Answer
The Bible does not tell us exactly how long Noah and his family were on the ark. However, the text of Genesis does provide us with sufficient information to arrive at a fairly good estimate for this time period. Working with the data we have, Noah was probably on the ark for (approximately) one full calendar year. The math works out to about 370 days.
We get a rough estimate by comparing Noah’s age when he entered the ark with his age when he left the ark: he was 600 years old when he entered the ark, and 601 years old when he exited the ark. In addition, Moses gives some specific time markers for various events in conjunction with the flood:
Genesis 7:6 says that Noah was 600 years old when the floodwaters began. That fact is confirmed in Genesis 7:11–13, which adds even more detail:
In the six hundredth year of Noah’s life, on the seventeenth day of the second month—on that day all the springs of the great deep burst forth, and the floodgates of the heavens were opened. And rain fell on the earth forty days and forty nights. On that very day Noah and his sons, Shem, Ham and Japheth, together with his wife and the wives of his three sons, entered the ark.
The flood waters receded enough for the ark to run aground on Mt. Ararat on the seventeenth day of the seventh month (Genesis 8:3–4), and the mountain tops became visible above the water on first day of the tenth month (Genesis 8:5). After that, Noah waited forty days and then began to send out birds to see if the earth could sustain life. That process took another three weeks (Genesis 8:7–12).Noah had turned 601 years old by the time the earth was dry (Genesis 8:13). After observing dry ground, he exited the ark the next month. Again, Scripture gives some precise detail in Genesis 8:13–18:
By the first day of the first month of Noah’s six hundred and first year, the water had dried up from the earth. Noah then removed the covering from the ark and saw that the surface of the ground was dry. By the twenty-seventh day of the second month the earth was completely dry. Then God said to Noah, “Come out of the ark, you and your wife and your sons and their wives. . . .” So Noah came out.
So, Noah entered the ark on Month 2, Day 17, of one year and exited the ark on Month 2, Day 27 of the next year. That’s a total of one year and ten days from Genesis 7:11 to 8:18. Assuming a lunar calendar of about 360 days, Noah would have been on the ark for approximately 370 days. Clearly, since we must make certain assumptions to arrive at this number, we should not treat this number as totally certain. However, one full calendar year seems like a reasonable estimate of the time Noah and his family spent on the ark, based on the information that we have.