DNA Relationship Probability Calculator
DNA Relationship Probability Calculator: Model-Based Shared cM Predictor
A statistical comparison of possible relationships based on shared DNA
This calculator compares which biological relationships may be consistent with the DNA data you enter. Instead of only looking up your total shared cM in a table, it uses a simplified statistical model: the number of shared segments is treated as Poisson-distributed, and segment lengths as exponentially distributed, a common approximation for identity-by-descent (IBD) segments. The expected values used by the model are derived from population-genetics theory rather than taken from any survey or lookup table. If you also enter your largest segment and segment count, the model uses them as additional evidence when comparing relationships. This can help when relationships have similar total cM, but it cannot separate them reliably. The model has not yet been formally validated against datasets of known relationships; see “Model assumptions, calibration and limitations” below for details.
Model assumptions, calibration and limitations
What the model does
For each relationship category, the calculator computes a likelihood of your input and then normalizes these likelihoods so they sum to 100%. The displayed percentages are therefore relative to the 11 categories in the model, with equal prior weight given to each. A relationship that is not in the list cannot appear in the results, and the categories are not equally common in real families.
Where the expected values come from
No survey data, lookup table or third-party dataset is used. Expected values are calculated from standard population-genetics theory:
- Expected total cM = 2 × r × G, where r is the classical coefficient of relationship (the sum of ½n over each shared-ancestor path of n meioses; Wright, 1922) and G is the approximate sex-averaged autosomal genetic length, set here to 3,500 cM. Full siblings are treated separately: they share at least one copy over about 75% of the genome, so the expected total is 0.75 × G. Parent/child is capped at G.
- Mean segment length for a relationship separated by m meioses is 100 / m cM, following the standard result that segment lengths are approximately exponential with mean 1/m Morgans (Haldane, 1919; Donnelly, 1983). For cousins of degree n, m = 2(n + 1).
- Segment count is assumed Poisson-distributed, with mean equal to expected total cM divided by mean segment length.
- Where a category groups several relationships with different m (for example grandparent, half-sibling and aunt/uncle), the likelihood of the category is the equal-weight average of its members. The equal weighting is a modeling choice, not an empirical estimate.
- The final category (“Distant Cousin”) uses an arbitrary placeholder of 10 cM chosen by this site to represent matches near typical detection limits; it is not derived from any dataset.
Other assumptions
- Total cM is evaluated with a normal approximation to the sum of the segment lengths.
- Largest segment is evaluated as the maximum of N exponential segments, using your segment count if provided.
- Total cM, segment count and largest segment are combined as if they were independent, although they are in fact correlated. This can make the result look more certain than it is.
- Because testing companies only report segments above a minimum length, observed totals for distant cousins tend to be higher, and observed segment counts lower, than these theoretical expectations. Detection thresholds, phasing errors and differences between testing companies are not modeled.
- Input checks: the largest segment cannot exceed the total, values cannot be negative, and the segment count is limited to 500.
What is not modeled
- IBD2 sharing (for example in full siblings) beyond the simple expected-coverage figure above
- Endogamy, pedigree collapse and multiple shared ancestral lines
- Sex-specific recombination differences, including on the X chromosome
- Truncation of segment lengths at a detection threshold, and caps at chromosome length
- Separate half- versus full-relationship variants beyond the combined categories listed below
Validation status
This model has not yet been systematically tested against datasets of known relationships, and no claim is made that it is more accurate than other methods, such as lookup tables or other published tools. Treat the output as one input among several.
