Ancestors per Generation & Generation Year Calculator
How many ancestors you have at each generation (2ⁿ) and in total, roughly when they were born, how many generations back a given year is, who any ahnentafel number is (relationship, side, sex, path), when pedigree collapse sets in, and how many of those ancestors actually passed you DNA.
How it works
Ancestors at generation n = 2ⁿ; cumulative = 2ⁿ⁺¹ − 2 (plus you = 2ⁿ⁺¹ − 1); birth year ≈ your year − n × generation length; generations back to a year = (your year − that year) ÷ generation length; ahnentafel range = 2ⁿ … 2ⁿ⁺¹ − 1, generation of number A = ⌊log₂ A⌋, father = 2A, mother = 2A + 1; DNA per ancestor ≈ (½)ⁿ; ancestors expected to share DNA ≈ 2ⁿ × (1 − e^(−(22 + 33(n − 1)) ÷ 2ⁿ⁻¹)); collapse generation = ⌈log₂ population⌉
Everyone has two parents, four grandparents and eight great-grandparents, so the number of ancestral positions doubles each generation: about a thousand ten generations back, a million at twenty, and by thirty generations, around the year 1100, more positions than there were people. Pedigree collapse resolves the paradox. Distant cousins married, the same people fill many positions, and the number of distinct ancestors levels off near the size of the population your forebears married within. The calculator shows the point where 2ⁿ passes the population you enter, and a random-mating estimate of how many different people could fill the positions. Generation length turns generations into years: historically about 29 years averaged over both sexes, longer on all-male lines and shorter on all-female ones. You can also enter a year to see how many generations back it is, or enter an ahnentafel (Sosa-Stradonitz) number to see who that person is: generation, sex, which side of the family, and the father-or-mother path from you. DNA adds a twist. Recombination passes DNA down in blocks: your genome arrives as about 22 + 33 pieces per generation, so beyond seven or eight generations more of your ancestors left you no detectable DNA than did. The expected count uses Graham Coop’s block model.
Worked example
Someone born in 1990 has 1,024 ancestors at the tenth generation (8× great-grandparents), born around 1700, and 2,046 ancestors in total over those ten generations, 2,047 counting themselves. They hold ahnentafel numbers 1,024–2,047. In a region of 5 million people the count passes the population at generation 23 (about 1323), so collapse is certain before then. Of the 1,024 tenth-generation ancestors, about 475 (46%) are expected to have passed on any autosomal DNA. Going the other way, the year 1700 is (1990 − 1700) ÷ 29 = 10 generations back. Ahnentafel number 37 is 100101 in binary: after the leading 1, the digits 0-0-1-0-1 mean father, father, mother, father, mother. That makes number 37 a 3× great-grandmother on the father’s side, born around 1845.
Sources: FamilySearch — How many ancestors do I have? · Graham Coop — How many genetic ancestors do I have? · Graham Coop — How much of your genome do you inherit from a particular ancestor? · FamilySearch Wiki — Genealogy numbering systems
Frequently asked questions
How many ancestors do I have in 10 generations?
The tenth generation has 2¹⁰ = 1,024 positions, your 8× great-grandparents. Adding every generation from your parents up gives 2,046, or 2,047 counting yourself. The number of different people is usually somewhat lower, because cousin marriages put the same person in more than one position.
What generation length should I use?
Studies of historical pedigrees give about 32 years for father-to-child and 26 for mother-to-child, averaging 28–30. For a specific line use the actual birth years; for rough dating use 25 for early-marrying populations and 30–33 for later ones.
How do ahnentafel numbers work?
You are number 1. Anyone’s father is twice their number and their mother twice plus one, so your father is 2, your mother 3, your father’s parents 4 and 5, and so on. Even numbers are men, odd numbers (above 1) are women, and generation n holds numbers 2ⁿ to 2ⁿ⁺¹ − 1. Choose Ahnentafel number to see who any number is and the path from you.
Did all my ancestors pass me DNA?
No. Up to about five or six generations back you almost certainly carry DNA from every ancestor. Further back the pieces get spread too thinly: at ten generations only about 46% of your 1,024 ancestors are expected to have left you any autosomal DNA, and at fifteen generations only about 3%. They are still your ancestors; they are just invisible to a DNA test.
How can I be descended from Charlemagne?
Because of pedigree collapse: with 2⁴⁰ ancestral slots at 40 generations and only tens of millions of Europeans alive then, essentially everyone of European descent descends from every person of that era who left descendants at all.
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This calculator is for educational purposes. Double-check important results before acting on them.