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I've had my autosomal DNA tested and the site I've used (FamilyTreeDNA) tells me that I have a "Shared centiMorgan length" of 48.08 with my closest match and the "longest block" is 28.89. FamilyTree DNA says:

Based on the extensive Family Finder database, it is rare for two genuine genealogical cousins to have a largest shared segment of less than 7 cM

but I can't find anything else that tells me how to interpret the number.

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The first thing to understand is that this is a defined unit (actually a centiMorgan, one hundredth of the original invented unit named for the geneticist T H Morgan) not something that is based on a physical standard.

Although it is talked about as though it were a measured length,the cM (also called a mapping unit) is actually a statistical notion. The idea of a "1 in a hundred year flood" is broadly similar in linking a measure of length (water depth) to the probability of its occurrence. In the case of genetics, the claim is that if you work 1 cM along a chromosome, then there is a 1% of chance of encountering a "crossover event".

The complication is that crossovers are not equally likely on all chromosomes so that not all centiMorgans contain the same number of base pairs (another way of measuring its length. That's right, not all cM are the same length.

In many ways this is the perfect feature for selling genetic genealogy information. It looks straight forward (compare your number to this range) but very few clients will have the time or the expertise to investigate its basis and to calculate the maths.

To my mind, the best (but expensive) way to use this is to get data for a range of people whose relationships you know (from traditional study) and then form an intuitive notion of how the cM data aligns with that prior knowledge. Then you can make some semi-informed extrapolations about hypothesised relationships on the basis of the cM data alone.

The Human Genome: A User's Guide may be a suitable starting point for further study.

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The ISOGG Wiki section on the centiMorgan has the definition already posted by Fortiter and includes the following:

Converting centiMorgans into percentages

In order to get an approximate percentage of shared DNA from a Family Tree DNA Family Finder test, take all of the segments above 5 cM, add them together and then divide by 68.

The way the calculation works is that your total genome in cMs with the Family Finder test is 6770 cM. A half-identical match (such as a parent/child) is 3385 cM. This number has to be doubled to represent both the maternal and paternal sides giving a total of 6770 cM. Matt Dexter explains: "The reason the number is not 6770 or 6800, but rather 68, is that it saves an additional step doing the math to convert an answer to percent. For example, 3385 / 6770 = .5 then as a second step, .5 times 100 = 50%. Using 68 to start with saves the added math step. So (3385 / 6800) * 100 is the same thing as 3385 / 68, which results in = 50%."

Their source for the Matt Dexter quote is: "Dexter Matt. Message posted on the ISOGG DNA Newbie list in a thread entitled "DNA Conference Thank You", 13 November 2013." with a link to the list, which goes to a login for Yahoo Groups.