# How Many Ancestors Do You Have?

NOTE: This is a repeat of an article I published 2 years ago. The subject popped up again recently so I decided to republish this article again for the benefit of those new readers of this newsletter who did not see the original article. I also made a couple of minor updates to  the original article.

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 2 parents + 4 grandparents + 8 great-grandparents + 16 great-great-grandparents 6 62 2 parents + 4 grandparents + 8 great-grandparents + 16 great-great-grandparents + 32 great-great-great-grandparents 7 126 and so on and on… 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.

This is often called “pedigree collapse.” See Wikipedia at https://en.wikipedia.org/wiki/Pedigree_collapse for more information about “pedigree collapse.”

Thanks, Dick. For those of us who are math challenged, what is the formula you used?

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The formula for the NUMBER OF ANCESTORS in any one generation is:
2n = x
where n is the number of generations back
and x equals the number of individuals in that generation.

However, I prefer to count the TOTAL NUMBER of ancestors up to and including that generation, not limiting it to only one generation. To do that, have the spreadsheet simply add all the cells above it in the “Total ancestors” column.

In other words, the 6th generation shows as 32 great-great-great-grandparents in that generation but adding together ALL GENERATIONS from generation #1 through generation #6 equals a TOTAL of 62 ancestors.

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And when would that be? If we figure 4 generations per 100 years….would 42 generations be at 970 AD/ or?

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—> And when would that be? If we figure 4 generations per 100 years….would 42 generations be at 970 AD/ or?

Yes, although that would be a VERY approximate number. In some ethnic groups, the average age of parents can be considerably higher or lower than 25 years. For instance, in French-Canadian ancestors, the mothers tend to be between 15 to 30 years of age when children are born, while the fathers tend to be about 10 years older (25 to 40 years of age). All numbers are rough approximations and vary over time, over geography, over religion, and perhaps by other factors as well.

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Interesting. A few years ago for fun, I traced (sure I did) my ancestry back to Adam and Eve. According to my genealogy program, they are my 124th great-grandparents and that is sure a lot more than 42 generations. Of course, some of that research does not have good evidence to support it. (vbg)

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So, ultimately, we’re all related to one another?

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William DeW. Horrocks February 9, 2020 at 9:39 am

You might be interested in my method for calculating the number of ancestors one has. It is described in my article “THE UNLIKELIHOOD OF ONE’S EXISTENCE” published in the Journal of the Cape Cod Genealogical Society, 8, 183-189, 2018 (Vol 8, Number 2, Fall 2018).

To address the Pedigree Collapse problem, I introduced a method which I call quantitative pruning of the binary tree. This method eliminates duplicate entries (proxy ancestors) and all ancestors of those proxies from the ever-expanding binary tree. Using this method, along with some reasonable assumptions, it is easy to show how one’s number of real ancestors in a particular earlier generation can be equal to or even less than the number of real ancestors in a more recent generation. As an example I used parameters which cause an ancestry line to remain constant at 818,341 individuals per generation beyond 28 generations, (at this point the (unpruned) binary tree has 268,435,456 nodes and the time-frame would be around 1100 CE when the population of Great Britain is estimated to have been between 1.25 and 2 million) I go on to calculate the total number of real ancestors of the subject person back 10,000 generations to when species Sapiens appeared, about 300,000 years ago. This number is 8.2 x 109 distinct individuals. This result depends, of course, on some unknown and unknowable parameters, but it gives a possibly realistic analysis of the situation. Your comments are welcome.

William DeW. Horrocks, Ph.D.

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