It is generally accepted that Abraham lived 175 years. However, the dates when he lived are rather fuzzy and hotly debated.
When was he alive and what reasons would you give for your conclusion?
What methods have gone into determining the dates in which Abraham (and perhaps other early biblical figures) lived and died?
The best way to find this estimate is to take known historical dates and work backwards from there using dates and durations in the Bible.
The Mesha Stele has been dated to about 840-850 BCE, and seems to pretty clearly describe the time of Omri. If we assume it was written when the events happened, not long afterwards, we can use it to work backwards. Omri's reign began in the 31st year of Asa and lasted twelve years, which means that Asa's reign began around 870-890. Previously, Rehoboam ruled for 17 and Abijah for three. Although the transition is not entirely clear to me, the prior ruler was apparently Solomon for 40 years. In his fourth year, he started to build the temple, which was 480 years after leaving Egypt. So that takes us back 20+36+480 = 536 years further, to 1406-1426 BCE as the dates for the exodus.
Now we come to a difficult stretch because there are, to my knowledge, no clear chronological links between Moses and, say, Joseph. Moses' grandfather Kehat was with Jacob on the way into Egypt, and if you add up all the ages that's a maximum of 350 years (actually surely less, since Kehat was not an infant), but it's not clear what the minimum was. The most direct statement is Genesis 15:13, which puts four hundred years between Abraham's offspring and the exodus. Since the phrase is "in a land that is not theirs", and Ishmael and Isaac did not start off owning the land, it seems that the most harmonious interpretation is that this was 400 years from Ishmael's birth. We find that Abraham was 86 years old at the time. The 400 years probably didn't end until after wandering in the wilderness for 40 years, so that's 360 years from Ishmael's birth to the exodus.
Therefore, according to historical and Biblical evidence, Abraham was born somewhere in the range of 1852-1872 BCE and died 175 years later (1677-1697). If the 400 years are accounted for differently, these dates could change significantly.
For what it's worth, other people have studied the matter and come up with different timelines; it's complicated by the lack of accurately-dated historical evidence for events prior to David upon which to anchor the timeline.
(Beware of lots of little edits to fix up small mathematical errors and other details.)
According to the Bible, Abraham was born 2166 BC, and died 1991 BC, starting from well-established dates.
The reign of King Solomon began 971 BC. (See "Mysterious numbers of the Hebrew Kings" by Edwin Thiele.)
(You could also use 587 BC for destruction of Jerusalem by Babylonians, and the year of Ezekiel 40:1 (14th after destruction of city), together with Leviticus 25:9-10, and the Seder Olam's information that the Jubilee Year in Ezekiel 40:1 was the 17th Jubilee (with Jubilees happening every 49 years, plus 40 years in the wilderness, to get 1446 BC for the year of the Exodus. See answer to "When was David born?" for an explanation of this route.)
1 Kings 6:1 :- 971 BC - 4 = 967 BC, Solomon’s Temple began to be built
1 Kings 6:1 :- 967 + 479 = 1446 BC, Exodus
Exodus 12:40,41 :- 1446 BC + 430 = 1876 BC, Jacob enters Egypt at Passover after two failed harvests, before the third failed harvest, early 3rd year of famine in days of Joseph.
Genesis 47:9 :- 1876 BC + 130 = 2006 BC, Jacob born
Genesis 25:26 :- 2006 + 60 = 2066 BC, Isaac born
Genesis 21:5 :- 2066 + 100 = 2166 BC Abraham born
Genesis 25:7 :- 2166 – 175 = 1991 BC Abraham went to glory.
So Abraham was born 2166 BC, and died 1991 BC.
I, along with others, have done studies on the chronology of the Old Testament genealogies - which puts Abraham being born ~1950 years after Adam, and about 300 years after the flood.
Given that the earth is approximately 6000 years old, that makes Abraham's birth about 2050BC.
Dating biblical events from Creation and/or from the Christian Era depends on the positions adopted on two disputed points:
The birth of Abraham. There are two positions on the age at which Terah begot Abraham:
The position on this point affects the date from Creation of biblical events from Abraham's birth forward, and the date from the Christian Era of biblical events previous to Abraham's birth.
The sojourn in Egypt. There are two positions on the time elapsed between Jacob's entry into Egypt and the Exodus:
The position on this point affects the date from Creation of biblical events following Jacob's entry into Egypt, and the date from the Christian Era of biblical events previous to the Exodus.
Thus, each of the 4 possible combinations of the positions on these disputed points can give a different date for a biblical event, either from Creation, or from the Christian Era, or from both.
