Coefficient of Inbreeding (COI): What It Means, How to Calculate It, and Linebreeding Explained

The coefficient of inbreeding (COI) is the probability that an animal inherits two identical copies of a gene from a single ancestor that appears on both its sire’s side and its dam’s side of the pedigree. It is written as a percentage. When the grandparents are unrelated and not inbred, a puppy whose parents are half siblings has a COI of 12.5% and a puppy from a full brother and sister mating has 25%; a puppy whose recorded parents share no ancestors at all has 0% within that pedigree. The number is calculated from the pedigree with a formula Sewall Wright published in 1922, and it is only as good as the number of generations you feed it.

That last point is where most breeders get caught out, and it is why this guide spends as long on pedigree depth as on the math. If you want to see the idea on your own dogs, start by laying out the family tree: the free dog pedigree chart maker builds a printable three-generation pedigree with no account, and an online pedigree on Creatures goes further and calculates the COI for you from every generation you record.

Below: what COI measures, how to calculate it by hand with worked examples, how linebreeding differs from inbreeding, what a “good” COI looks like, why two calculators can disagree about the same dog, and how to check a planned pairing before you breed it. The math is identical for dogs, goats, rabbits, cattle, horses and every other species, so the examples use dogs but apply across the board.

What the coefficient of inbreeding actually measures

Every animal carries two copies of each gene, one from its sire and one from its dam. If a single ancestor sits behind both parents, there is a chance that the same copy of a gene travelled down both sides and landed in the offspring twice. Geneticists call those two copies “identical by descent”. The COI is the probability of that happening at any given gene, which also makes it the expected share of the genome where it has happened.

The Royal Kennel Club puts it plainly: the COI “calculates the probability that two copies of a gene variant have been inherited from an ancestor common to both the mother and the father” (Royal Kennel Club). A COI of 12.5% therefore means roughly a 1 in 8 chance at each gene.

Why breeders care: most harmful recessive variants do no damage in a single copy. They show up when an animal inherits two. Inbreeding raises the odds of doubling up on whatever variants the shared ancestor carried, good or bad, and across a whole population it is linked to what the University of Missouri Extension describes as poorer reproductive efficiency, higher mortality, lower growth rates and more hereditary abnormalities (Missouri Extension G2911). The Kennel Club is careful to call COI “a measure of risk, rather than a direct measure of health”: a low number does not guarantee healthy puppies and a higher one does not doom them.

How to calculate COI with Wright’s formula

The standard method, and the one Creatures uses, is Sewall Wright’s path method, first published in The American Naturalist in 1922 (Wright 1922). For an animal X with sire S and dam D:

F(X) = the sum, over every path through a common ancestor, of (1/2)^(n1 + n2 + 1) x (1 + FA)

• n1 is the number of generations from the sire up to the common ancestor.
• n2 is the number of generations from the dam up to the same common ancestor.
• FA is the common ancestor’s own COI (zero if it is not inbred).
• Each path runs from the sire up to the common ancestor and back down to the dam, and may not pass through any animal twice. Every separate path counts, and you add them all up.

This is the same formula, with the same variable definitions, that Missouri Extension uses in its guide to inbreeding in farm animals. The easiest way to understand it is to run a few examples.

Worked example 1: half sibling parents (12.5%)

Rook sires two litters with two unrelated females. You then breed a son from the first litter to a daughter from the second. The son and daughter are half siblings, and Rook is their only common ancestor.

• From the sire up to Rook: 1 generation, so n1 = 1.
• From the dam up to Rook: 1 generation, so n2 = 1.
• Rook is not inbred, so FA = 0.

F = (1/2)^(1 + 1 + 1) = (1/2)^3 = 1/8 = 12.5%.

Worked example 2: linebreeding on a grandsire (6.25%)

Now a milder, very common pattern. Rook is the sire’s sire (the puppy’s paternal grandsire), and he also appears on the dam’s side as her maternal grandsire, making him the puppy’s great-grandsire on that side.

• From the sire up to Rook: 1 generation, n1 = 1.
• From the dam up to Rook: 2 generations (dam to her mother, her mother to Rook), n2 = 2.

F = (1/2)^(1 + 2 + 1) = (1/2)^4 = 1/16 = 6.25%.

