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Shared cM by relationship: what the number means, with a chart of averages

Shared cM is the length of DNA two relatives inherited from the same ancestors. A chart of expected averages by relationship, and why real totals vary.

Portrait of Stefan NovakStefan Novak · · 9 min read
Shared cM by relationship: what the number means, with a chart of averages

Shared cM is the total length of the DNA segments two people both inherited from the same ancestors, measured in centimorgans (cM), a unit of distance along a chromosome. The closer the relationship, the bigger the number: on average about 3,500 cM between a parent and child, 875 between first cousins and 55 between third cousins. Those are averages, and a real pair of relatives can land far above or below them, which is why one total rarely settles a relationship on its own.

What a centimorgan measures

A centimorgan is not a count of DNA letters. It measures how likely a stretch of chromosome is to be split when it passes to the next generation. The National Human Genome Research Institute defines one centimorgan as a 1% chance that two markers on a chromosome will be separated by recombination during meiosis, the cell division that makes eggs and sperm. On average 1 cM corresponds to roughly a million base pairs, though the ratio changes along the genome. The unit is named after Thomas Hunt Morgan, the American geneticist who worked on fruit flies.

That definition is why genealogists use it. In each generation a chromosome is cut and spliced in only a few places, so DNA travels down a family in long blocks. A testing company compares two people, finds the stretches where they match closely enough to suggest a shared ancestor, and adds up the lengths of those stretches in cM. The sum is the shared cM. Long blocks point to a recent common ancestor, since there have been few generations of cutting since.

The chart: expected shared cM by relationship

Every row below comes from the code behind our cousin calculator, so you can reproduce any of them there. Each relationship works both ways: a niece is expected to share as much with her aunt as the aunt shares with her.

Relationship r Expected share Expected shared cM
Parent and child 1/2 50% 3,500
Full siblings 1/2 50% 2,625
Grandparent, aunt or uncle, half sibling 1/4 25% 1,750
First cousin, great-grandparent, great-aunt or great-uncle, half aunt or half uncle 1/8 12.5% 875
First cousin once removed, half first cousin 1/16 6.25% 438
Second cousin, first cousin twice removed, half first cousin once removed 1/32 3.13% 219
Second cousin once removed, half second cousin 1/64 1.56% 109
Third cousin, second cousin twice removed 1/128 0.78% 55
Third cousin once removed, half third cousin 1/256 0.39% 27
Fourth cousin 1/512 0.20% 14
Fifth cousin 1/2,048 0.05% 3

The second column is Sewall Wright's coefficient of relationship, r. The third restates it as a percentage of all the DNA a person carries. The fourth is the number most people search for.

How the averages are computed

Two rules produce every row.

The first is Wright's coefficient. Count how many generations each person sits below the nearest shared ancestors, and call the counts a and b. Every parent and child link on a path through a shared ancestor halves the contribution, and a couple supplies two paths, one through each partner:

full relationships: r = 2 × (1/2)^(a + b)

half relationships and direct lines: r = (1/2)^(a + b)

The path counting is set out diagram by diagram in the coefficient of relationship, worked out by hand.

The second rule converts r into length. The calculator takes one copy of the autosomes (the 22 chromosome pairs other than X and Y) as 3,500 cM, rounded. Apart from full siblings, two relatives in this chart can share at most one of their two copies at any spot, so the stretches they share are expected to cover 2r of one copy:

shared cM = 2r × 3,500

Other charts round differently. The table of expected values in the Shared cM Project report gives half siblings 1,700 cM where ours gives 1,750, so expect gaps of a few percent between charts.

Here is the calculation for second cousins, each a great-grandchild of the shared couple, so a = 3 and b = 3.

  1. r = 2 × (1/2)^6 = 2/64 = 1/32
  2. 2r = 2/32 = 1/16
  3. 3,500 / 16 = 218.75, which the chart rounds to 219 cM.
  4. As a share of everything a person carries, both copies or 7,000 cM: 218.75 / 7,000 = 3.125%, which is r again.

Step 4 clears up a common puzzle. A parent and child share "50%" and also 3,500 cM, the whole length of one copy. Both are right: the percentage counts two copies, the cM total measures length along one.

Why full siblings get 2,625 and not 3,500

Full siblings and parent and child both have r = 1/2, yet the chart gives siblings less. At any spot in the genome, each parent hands the same copy to both children with probability 1/2, independently of the other parent. So for a pair of full siblings:

  • both copies shared: 1/2 × 1/2 = 1/4 of the genome
  • exactly one copy shared: 1/2 of the genome
  • neither copy shared: 1/4 of the genome

A shared-cM total adds every stretch where at least one copy matches, which is 1/4 + 1/2 = 3/4 of the genome, and 0.75 × 3,500 = 2,625 cM. Count by copies instead and the doubly shared quarter counts twice: (2 × 1/4 + 1 × 1/2) / 2 = 1/2, and r returns. A parent and child share exactly one copy along the whole length, so their total is the full 3,500 cM with nothing shared twice.

