How Many Ancestors Do You Have?

A newsletter reader asked a simple question this week that generates a longer answer:

How many individuals does it take to make up 42 generations? Is there a website or other source that would help me calculate the answer?

I am sure there are such web sites, but you can also calculate the same numbers within a few seconds by using Excel or any other spreadsheet. I used a spreadsheet to generate the following:

# of generations

Total ancestors

1

0

2

2

2 parents

3

6

2 parents + 4 grandparents

4

14

2 parents + 4 grandparents + 8 great-grandparents

5

30

etc.

6

62

7

126

8

254

9

510

10

1,022

11

2,046

12

4,094

13

8,190

14

16,382

15

32,766

16

65,534

17

131,070

18

262,142

19

524,286

20

1,048,574

21

2,097,150

22

4,194,302

23

8,388,606

24

16,777,214

25

33,554,430

26

67,108,862

27

134,217,726

28

268,435,454

29

536,870,910

30

1,073,741,822

31

2,147,483,646

32

4,294,967,294

33

8,589,934,590

34

17,179,869,182

35

34,359,738,366

36

68,719,476,734

37

137,438,953,470

38

274,877,906,942

39

549,755,813,886

40

1,099,511,627,774

41

2,199,023,255,550

42

4,398,046,511,102

43

8,796,093,022,206

44

17,592,186,044,414

45

35,184,372,088,830

46

70,368,744,177,662

47

140,737,488,355,326

48

281,474,976,710,654

49

562,949,953,421,310

50

1,125,899,906,842,620

In 42 generations you have more than 4 trillion ancestors!

Of course, that is far more than the total of all the people who ever lived on the face of the earth. The fact is that there are not 4 billion unique ancestors. We all have multiple lines of descent from many individuals. That is, if we were able to create a complete pedigree chart for 42 generations or more, we would see the same individuals appearing at multiple locations on the same chart.

7 Comments

This is very interesting and thanks for doing the math!
In reality, when people settle in a place and stay there for a while, they do some intermarrying and that changes the total number considerably. I can’t imagine being able to predict the number of ancestors in that situation. It does make it easier to find ancestors sometimes. Your interesting newsletter is much appreciated.

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Or, to put it simple, it’s 2^n – 2, where n is the number of generations.

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This post reminded me of the challenge to new parents to start saving a penny on the day the baby was born, then double it the next day, and continue doubling the amount from the previous day. Who can keep up with pennies or ancestors?!

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I know I am probably missing something obvious, so can someone provide a counter-example that demonstrates how a person “see the same individuals appearing at multiple locations on the same chart”?
The math is certainly correct as surely as the ultimate conclusion is impossible, so somewhere between there has to be a disconnect. What is it?
Thanks,

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My 4th Great Grandfather married his second cousin and in another line my 5th Great Grandfather married his first cousin once removed, so how many times will the names of those ancestors appear on my ancestor charts?

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Because of endogamy (marrying within a community) among my Quaker ancestors, I can trace my Gardner line to William through seven of his children, my Macy line through five of John’s children, and so on. An example of one individual appearing at multiple locations is Eunice Coleman who is my 6th great grandmother. She is also my 2nd cousin 6 times removed. Her mother is my 7th great grandmother and my 1st cousin 7 times removed!!

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“. pedigrees begin to fold in on themselves a few generations back, and become less arboreal, and more web-like. In 2013, geneticists Peter Ralph and Graham Coop showed that all Europeans are descended from exactly the same people. Basically, everyone alive in the ninth century who left descendants is the ancestor of every living European today, including Charlemagne…”

https://www.theguardian.com/science/commentisfree/2015/may/24/business-genetic-ancestry-charlemagne-adam-rutherford

And if you want to go back several hundred thosand years, every human who has ever existed has the same maternal ancestor…Mitochondrial Eve. We each have several thousand ancestors, not several million, and certainly not several billion or trillion.

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