When the common ancestor is inbred himself

Suppose Rook was himself linebred, with a COI of 10%. That makes each path through him slightly stronger, because he was more likely to pass on duplicate copies in the first place. The same pedigree as example 2 becomes:

F = (1/2)^4 x (1 + 0.10) = 0.0625 x 1.10 = 6.875%.

Adding paths together: full siblings and deeper repeats

Full siblings share two common ancestors, their sire and their dam. Each gives a path worth (1/2)^3 = 12.5%, and the two add up to 25% for a full brother x sister mating when the siblings’ parents are unrelated and not inbred. A parent x offspring mating also comes out at 25% when that parent is not inbred and is unrelated to the offspring’s other parent.

Paths deep in the pedigree add up too. Go back to example 2 and suppose an older bitch, Juniper, also appears three generations behind the sire and three generations behind the dam. Her path adds (1/2)^(3 + 3 + 1) = (1/2)^7, about 0.78%, bringing the puppy’s COI to about 7.03%. Each distant repeat looks tiny, but a pedigree built around the same few kennels can carry dozens of them, which is why a deep COI is often several points higher than a three-generation one.

Quick reference, offspring COI by how the parents are related:

• Unrelated in the recorded pedigree: 0%
• Half first cousins: 3.125%
• First cousins: 6.25%
• Half siblings, uncle x niece, aunt x nephew, or grandparent x grandchild: 12.5%
• Full siblings or parent x offspring: 25%

These values assume the shared ancestors are not inbred themselves; if they are, each path is multiplied up by (1 + FA). The first cousin, half sibling and full sibling figures match the reference values given by Bannasch and colleagues in their study of inbreeding across dog breeds (Bannasch et al. 2021).

Linebreeding vs inbreeding: what is the difference?

Genetically, there is no difference in kind. Linebreeding is inbreeding, done deliberately and usually at a milder level. Missouri Extension defines linebreeding as a “generally mild form of inbreeding” that tries to keep or increase the offspring’s relationship to a specific admired ancestor. A breeder who pairs two dogs that both descend from an outstanding stud, as in example 2, is linebreeding on that stud.

The terms breeders use in practice:

• Inbreeding, in the everyday sense, means close matings: parent x offspring, full siblings, half siblings. Each produces a COI of 12.5% or 25% in a single step, or more if the family behind it was already inbred.
• Linebreeding means concentrating one or two ancestors a little further back, such as grandparents, great-grandparents and cousins, so each step adds a few percent rather than 12.5 or 25.
• Outcrossing means breeding to a mate with little or no shared ancestry in the recorded pedigree, which brings the puppies’ COI down.

The COI does not care about intent. A pedigree that repeats the same ancestor on both sides raises the number whether the breeder called it linebreeding, a line cross, or did not notice. That is the practical value of calculating it before a breeding rather than after: it shows you the relatedness you are actually creating.

Across a whole breed, the biggest driver of rising inbreeding is not one breeder’s linebreeding but the popular sire, the stud used so often that his genes turn up behind a large share of a later generation. A study of every breed registered with the UK Kennel Club from 1980 to 2014 found popular sires in all of them and concluded that popular sires are the major contributor to high rates of inbreeding (Lewis et al. 2015). The same study found the rate of inbreeding was highest in the 1980s and 1990s and tended to decline after 2000. If you are choosing a stud, a heavily used one can quietly add paths to every future litter in the breed; our guide to dog stud fees and how stud service works covers the contract side of that choice.

What is a good COI for dogs?

There is no single safe number that applies to every dog breed. Closed breeds started from different numbers of founders and have had different histories, so a COI that is low for one breed can be high for another. The practical benchmark most kennel clubs use is the breed’s own average. The Royal Kennel Club advises breeders to produce puppies with a COI “at, or below, the breed average and ideally as low as possible”, and says that where a breeder does go ahead with a higher mating and keeps puppies for breeding, they should choose a highly unrelated mate next time (Royal Kennel Club). There is one hard line: the Royal Kennel Club does not register puppies from father x daughter, mother x son or brother x sister matings, save in exceptional circumstances or for scientifically proven welfare reasons (Royal Kennel Club registration rules). Beyond those matings, its COI advice is guidance rather than a rule, and litters above the breed average can still be registered. Other registries set their own rules, so check yours.

