What was the total population, including men, woman, and children, of the children of Israel at the time of the giving of the Torah on Mount Sinai?

We don’t know exactly, but the following rough estimate comes out to about 2,365,000: We know that the number of army aged men in that generation, ages 20-60, is 600,000 (Bamidbar 1, 45, and Bamidbar Rabba 1, 2). According to this average of 15,000 males born every year, plus the natural growth rate which increases every year, we can estimate that ages 0-20 is an additional 400,000. The life expectancy at the time was 70 but strong people lived until 80 (Tehillim 90, 10, note, this chapter was written in exactly that generation by Moshe and not David). Accordingly, if we figure that there were a little less than 15,000 males a year ages 60-70 (say 130,000), even a little less 71 year olds, a little less 72 year olds, and so forth until 80, that would add about another 160,000 men, ages 60-80. These numbers do not count the men of Levi, who we know that counting all ages, numbered 22,000 men (Bamidbar 3, 39). Accordingly, 600,000 + 400,000 + 160,000 + 22,000 = 1,182,000. For every male, we must count another female as well, which means 1,182,000 x 2= 2,364,000. [These numbers aren’t that surprising, for over 210 years in Egypt, when people married relatively young, that could easily amount to 10 generations (remember, there’s a lot of overlap). Only 70 men (+70 women) came down to Egypt (Shmot 1, 5), but the power system shows that even if 2 parents had 6 children who survived, that means that every generation triples itself. Accordingly, to figure out the logical increase of 10 generations, the computation is 3 (=triple) to the 10th power (=10 generations). If we are to use round numbers, that figures: 9; 27; 80; 240; 700; 2,000; 6,000; 18,000; 50,000 (to be exact: 59,049). If we multiply those 140 people who came down to Egypt x 59,000, we get 7,000,000- so the number mentioned in the Tanach isn’t surprising.] Rounding it out, there were between 2-2.5 million Jews who left Egypt during the Exodus and stood at Mount Sinai.