What real relatives share

These numbers are expectations. Inheritance is a lottery played with long blocks, so real totals scatter, and Speed and Balding (2015) stress in their review that actual genome sharing can differ considerably from what a pedigree predicts. Hill and Weir (2011) showed that as relatives get more distant, the variance of their actual sharing falls but its coefficient of variation rises and the distribution grows more skewed, so the share of genome alone tells distant relationships apart less and less well.

The largest collection of real totals is the Shared cM Project, run by the genetic genealogist Blaine Bettinger. Version 4.0, released in March 2020, drew on 59,714 submissions made between March 2015 and July 2019 by testers who knew how they were related to a match. Bettinger analyzed 48 relationships and trimmed 1% of the submissions for each one, half from each end of the range.

For close kin, the averages sit near the calculator's: 3,485 cM for parent and child, 2,613 for full siblings, 866 for first cousins and 229 for second cousins. The ranges carry the real lesson. Full siblings ran from 1,613 to 3,488 cM, first cousins from 396 to 1,397, and second cousins from 41 to 592, a fourteenfold spread. Even parents and children, who share one full copy by definition, were reported anywhere from 2,376 to 3,720 cM, so part of the scatter comes from testing and reporting rather than inheritance.

Three relationships with the same expected 1,750 cM make a neat comparison. Grandparent and grandchild averaged 1,754 cM, half siblings 1,759 and aunt or uncle with niece or nephew 1,741, but their standard deviations were 236, 207 and 180 cM. Equal r does not mean an equal spread, which is the point Hill and Weir made with their formulas.

Why distant cousins seem to share more than the chart says

From third cousins outward, the project's averages climb above the calculator's: 73 cM against 55 for third cousins, 35 against 14 for fourth cousins. Bettinger's own notes on the data account for most of the gap.

  1. Zeros are left out. Where some pairs share nothing detectable, the project averaged only the pairs sharing more than 0 cM. The calculator's figure is an average over everyone, zeros included.
  2. Matching thresholds. Each company sets its own minimum for reporting a match, and Bettinger notes that this can affect totals, especially for distant relationships. A pair that falls below the cut never shows up as a match, which lifts the average of the pairs that do.
  3. Endogamy and pedigree collapse. When the same ancestors sit in a tree more than once, relatives share extra DNA through the extra paths, and many testers do not know such loops exist in their families. Pedigree collapse explained shows how quickly they build up.
  4. Wrong labels. Some relationships were almost certainly entered incorrectly, through confusion over "removed" or through misattributed parentage.

Reading your own number

Running the chart backwards is harder than reading it forwards. Suppose a match shares 220 cM with you. That is the expected figure for a second cousin, a first cousin twice removed or a half first cousin once removed. The project's ranges add more candidates: first cousins once removed went as low as 102 cM, second cousins once removed as high as 353, and third cousins as high as 234. The total narrows the list; the paper trail, the ages involved and the other matches you and the match have in common have to finish the job.

Consumer tests such as AncestryDNA and 23andMe report how much DNA you share with each match in centimorgans, and both companies were among the sources testers named when they sent totals to the Shared cM Project. Bettinger's report credits Jonny Perl with an interactive version at DNA Painter, which takes a total and lists the relationships it fits. The cousin calculator works in the other direction: enter the relationship your tree suggests and it returns the average to compare with your match.

Questions

Is shared cM the same as a percentage?

No, but for every relationship in the chart except full siblings you can convert one to the other. Divide the cM total by 7,000, the two-copy length the calculator assumes: 875 cM is 12.5%. Full siblings break the rule for the reason worked out above.

Can two documented cousins share no DNA at all?

Yes, at third cousin and beyond. The Shared cM Project gives a minimum of 0 cM for every relationship more distant than half second cousins, and its averages for those relationships leave out the pairs who share nothing. A missing match is not evidence against a well-documented tree.

Does a bigger total always mean a closer relative?

On average, yes; case by case, no. The ranges overlap. A pair of first cousins at the low end of the project's range (396 cM) shares less than a pair of second cousins at the high end (592 cM).

Why might my total differ from one company to another?

Each company applies its own matching threshold, and Bettinger lists those thresholds among the reasons totals vary, especially for distant matches. Compare like with like: a total from one company against an average, not two companies' totals against each other.

Sources and further reading

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