Categories and parameters used
| Category | Theoretical mean total cM | Meioses (m) |
|---|---|---|
| Parent / Child | 3500 | 1 |
| Full Sibling | 2625 | 2 |
| Grandparent/Grandchild, Aunt/Uncle – Niece/Nephew, or Half-Sibling | 1750 | 2 (grandparent, half-sibling), 3 (aunt/uncle) |
| Half-Aunt/Uncle – Niece/Nephew, Great-Grandparent/Great-Grandchild, or First Cousin | 875 | 3 (half-aunt/uncle, great-grandparent), 4 (first cousin) |
| Half-First Cousin, First Cousin Once Removed, or Great-Great-Grandparent | 438 | 4 (half-first cousin, great-great-grandparent), 5 (first cousin once removed) |
| Second Cousin | 219 | 6 |
| Second Cousin Once Removed | 109 | 7 |
| Third Cousin | 55 | 8 |
| Third Cousin Once Removed | 27 | 9 |
| Fourth Cousin | 14 | 10 |
| Distant Cousin (5th+) or below typical detection confidence | 10 (placeholder) | 12 (fifth cousin) |
1. What the DNA Relationship Probability Calculator Helps You Do
Your cousin match list at AncestryDNA, MyHeritage, 23andMe or FamilyTreeDNA shows one main number: the amount of shared DNA in centimorgans (cM). Turning that number into a place in your family tree is rarely straightforward, because random recombination means the same amount of shared DNA can fit several relationships.
This free, client-side calculator compares your numbers against a likelihood model grounded in classical population genetics (Wright, 1922; Haldane, 1919; Donnelly, 1983). It does not use any survey or lookup table.
Key capabilities
- Multi-metric evaluation: total shared cM, largest segment and segment count.
- 11 relationship categories: from Parent/Child (1 meiosis) to Distant Cousin 5th+ (12 meioses).
- Recombination modeling: Poisson segment counts and exponential segment lengths.
- Privacy: everything runs locally in your browser. No values are sent to any server.
2. Step-by-Step Instructions
Gather the match details from your testing company’s dashboard, then follow these four steps.
Enter total shared cM (required)
Type the total centimorgans you share with the match, for example 1750 or 250.
Enter largest segment (recommended)
If your platform reports segment details, enter the length in cM of the single largest segment, for example 145.
Enter segment count (recommended)
Enter the number of matching segments, for example 24. Values up to 500 are accepted.
Select chromosome (optional)
Choose the chromosome of your largest segment. It is used only for a plausibility warning and does not change the result.
Where to find segment data: which numbers are shown (total cM, segment count, largest segment, chromosome browser) differs between AncestryDNA, MyHeritage, 23andMe, FamilyTreeDNA and GEDmatch, and the platforms change their pages from time to time. Check each platform’s current help pages. If a value is not shown, leave that field empty.
3. Understanding and Interpreting Your Results
When you click Compare Possible Relationships, the tool scores your input against all 11 categories and normalizes the scores so that they sum to 100%.
Relative probability, not certainty
Each percentage is a relative likelihood among the 11 categories, assuming equal prior weight for each. In real genealogy:
- A category at 75% is three times as consistent with the model as one at 25%. That is not the same as a 75% chance of being true.
- A high percentage does not prove a relationship, because real families do not have equal numbers of every relationship type.
- Grandparent/Grandchild, Aunt/Uncle – Niece/Nephew and Half-Sibling share the same expected total (about 1,750 cM) and are grouped in one category. Birth years, generation gaps and shared matches are needed to separate them.
How segment data refines the estimate
More, shorter segments point to more meioses (more connecting generations). Fewer, longer segments point to fewer meioses. This helps separate neighbouring categories, such as a sibling-level total from a half-sibling or grandparent total, but not relationships with identical expected sharing.
Full siblings typically share roughly 2,200–3,300 cM across many segments, including fully identical regions (IBD2) where both parental copies match. The model does not treat IBD2 separately.
4. Mathematical and Statistical Methodology
The calculator implements a theoretical likelihood model built from first principles. Nothing is fitted to or copied from a dataset.
A. Expected shared cM
For a relationship with m connecting meioses, the coefficient of relationship is r = (½)m for each shared ancestor, summed over all shared ancestors (for example two ancestors for a full aunt/uncle or full first cousin). With an approximate sex-averaged autosomal genetic length G = 3,500 cM, the expected total is:
Full sibling exception: full siblings share at least one copy over about 75% of the genome (IBD1 about 50%, IBD2 about 25%), so the expected coverage is 0.75 × 3,500 = 2,625 cM.
