The doubling math
Everyone has two biological parents, each of them had two parents, and so on. So the number of ancestors in any generation is 2 raised to the number of generations back: 2n. Your parents are generation 1 (2 people), your grandparents generation 2 (4), your great-grandparents generation 3 (8).
To get everyone up to a given generation, add the generations together. The total always comes out as 2n+1 − 2: ten generations back means 1,024 ancestors in that generation and 2,046 altogether. The numbers grow fast. Twenty generations back, around the 1400s for most people alive today, there are over a million places in your family tree. Thirty generations gives more than a billion.
Names for each generation of grandparents
After great-great-grandparents, genealogists usually number the greats rather than repeating them. Your 3rd great-grandparent is the same as a great-great-great-grandparent.
| Generation | Relationship | Ancestors | Running total |
|---|---|---|---|
| 1 | Parents | 2 | 2 |
| 2 | Grandparents | 4 | 6 |
| 3 | Great-grandparents | 8 | 14 |
| 4 | Great-great-grandparents | 16 | 30 |
| 5 | 3rd great-grandparents | 32 | 62 |
| 6 | 4th great-grandparents | 64 | 126 |
| 7 | 5th great-grandparents | 128 | 254 |
| 8 | 6th great-grandparents | 256 | 510 |
| 9 | 7th great-grandparents | 512 | 1,022 |
| 10 | 8th great-grandparents | 1,024 | 2,046 |
| 11 | 9th great-grandparents | 2,048 | 4,094 |
| 12 | 10th great-grandparents | 4,096 | 8,190 |
Pedigree collapse: why the numbers stop making sense
Keep doubling and you soon need more ancestors than there were people. For someone born around 1990, the 2n count passes the estimated world population roughly 30 generations back, in the 1100s. The explanation is pedigree collapse: the same person can occupy more than one place in your family tree.
It happens whenever two of your ancestors are related to each other. If your parents are first cousins, they share a pair of grandparents, so you have 6 different great-grandparents instead of 8. If they are second cousins, you have 14 different great-great-grandparents instead of 16. Each marriage between relatives, however distant, removes people from the top of the tree.
For most of history, people married within a day’s walk of where they were born. In a village of a few hundred people, couples several generations on were very often distant cousins without knowing it. Island populations and closed religious communities show the effect strongly. Royal families show it most clearly of all: Charles II of Spain, the last Habsburg king of Spain, was the son of an uncle and niece, from a family that had married cousins for generations, and his tree contains far fewer people than it has places.
Scaled up, this means everyone’s family trees merge. A 2013 genetic study by Peter Ralph and Graham Coop found that any two people of European descent share many ancestors from roughly the last thousand years. A 2004 modeling study in Nature by Douglas Rohde, Steve Olson and Joseph Chang estimated that the most recent common ancestor of everyone alive today may have lived only a few thousand years ago.
The world population figures in the calculator are rounded estimates from long-run historical reconstructions such as the HYDE database and UN figures, as compiled by Our World in Data. Treat them as approximate; estimates for the distant past vary widely.
How many ancestors are in a typical family tree?
Far fewer than the math allows. A standard four-generation pedigree chart, back to your great-grandparents, has places for 14 ancestors, and a five-generation chart has 30. Filling in all 30 names is a realistic goal for most families with some research, and a good place to start is a pedigree chart, which numbers each ancestor in the standard Ahnentafel order.
Beyond that, most trees thin out quickly. Some lines run back for centuries; others stop at a great-grandparent nobody can trace. When you want aunts, uncles, cousins and remarriages as well as direct ancestors, build a full tree with the family tree maker.
How far back can records take you?
- United States: the federal census began in 1790, but it named only the head of each household until 1850, when every free person was listed by name. Enslaved people were counted without names in 1850 and 1860, which makes African American research before 1870 depend on other records.
- England and Wales: civil registration of births, marriages and deaths began on 1 July 1837. Before that, church parish registers, required from 1538, record baptisms, marriages and burials.
- Scotland began civil registration in 1855 and Ireland in 1864 (1845 for non-Catholic marriages).
With good records, many family lines can be traced to the 1700s, around 8 to 10 generations back. Earlier than that usually depends on property, wills and court records, which mostly exist for people who owned land. Families who can follow a line into the Middle Ages almost always do so through a link to the gentry or nobility, whose records survived.
DNA and your ancestors
You inherit about half of your autosomal DNA from each parent, and on average about a quarter from each grandparent. The real share from a grandparent varies, because DNA is passed on in large chunks and recombination shuffles them differently each time. On average you carry about 3% of your DNA from each 3rd great-grandparent (5 generations back), but the actual figure can be noticeably higher or lower.
Because the chunks are finite, the number of your genetic ancestors grows much more slowly than the number of your genealogical ancestors. Somewhere around seven generations back, some of your ancestors begin to have left no detectable DNA in you, and by ten generations a large share of your 1,024 ancestors have not. They are still your ancestors; a DNA test just cannot see them. Y-DNA tests follow only your father’s father’s line, and mitochondrial DNA tests only your mother’s mother’s line, which is one ancestor out of each generation.