The statement in the gemara is that the height was usually sufficient to kill the person immediately. Note that he was standing when he was pushed so that his head was at three times the height of a person (about 17 - 20 feet). This would usually be enough to break his neck. Note that even a fall of ten tefachim could be enough to kill him. Dropping the stone on him from the height would actually be less certain as he may move and it may hit him wrong.
If a fall of ten handbreadths is sufficient to kill a person, why must
the platform from which the condemned man is pushed be twice the
height of an ordinary person?
Halachically, this means that if an animal dies from a fall into a pit of this depth, then the person who dug the pit is legally responsible, because it can be a fatal drop. Having the person stand on a platform of a full height of twice the height of a man (6 amos) is used to ensure that it would be fatal in most cases.
This then means.
Therefore, even though the one being executed is likely to die from a
fall from a lesser height, a platform is built that is twice the
height of an ordinary person in order to ensure a quick and relatively
The average height of a person is about 3 amos. Thus the head of the person being executed is about 9 amos above the ground. The gemara also indicates that most times the dropping of the second stone was not required. However, if it was required, the fall was enough to ensure that the stone would be immediately fatal.
Wikipedia estimate a tefach as 3.16–3.76 in so that ten tefachim is on the order of 40 inches. It says that an amah is 6 tefachim so that 6 amos is 36 tefachim. The criminal's head at about 9 amos would be 54 tefachim. The wikipedia estimate is 18.96–22.56 in which is close to two feet, making the persons head almost 18 feet above the ground.
And then Art Scroll Sanhedrin 45a4 notes 33 and 39 explains that this is the procedure required based on the pasuk in the Torah.
33 i.e. by being pushed off a precipice.
Up to this point the Baraisa has spoken only of the penalty
to be administered to those who touched the mountain during the
revelation at Sinai. The Baraisa now teaches that the same procedures
are to be followed in every case the Torah mandates the penalty of
These notes apply to the following gemara.
The mishna teaches that one of the witnesses who had testified against
the condemned party pushes him off the platform. Concerning this
halakha the Sages taught in a baraita: From where is it derived that
the punishment of stoning can be fulfilled by pushing the condemned
party from a high place, so that he dies from his fall? The verse
states with regard to those who crossed the boundaries that were set
up around Mount Sinai and touched the mountain: “Take heed to
yourselves, that you not go up into the mountain, or touch the border
of it; whoever touches the mountain shall be put to death; no hand
shall touch him, but he shall be stoned or shall be thrown down”
(Exodus 19:12–13). And from where is it derived that this punishment
can be fulfilled with actual stoning? The verse states: “He shall be
And from where is it derived that this punishment is sometimes
fulfilled both by stoning and by pushing, i.e., if the transgressor
did not die from his fall, he is then stoned? The verse states: “He
shall be stoned or shall be thrown down.” And from where is it derived
that if the condemned man died from the pushing, the obligation to
stone him has been fulfilled, and there is no further need to actually
stone him? The verse states: “Or shall be thrown down,” with the term
“or” indicating that only one of the two options must be fulfilled.
And from where is it derived that this is the halakha not only at
Mount Sinai, but even with regard to future generations?