Number of Ancestors in a Given Generation Back

Diana, Goddess of the Hunt — for Ancestors!

Number of Ancestors in a Given Generation

The formula for the number of ancestors in a given generation is:

x = 2ⁿ

where n is the number of generations back
and x equals the number of individuals in that generation.

Based on the chart below, if one goes back 40 generations, one has a trillion ancestors! Of course, this number doesn't mean you have a trillion unique ancestors in the 40th generation. What is happening is repetition of ancestors, that is, the same ancestors appearing over and over again in a pedigree. Repetition seldom appears within the first ten generations, but the further back one goes, the more repetition one finds.

As an example of repetition of ancestors, there is a famous pedigree that begins having significant repetition within the first few generations: that of outlaw, Jesse JAMES. There is even more pronounced repetition in his wife's pedigree, so the repetition is further compounded for their children.

Pedigrees of Jesse Woodson JAMES & Zerelda Cole MIMS

When repetition happens in the near generations, we call it "inbreeding." It happens so often among southerners, like Jesse & Zerelda, that it's become a cultural cliché, as in the movie, Deliverance.

The table below is based on an average generation time of 30 years and uses a person born in 1950 as an example.

GENERATIONS BACK (n)		NUMBER OF INDIVIDUALS (x)		BIRTH
Name of Generation	#	Decimal	Binary	Year
self	`0`	`1`	`1`	`1950`
parents	`1`	`2`	`2`	`1920`
grandparents	`2`	`4`	`4`	`1890`
great-grandparents	`3`	`8`	`8`	`1860`
2^nd great-grandparents	`4`	`16`	`16`	`1830`
3^rd great-grandparents	`5`	`32`	`32`	`1800`
4^th great-grandparents	`6`	`64`	`64`	`1770`
5^th great-grandparents	`7`	`128`	`128`	`1740`
6^th great-grandparents	`8`	`256`	`256`	`1710`
7^th great-grandparents	`9`	`512`	`512`	`1680`
8^th great-grandparents	`10`	`1024`	`1K`	`1650`
9^th great-grandparents	`11`	`2048`	`2K`	`1620`
10^th great-grandparents	`12`	`4096`	`4K`	`1590`
11^th great-grandparents	`13`	`8192`	`8K`	`1560`
12^th great-grandparents	`14`	`16,384`	`16K`	`1530`
13^th great-grandparents	`15`	`32,768`	`32K`	`1500`
14^th great-grandparents	`16`	`65,536`	`64K`	`1470`
15^th great-grandparents	`17`	`131,072`	`128K`	`1440`
16^th great-grandparents	`18`	`262,144`	`256K`	`1410`
17^th great-grandparents	`19`	`524,288`	`512K`	`1380`
18^th great-grandparents	`20`	`1,048,576`	`1M`	`1350`
19^th great-grandparents	`21`	`2,097,152`	`2M`	`1320`
20^th great-grandparents	`22`	`4,194,304`	`4M`	`1290`
21^st great-grandparents	`23`	`8,388,608`	`8M`	`1260`
22^nd great-grandparents	`24`	`16,777,216`	`16M`	`1230`
23^rd great-grandparents	`25`	`33,554,432`	`32M`	`1200`
24^th great-grandparents	`26`	`67,108,864`	`64M`	`1170`
25^th great-grandparents	`27`	`134,217,728`	`128M`	`1140`
26^th great-grandparents	`28`	`268,435,456`	`256M`	`1110`
27^th great-grandparents	`29`	`536,870,912`	`512M`	`1080`
28^th great-grandparents	`30`	`1,073,741,824`	`1G`	`1050`
29^th great-grandparents	`31`	`2,147,483,648`	`2G`	`1020`
30^th great-grandparents	`32`	`4,294,967,296`	`4G`	`980`
31^st great-grandparents	`33`	`8,589,934,592`	`8G`	`950`
32^nd great-grandparents	`34`	`17,179,869,184`	`16G`	`920`
33^rd great-grandparents	`35`	`34,359,738,368`	`32G`	`890`
34^th great-grandparents	`36`	`68,719,476,736`	`64G`	`860`
35^th great-grandparents	`37`	`137,438,953,472`	`128G`	`830`
36^th great-grandparents	`38`	`274,877,906,944`	`256G`	`800`
37^th great-grandparents	`39`	`549,755,813,888`	`512G`	`770`
38^th great-grandparents	`40`	`1,099,511,627,776`	`1T`	`740`

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