What the research on health says, with its limits stated:

• Bannasch and colleagues estimated inbreeding from DNA in 227 breeds and compared it with insurance claims data from Sweden. Breeds with DNA-based inbreeding over 0.25 had about 29% more veterinary care events than mixed breed dogs, and breeds between 0.126 and 0.25 about 22% more. Body size mattered as well: smaller, less inbred breeds were the healthiest (Bannasch et al. 2021).
• Those are breed-level averages measured from DNA, not pedigree COIs for individual dogs. DNA-based and pedigree-based numbers are on different footings, so do not compare a figure from a genetic test directly with a pedigree COI (more on that below).

A sensible way to use the number: compare the COI of each pairing you are considering, and against your breed’s average where your kennel club publishes one, rather than chasing a universal cut-off. Then combine it with the things COI cannot tell you: health screening results, DNA tests for known inherited diseases in your breed, temperament and structure. For decisions about a specific health concern, talk to your veterinarian and your breed club’s health committee.

Why pedigree depth changes the number

A pedigree COI only counts the ancestors you have recorded. Anything behind an unknown or unrecorded ancestor is treated as unrelated, because the formula has nothing to work with. That makes depth the single biggest source of error:

• A three-generation pedigree has 14 ancestors. A five-generation pedigree has 62. Ten generations can hold 2,046 ancestor slots.
• A COI of 0% on a three-generation pedigree only means no recorded common ancestor connecting the sire and the dam was found in those generations. The parents can still share ancestors in generation six.
• A name that repeats on one side only does not make the puppy’s COI positive. If the sire’s own parents were related, the sire is inbred, but his puppies with an unrelated dam still have a COI of 0% in that pedigree, because the formula only counts ancestors that link the sire to the dam.
• Adding generations can only add paths, never remove them, so a deeper pedigree gives the same COI or a higher one, never a lower one.

The Royal Kennel Club’s own calculators use every electronically held generation rather than a fixed number, and the club warns that for imported dogs with only three-generation pedigrees the result should be used “with care”. Bannasch and colleagues note that unless the complete pedigree is included, pedigree-based COI may underestimate actual inbreeding by 5 to 10 fold.

This also explains why two tools can report different COIs for the same dog. One might stop at five generations, another at ten, a third might use every generation in its database, and each may hold different records for the older ancestors. When you compare numbers, compare them from the same source and the same depth, and always look at how many generations were complete behind the figure.

Pedigree COI vs DNA COI. Commercial canine DNA tests can estimate inbreeding directly from the genome, by measuring how much of it sits in long identical stretches. That captures ancient shared ancestry no pedigree records, so DNA-based figures for pedigree dogs usually run far higher than pedigree COIs; the average across the 227 breeds in the Bannasch study was about 0.25. It is a different measurement with a different baseline, not a contradiction. Pedigree COI remains the tool for comparing pairings before a litter exists.

The same rules hold for every species. Goat, rabbit, sheep, cattle and horse breeders use exactly the same formula and face the same depth problem, and small closed herds and rabbitries can climb quickly because the pool of unrelated mates is small. If you breed those species, the sister guides to reading a goat pedigree and what an ARBA rabbit pedigree must contain cover their registries’ paperwork, and the goat breeding guide and rabbit breeding guide cover timing once you have chosen a pair. For herds, the goat record keeping guide covers the parentage and breeding records a COI depends on.

Checking COI and a planned pairing on Creatures

Creatures does not have a separate calculator page where you type numbers in. The COI comes from the pedigree itself: record the family tree once, and the number is calculated and kept current as you add ancestors. Here is how that works, including what you can do without an account.

1. Lay out the tree, free. The dog pedigree chart maker takes registered names, registration numbers and colors for three generations and gives you a printable PDF, free and with no account. It is a quick way to spot repeated names by eye, but it does not calculate COI. There are versions for goats, rabbits, cattle, horses and cats on the pedigree chart maker page. Save the chart to a free account and you can attach it to a real profile.

2. Build the online pedigree. Add your dog and link its sire and dam. For ancestors you do not own, create reference animals so the tree can go back as far as your papers do. If you have the registration certificate or an existing pedigree as a PDF or photo, you can import it rather than typing every ancestor. The deeper you go, the more the COI means.

