Commentary for Genesis 7:20

חמש עשרה אמה מלמעלה FIFTEEN CUBITS ABOVE —above the summits of all the mountains when once the waters reached the level of the mountains (Yoma 76a).

חמש עשרה, this number describes how much above the highest mount the keel of the ark had risen.
ויכוסו ההרים, even the tallest of the mountains were covered by at least 15 cubits of water.

Once the water reached the level... You might ask: How does Rashi know this? Perhaps it means fifteen amos above the ground! The answer is: Then the high mountains would not have been covered with water. And in the verse it is written (v. 19), “And they covered all the high mountains.” Thus Rashi explains, “Above the peaks...”

ויכוסו ההרים, “the mountains were covered (with water) hence what follows: ויגוע כל בשר “all flesh perished.” (verse 21) There was no place left to take refuge from the water.

'חמש עשרה אמה מלמעלה גברו המים וגו. This verse teaches us, using our intellect, that the ark could not have been submerged in the waters to an extent of more than six cubits. How do we arrive at this conclusion? The water level on earth has been described as at its highest level being 15 cubits above the top of the highest mountain. This level had been attained during the 7 days from the 17th day in Tishrey in which the ark ran aground on Mount Arrarat. By the first day in Tevet, the highest mountain tops became visible. It was then easy to determine the level at which the ark had been waterlogged prior to having run aground. The water leaves marks on the outside that can easily be distinguished. The inhabitants of the ark were therefore able to calculate that the speed at which the waters had been receding was one cubit for each 12 days. Having arrived at this calculation they had to count another 180 days from the 28th of Sivan the day on which the rains had ceased. They were therefore able to calculate that at its highest point the waters had been 15 cubits above the highest mountain. [There is a very minor discrepancy, a few centimeters when allowing for 2 days not included in the above count. Ed.]