B. Exponential segment lengths
Following Haldane (1919) and Donnelly (1983), segment length across m meioses is approximately exponential with mean 100 / m cM:
C. Poisson segment count
The number of segments N is Poisson with mean λN = μC / L̄ = μC · m / 100:
D. Normal approximation of total cM
The total C is approximated as normal with mean μC = λN · L̄ and variance σC2 = λN · 2L̄2:
E. Largest segment
The largest segment S is treated as the maximum of Neff exponential segments (your entered count if given, otherwise the expected count):
F. Category mixture and normalization
Where a category groups several relationship types (for example Grandparent with m = 2, Aunt/Uncle with m = 3, Half-Sibling with m = 2), its likelihood is the equal-weight average of its members, computed with log-sum-exp. The final percentages are:
5. Theoretical Relationship Reference Table
These are the 11 categories in the calculator, with their theoretical mean total cM, meioses (m), expected segment count (λN) and mean segment length (L̄). Values for grouped categories are averages over the member relationships.
| Relationship category | Mean total cM (μC) | Meioses (m) | Expected segments (λN) | Mean segment (L̄) |
|---|---|---|---|---|
| Parent / Child | 3,500 cM | 1 | 35.0 | 100.0 cM |
| Full Sibling | 2,625 cM | 2 | 52.5 | 50.0 cM |
| Grandparent/Grandchild, Aunt/Uncle – Niece/Nephew, or Half-Sibling | 1,750 cM | 2–3 | 40.8 | 42.9 cM |
| Half-Aunt/Uncle – Niece/Nephew, Great-Grandparent/Great-Grandchild, or First Cousin | 875 cM | 3–4 | 29.2 | 30.0 cM |
| Half-First Cousin, First Cousin Once Removed, or Great-Great-Grandparent | 438 cM | 4–5 | 19.0 | 23.1 cM |
| Second Cousin | 219 cM | 6 | 13.1 | 16.7 cM |
| Second Cousin Once Removed | 109 cM | 7 | 7.7 | 14.3 cM |
| Third Cousin | 55 cM | 8 | 4.4 | 12.5 cM |
| Third Cousin Once Removed | 27 cM | 9 | 2.5 | 11.1 cM |
| Fourth Cousin | 14 cM | 10 | 1.4 | 10.0 cM |
| Distant Cousin (5th+) or below typical detection confidence | 10 cM (placeholder) | 12 | 1.2 | 8.3 cM |
6. Illustrative Examples
These worked examples use invented numbers to show how the model behaves. Percentages are what the calculator returns for the stated inputs.
Example 1: 1,750 cM
With total cM only, the calculator gives about 81% to the Grandparent / Aunt-Uncle / Half-Sibling category and about 14% to Full Sibling. Adding 24 segments and a 145 cM largest segment raises the first category to about 98%.
Note that the model cannot tell grandparent, aunt/uncle and half-sibling apart. They share one category, so ages, tree research and X-DNA must decide.
Example 2: 250 cM
With 14 segments and a 38 cM largest segment, the calculator gives about 95% to Second Cousin, about 4% to the Half-First Cousin / First Cousin Once Removed group, and about 1% to Second Cousin Once Removed.
Example 3: 850 cM
With 28 segments and an 85 cM largest segment, the calculator gives about 99% to the Half-Aunt/Uncle / Great-Grandparent / First Cousin category. Combined with birth-year analysis, this narrows the candidate branches, but the model alone cannot decide between those three relationship types.
7. Model Assumptions and Limitations
Mathematical models give objective theoretical predictions, but you should be aware of these limits:
- Limited IBD2 modeling: full siblings use a simple expected-coverage figure (0.75 × 3,500 = 2,625 cM). Fully identical regions are not modeled separately.
- Endogamy and pedigree collapse: inheritance through several ancestral lines inflates total cM and segment counts, so distant cousins can look closer than they are.
- Sex-specific recombination: female recombination rates are higher than male rates, so maternal transmission tends to give more and shorter segments (Bhérer et al., 2017). The model uses sex-averaged rates.
- Detection thresholds: testing companies report only segments above a minimum length, so observed totals for distant cousins tend to be higher, and observed segment counts lower, than the theoretical values.
- Correlated inputs: total cM, segment count and largest segment are treated as independent (log L = log LC + log LN + log LS) although they are correlated. Results can look more certain than they are.
- Equal priors: all 11 categories get equal prior weight. Real family structures and demographics are not considered.
- No validation yet: the model has not been tested against datasets of known relationships.
