart.
Which decan is this?
The first decan of Leo, zero to ten degrees. The Chaldean order gives it to Saturn and the triplicity scheme gives it to the Sun.
Why do two schemes disagree so widely here?
Because they were built on different principles. One counts planets by speed through every face in turn, the other keeps each face within its own element. Neither was retired.
Is a low solar degree a disadvantage?
No. The tradition does not weaken a sign at its edges. A low degree affects aspects, house placement and how soon a progressed Sun changes sign, and nothing more.