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	Just you, no ancestors
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	4,194,30
23	8,388,606
24	16,777,214
25	33,554,43
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!

Comments

[Cleaveland]

Or, to make it really easy, just put in a cell 2^42.

[theKiwi]

Except it's not quite that easy - the total number of ancestors is the sum of the ancestors in all of the generations, so for n generations the sum is actually 2^n - 2.

The number of ancestors in any particular generation is 2^(n-1).

In both cases you are generation 1, for your parents n = 2.

Roger

[Rootsguy]

And, if you want to find out how many generations there would have to be for a certain number of total ancestors, just take the logarithm, base 2, of (the total ancestors minus 2).

So, if I wanted to know at how many generations I had a million or more ancestors, it would be log base 2 of 999998, which yields 30.

(There are 10 kinds of people in the world, those who understanmd binary, and those who don't.)

[Paula]

This calculation presumes that every ancestor is a unique individual and it does not take into consideration any crossed lines or common ancestors.

Research done by the Population Reference Bureau estimates there have been about 106 billion births since the dawn of the human race [see http://tinyurl.com/gfxq ]

Based on this estimate from the PRB, the calculation of 4 trillion ancestors would be vastly overstated.

[genealogynut]

This chart appears to be the number of ancestors in EACH generation, not the total number of ancestors you have from today back to a certain generation.

[genealogynut]

Re: Paula's comment

I've been interested in the math of genealogy for a while now. When you start doing calculations like this, you start to understand how it is impossible *not* to be related to *everyone*.

20 generations ago is approximately the 1400s. The earth's population then was under 500,000,000 people, and you have about 1,000,000 ancestors in that generation, so that's not to difficult to see.

But look at the 40th generation. You have 1 trillion ancestors (!!!) in the 40th generation. 40 generations ago was about the year 1000. In 1000, there were about 300,000,000 people on earth. And that's only *1000 AD*!

It just goes to show, we are all cousins -- and in the not-so-distant past -- and we are cousins to ourselves millions of times over!

The DaVinci Code is about the theory that Jesus had children. If that was true, from approximately 30AD to today, imagine how many people would be descendants of Jesus!

Even without the conspiracy theories, it's a pretty safe bet to say you are a 100-something-th cousin, a few times removed from Jesus. :)

[Michael White]

Obviously, this does not account for duplicate ancestors. The human race is a hopeless mess of intermarriage, with distant cousins marrying. Even my mom and dad have three known common ancestors, the most recent of which being in the 1600s.

Obviously, 42 generations ago there were not 4 trillion people in the world. I forget the exact year, but the number of ancestors of a person living today passes the world population sometime in the late middle ages, so about 30 generations ago.

This also doesn't take into account generation shifts - what if someone marries their 2nd cousin once removed?

It recommend this site to every genealogist: http://humphrysfamilytree.com/ca.html. It is about most recent common ancestor - the most recent time in the past when a person lived who is an ancestor of everyone alive today.

[Michael White]

genealogynut: Yes, if Jesus had children, and his children had descendants for at least a few generations, it is probably reasonable to expect that he has descendants alive today. If that is the case, then it is almost certain that he is the ancestor of 99.99% of the world (all but the most isolated of aboriginal populations), and even more certain ;) that he is the ancestor of everybody in the western world. Again, see this site: http://humphrysfamilytree.com/ca.html .
Isn't the math of genealogy fascinating?

[Michael White]

A while back there was a story - http://othernews.eogn.com/2006/01/high_king_niall.html - about how Niall of the Nine Hostages of Ireland may have been the most fertile man. It claimed that as many as millions of men are descended from him, with 1 in 12 in Ireland being descended from him. But it was really just that millions of men have his Y-Chromosome - the part of DNA that is passed from father to son. If you think about it, this is astounding. There are millions of men alive today descended from him IN THE MALE LINE! With the female lines, it is certain that he is an ancestor of the entire western world. Similarly, the article claimed that Genghis Khan is the ancestor of more than 10 million men, but he is probably actually the ancestor of most of Asia and much of the West.

Geneticists should get a grasp of genealogy before they make statements like this, and the same thing goes for Mitochondrial DNA. Those four Jewish women claimed to be ancestor of most of the world's Jews? Well they are probably ancestors of most of the world.

[Michael White]

Sorry for all these double-posts, but I thought of something to add.

Geneticists attempt to trace ancestry using only small parts of a person's genome, usually the Y-Chromosome or Mitochondrial DNA, but sometimes specific genes. The problem with this method is that you can be descended from someone without inheriting their DNA on a specific spot on the genome (in fact it the likeliness of this increases as you go back further generations). Therefore, any genetic study of common ancestry would push the most recent common ancestor back, as the author of the site I mentioned says.

[Chris Z]

The scientist and author Guy Murchie theorized that everyone on the planet is related with the greatest number of generations being no more than 52nd cousin. So as I research, I'm looking to find all of my 52nd cousins (grin)

[wundercapo]

So, I didn't read the whole of the websites about common ancestry, but I'm fairly sure that some of the statements made in that page and posts above cannot be true. First, that anyone alive in 700AD was either the ancestor of no one or all? I think a study of history and migration patterns will show that this cannot be true. The comment directly above that everyone being 52nd cousins is also unlikely, since it puts the common ancestor even closer to the present.
I think perhaps these articles are a tad Eurocentric, which they sometimes admit, but not always. At some point, I'll read the mathematical articles, but sometimes reality does not fit mathematical models.

[Ken Mumper]

Hi,
I enjoy your newsletter, but did take offense to a word you used in the # of generations article. You refered to the human race being evolved! That is just a theory, and many of us believe that we were CREATED by God. Thank you,
Ken

[Dino (All Dino, All the Time)]

Ken,

I missed Dick's reference to evolution in his article, so I went back to find it and couldn't. Where is it?

I, too, believe that we were created by God, but I'm not sure what our original form was. I believe God created what was necessary for us to end up like we are and then set the laws of physics, biology and whatever in motion so that we could end up where we are now.

Seeing as how there was no one there at the beginning who could write down the story, and all of us genealogists know how errant word of mouth transmission of our family legends can be, I guess that we'll all just have to wait it out before we know how it all started.

[Dick Eastman]

The words "evolved" or "evolution" do not appear in the article nor is there any reference to the origins of the human race.

[Zoe]

Hello,

What about the inverse of all this - not how many ancestors does any individual have, but rather, how many living relatives does one have (approximately)?

Zoe

[Carlos]

Just a small note to Ken Mumper about evolution:

Whether he believes it or not, his body is undergoing evolution all the time, as is mine and just about every living thing. Over thousands of years these changes result in distinct traits, such as Darwin found in his observations. Those observations have been confirmed over and over.

Also, the comment that evolution is "just a theory" is correct, but not in the way Ken meant it, I suspect. A scientific theory is a hypothesis that evidence and proof have shown to be correct. By this definition, Darwin's theory of evolution is the best explanation we have of man's origins. God doesn't figure in it, it's just not needed to explain it.

It's amusing that some people persist in hanging on to such a primitive, superstitious, concept to try to explain things that have already been explained by science. Witness also the flat-earth believers.