In the particular case of Abraham's birth:
the date from Creation (AM, Anno Mundi) depends on the position on his birth; and
the date from the Christian Era (BC, Before Christ) depends on the position on the sojourn in Egypt.
IMHO, a good source for an introduction to the two disputed points and links to further bibliography is:
https://creationwiki.org/Biblical_chronology_dispute
From that source, I made this table with the year of Abraham's birth in the format (AM, BC) for each combination of the positions on the disputed points, according to Thiele's chronology:
| short sojourn | long sojourn |
------------+---------------+--------------+
Early birth | (1948, 1951) | (1948, 2166) |
------------+---------------+--------------+
Late birth | (2008, 1951) | (2008, 2166) |
------------+-------------- +--------------+
Plausible adjustment of the short sojourn position
To note, 215 years is the minimum value for the time in Egypt in the short sojourn position, not the only possible value. This can be easily seen from Paul's statement in Gal 3:17 that the Law came 430 years after God's promise to Abraham and to his offspring. Now, Abraham's act of faith mentioned in Gal 3:6 and God's promise to Abraham and to his offspring mentioned in Gal 3:16 are in Gen 15:6 and 15:18 respectively. Therefore we must estimate the time elapsed between Abraham's departure from Haran (Gen 12:4-5) and the promise in Gen 15:18. If, and only if, both events happened within a few months, so that Abraham was still 75 y.o. at the time of the promise, then the time elapsed from Abraham's birth to the Exodus was:
Abraham's birth - Exodus = 75 + 430 = 505 years
Substracting from that the time elapsed from Abraham's birth to Jacob's entry into Egypt:
Abraham's age at Isaac's birth (Gen 21:5)..: 100
Isaac's age at Jacob's birth (Gen 25:26)...: 060
Jacob's age at entering Egypt (Gen 47:9)...: 130
------------------------------------------------
Abraham's birth to Jacob's entry into Egypt: 290 years
we obtain the minimum short sojourn time: 505 - 290 = 215 years.
However, the Genesis narrative of ch. 12 to 14 clearly fits better with an elapsed time of a few years between Abraham's departure from Haran and the promise in Gen 15:18. Estimating that time as 3 years, then:
Abraham's birth - Exodus = 78 + 430 = 508 years
so that the short sojourn lasted: 508 - 290 = 218 years, and
Abraham's birth = Exodus + 508 = 1446 BC + 508 = 1954 BC
The short sojourn position, both in its usual minimum version or in the adjusted version presented above, fits a literal reading of Moses' genealogy from Levi (Ex 6:16-20), noting that Levi's son Kohath had already been born when Jacob entered Egypt (Gen 46:11). Denoting Kohath's age at the entry into Egypt as KE, Kohath's age at Amram's birth as KBA and Amram's age at Moses' birth as ABM, and knowing that Moses was 80 y.o. at the time of Exodus (Ex 7:7), we have:
Entry into Egypt - Exodus = KBA + ABM - KE + 80
where Kohath's and Amram's begetting ages must be less than their respective lifetimes, and KE must be greater than zero.
KBA + ABM - KE < 133 + 137 = 270
Thus, short sojourn times can be achieved in a number of ways, such as e.g.:
For (KE = 2, KBA = 50, ABM = 90), sojourn time = 218 years [Note 1]
Further observation in the adjusted short sojourn position
If Jesus Christ was born in 7 BC, the time elapsed from Abraham's birth to Jesus's birth: 1954 - 7 = 1947, is the same as the time elapsed from Creation to Abraham's birth in the "early birth" position (1948 - 1 = 1947, as Creation is assigned year # 1 in the chronologies in the linked source.)
[Note 1] This is fully compatible with Num 3:27-28 stating that the number of male descendants of Kohath was 8600, as e.g. in this way:
Years - Age --- Age ----- Age -- Age -- Kohath's
from -- of ---- of ------ of --- of --- patrilineal
entry - Kohath Jochebed Amram Moses male descendants
0 --- 2 --- .. ---- .. --- .. --- .
30 --- 32 --- 12 ---- .. --- .. --- 3
60 --- 62 --- 42 ---- 12 --- .. --- 3 x 5 + 1 = 16
90 --- 92 --- 72 ---- 42 --- .. --- 16 x 5 = 80
120 --- 122 --- 102 ---- 72 --- .. --- 80 x 5 = 400
150 --- xxx --- 132 ---- 102 --- 12 --- 400 x 3 = 1200
180 --- xxx --- xxx ---- 132 --- 42 --- 1200 x 3 = 3600
210 --- xxx --- xxx ---- xxx --- 72 --- 3600 x 2 = 7200