3. Read the COI on the Pedigree tab. Open the dog’s Pedigree tab and then Options. Creatures shows an estimated COI calculated with Wright’s method across every generation recorded, not a fixed three or five, treating unrecorded ancestors as unrelated. It labels the result so a number is not read out of context:

• Outcross under 5%, Moderate line-breeding from 5% to 12.5%, and Close breeding above 12.5%. These labels describe the size of the number, not the kind of mating, so a half-sibling pairing (exactly 12.5%) shows at the top of the moderate band even though breeders usually call it inbreeding rather than linebreeding; any further ancestor shared by both sides, or an inbred common ancestor, tips it into Close breeding. They are plain-language labels Creatures applies to every species, not health thresholds; your breed average is the better benchmark.
• If fewer than three generations are complete, Creatures says there is not enough data, or calls a low figure a shallow estimate, instead of showing a reassuring low label. A high result still shows as close breeding, because adding generations could only raise it.
• Select the COI to see the details: the method, how many generations are complete, the deepest generation, how many ancestors were used, and a reminder that deeper or private records can raise the estimate but not lower it. On a very large pedigree that is too big to analyze in full, Creatures says so and does not show a percentage.
• Use Highlight to color the repeated ancestors and trace their paths through the tree, including the ones that appear on both the sire’s and the dam’s side. Those cross-side repeats are the ones that drive the COI.

Viewers see figures based on the records they are allowed to see, so a pedigree with private ancestors can show the owner a higher COI than a visitor sees. The pedigree help article walks through the Pedigree tab and Pedigree Studio.

4. Test a pairing before you breed it. Sign in, open Pedigree Studio and choose Tasks. Hypothetical mating lets you pick a sire and a dam you have access to and shows the projected COI of their puppies, the repeated ancestors behind it, and how many generations support it. It is private, and it does not record a mating or change either pedigree, so you can try every stud on your shortlist. How are they related? compares any two animals you can access and names their closest recorded relationship, such as sharing a recorded parent or being first cousins, with the paths through each common ancestor; you can share or export the result.

5. Check other animals in the Herdbook. The public Creatures Herdbook lets anyone search public animal records without an account. Where lineage is public, a result can show a public COI along with how many complete generations and how deep the lineage goes. Read those alongside each other: “Public COI 0%” on a record with one or two complete generations means no common ancestor of the sire and dam was found in what is public, not that the animal is outbred.

6. Record the breeding you choose. Once you have picked the pair, record the breeding on the dam’s profile to get a projected due date (or estimate it now with the free dog gestation calculator), and when the litter arrives you can create puppy profiles linked to their dam. Make sure the sire is linked too, and each puppy’s COI is there from its first day on Creatures. See recording births and creating a litter. Our guide to how long dogs are pregnant picks up from there.

Frequently asked questions

What does a coefficient of inbreeding of 25% mean?

It means there is a 25% chance that both copies of any given gene came from the same ancestor. That is the figure a full brother x sister mating gives when the siblings’ own parents are unrelated and not inbred, and the figure a parent x offspring mating gives when that parent is not inbred and is unrelated to the offspring’s other parent. If the ancestors behind the mating are themselves inbred, the same kind of mating gives a higher COI, and repeated close matings push it higher still.

Is linebreeding the same as inbreeding?

Linebreeding is a milder, deliberate form of inbreeding aimed at keeping a particular ancestor’s influence in the pedigree. The COI treats them the same way: every repeated ancestor on both sides adds to the number regardless of what the breeding is called.

How many generations should a COI use?

As many as you can reliably record. The Royal Kennel Club’s calculators use every generation in its database, and a three-generation COI can badly understate inbreeding. At minimum, always check how many generations are complete behind any COI you are given.

Is there a free inbreeding coefficient calculator?

You can calculate COI by hand with Wright’s formula, as in the examples above. On Creatures, the COI is calculated automatically from the online pedigree once you add your dog and its ancestors; a free account saves the profiles, and the hypothetical mating check requires signing in.

Why do two COI calculators give different numbers for the same dog?

Usually because they use different numbers of generations or hold different records for the older ancestors. A calculator that goes back further will find more common ancestors and give a higher number. Compare figures from the same source and depth.

Does a low COI mean the puppies will be healthy?

No. COI measures the average risk of inheriting duplicate gene copies, not whether a particular harmful variant is present. Two carriers of the same recessive disease can produce affected puppies at any COI, which is why health screening and DNA tests for known conditions in your breed matter alongside it. Your veterinarian and breed club can tell you which tests apply.

Do this next on Creatures

If you are weighing up a pairing, or starting to track your dogs’ lines, these are the useful next steps in the order most breeders take them.