8. Frequently Asked Questions
How does a DNA relationship probability calculator work?
The calculator evaluates total shared centimorgans (cM), largest segment size and segment count against 11 theoretical relationship categories. It uses a Poisson distribution for segment counts and an exponential distribution for segment lengths to compute likelihoods, which are then normalized into relative percentages.
Why can the same amount of shared DNA mean different relationships?
Random recombination during gamete formation makes the amount of DNA passed down vary statistically. Relationships with the same average expected shared cM, such as grandparents, half-siblings and aunts/uncles, therefore overlap heavily in observed cM values.
Does adding the largest segment size and segment count make predictions more accurate?
It can help. Total shared cM sets the general genetic distance, while segment count and largest segment provide extra evidence about recombination history. This helps separate some neighbouring relationships, but not those with identical expected sharing.
Can this calculator distinguish half-siblings from grandparents or full aunts/uncles?
No. All three have an expected average of about 1,750 cM (25% shared DNA) and overlapping segment statistics, so the calculator places them in one category. Ages, family tree research and X-DNA inheritance are needed to separate them.
How does endogamy affect DNA relationship predictions?
Endogamy (repeated intermarriage within a closed community) lets people inherit DNA through several ancestral lines. This inflates total shared cM and segment counts, so distant cousins can look like closer relatives in standard models.
What is a good centimorgan threshold for a reliable DNA match?
As a rule of thumb, matches above about 20 cM are often useful for genealogy, while matches below about 10 cM are more likely to be false positives. The right cut-off depends on the testing company and on whether the match is confirmed by other evidence such as shared matches or triangulation.
9. Scientific References
- Wright, S. (1922). “Coefficients of Inbreeding and Relationship.” The American Naturalist, 56(645), 330–338. doi:10.1086/279872. Defines the coefficient of relationship.
- Haldane, J. B. S. (1919). “The Combination of Linkage Values and the Calculation of Distances between the Loci of Linked Factors.” Journal of Genetics, 8(4), 299–309. doi:10.1007/BF02983182. Origin of the exponential recombination model.
- Donnelly, P. (1983). “The Probability that Related Individuals Share Some Section of Genome Identical by Descent.” Theoretical Population Biology, 23(1), 34–63. doi:10.1016/0040-5809(83)90004-7. IBD segment length distributions.
- Bhérer, C., Campbell, C. L., & Auton, A. (2017). “Refined genetic maps reveal sexual dimorphism in human meiotic recombination at multiple scales.” Nature Communications, 8, 14994. doi:10.1038/ncomms14994. Sex-specific recombination.
- ISOGG Wiki. “Centimorgan” and “Autosomal DNA statistics.” isogg.org/wiki/Autosomal_DNA_statistics. Background definitions.
10. Next Steps on Your Genetic Voyage
Relationship probabilities are only one step in genetic genealogy. Combine them with these tools and guides:
DNA Academy - Quick Answers
How do I use a centimorgan (cM) calculator?
Simply enter the total centimorgan (cM) value you share with a match (e.g., 876 cM). Our calculator gives you an immediate probability list of relationships. For 876 cM, it might show 60% chance of grandparent, 30% of half-aunt/uncle, etc. This removes the guesswork when you see unfamiliar names in your match list.
What is a good centimorgan threshold for a reliable match?
Matches over 20 cM are generally considered genealogically useful. Matches under 10 cM are often “identical by chance” (IBC) and not from a recent ancestor. According to the ISOGG, we recommend focusing on matches > 50 cM for building your tree, as these are almost always valid. Test our calculator to see the probabilities.
What does "shared DNA segments" mean on my report?
A segment is a continuous stretch of DNA on a specific chromosome. Your total cM is the sum of all segments you share with a match. For example, you might share 120 cM spread across 4 segments (each on different chromosomes). Our calculator uses the total cM to determine relationship probabilities.
Can the calculator predict half-relationships (half-siblings, half-aunts)?
Yes! Our calculator includes half-relationships in its probability list. For example, 1,700 cM might show a 50% chance of grandparent and a 30% chance of half-sibling. The tool uses the latest Shared cM Project data to give you the most accurate probabilities, including half-aunt/uncle and half-first-cousin options. Try our calculator yourself.