Coefficient of Inbreeding Calculator

The coefficient of inbreeding calculator computes Wright's inbreeding coefficient, written F, which is the probability that the two alleles an individual carries at a randomly chosen locus are identical by descent — that is, both copies are inherited from the same ancestral gene through both the maternal and paternal lines. This single number captures how much consanguinity, or shared ancestry between an individual's parents, has reduced genetic diversity. It is one of the central quantities in population genetics, conservation breeding, and pedigree analysis.

This tool works in two ways. First, you can pick a common relationship from a menu — self-fertilization, full siblings, parent-offspring, half siblings, uncle-niece, double first cousins, first cousins, or second cousins — and the calculator returns the standard inbreeding coefficient for offspring of that mating. Second, you can switch to custom path calculation mode and supply the number of common ancestors, the inbreeding level of those ancestors, and the two path lengths through the pedigree, letting the calculator apply Wright's path-counting formula directly.

Beyond the raw F value, the coefficient of inbreeding calculator also reports the cumulative inbreeding after several generations of repeated mating, the percentage of heterozygosity lost and retained, an estimate of inbreeding depression, and the equivalent effective population size. Together these outputs translate an abstract probability into the practical genetic consequences that breeders, conservationists, and students most often need to understand.

For a known relationship the calculator uses the established inbreeding coefficient for offspring of that pairing. These are not arbitrary numbers: they come from the same path logic applied to canonical pedigrees. Self-fertilization gives F = 0.5, full siblings and parent-offspring give F = 0.25, half siblings, uncle-niece, and double first cousins give F = 0.125, first cousins give F = 0.0625, and second cousins give F = 0.015625.

In custom path calculation mode the tool applies Wright's path-counting method. For each common ancestor you trace the loop from one parent, up to the shared ancestor, and back down to the other parent. If one parent connects to the ancestor through n₁ links and the other through n₂ links, that ancestor contributes (1/2) raised to the power (n₁ + n₂ + 1), multiplied by (1 + F_A) to account for any inbreeding already present in the ancestor itself. The calculator multiplies this by the number of independent common ancestors that share the same path geometry.

The calculator then models repeated inbreeding across generations. Starting from the single-generation F, it builds up the cumulative coefficient using the recursion F_t = F_t-1 + (1 − F_t-1) × F, where F is the per-generation increment from the chosen mating. From the final cumulative value it derives the heterozygosity lost (equal to F as a percentage), the heterozygosity retained (1 − F), a simple inbreeding-depression estimate of ten percent fitness loss per unit F, and the equivalent effective population size Ne = 1 / (2F).

The headline output of the coefficient of inbreeding calculator is F, shown both as a decimal to six places and as a percentage. An F of 0 means the parents share no recent common ancestor and the offspring is fully outbred at the level being modelled. An F of 0.25, typical of full-sibling or parent-offspring matings, means there is a 25% probability that any given locus is homozygous by descent. The theoretical maximum approached by repeated self-fertilization is F = 1, complete inbreeding.

The heterozygosity lost figure equals F expressed as a percentage, because inbreeding converts heterozygous loci into homozygous ones at exactly that rate. The heterozygosity retained value, 1 − F, tells you what fraction of genetic variation within the individual is preserved. These two numbers always sum to 100% and are the most intuitive way to communicate the genetic cost of a given mating to non-specialists.

The calculator also reports an estimated inbreeding depression, computed as F × 10%, reflecting the common rule of thumb that fitness traits decline by roughly ten percent for each unit increase in F. This is a coarse estimate and the true slope varies by species and trait, but it usefully flags when a mating crosses into a range likely to harm survival, fertility, or vigour. Finally, the equivalent effective population size Ne = 1 / (2F) expresses the same inbreeding pressure in the language of population size: a high F corresponds to a small, genetically depleted breeding pool.

The inbreeding coefficient is a working tool across many fields. In animal breeding, kennel clubs, livestock registries, and laboratory animal facilities track F to avoid pairings that would push it dangerously high; a litter from full siblings (F = 0.25) carries far greater risk of recessive disease than one from unrelated parents. In plant breeding, controlled selfing deliberately raises F to fix desirable traits and create inbred lines, which are then crossed to exploit hybrid vigour.

• Pedigree management: Compare the F of candidate matings before breeding to keep cumulative inbreeding within safe limits.
• Conservation genetics: Monitor rising F in small or captive populations to detect loss of diversity and schedule outcrossing or genetic rescue.
• Human genetics and counselling: Estimate the increased risk of autosomal recessive conditions for offspring of consanguineous unions such as first cousins (F = 0.0625).
• Quantitative genetics: Use F to partition variance and predict inbreeding depression in fitness and yield traits.

By converting a pedigree relationship into a precise probability, the coefficient of inbreeding calculator lets breeders and biologists make informed, quantitative decisions rather than relying on intuition about how "closely related" two individuals are.

The path-counting method assumes you have correctly identified every common ancestor shared by the two parents and traced each loop accurately. Missing a shared ancestor, or double-counting one, will under- or over-estimate F. The standard relationship values built into the calculator assume the named relatives are themselves non-inbred and that the only shared ancestry is the one defining that relationship; real pedigrees often contain hidden additional connections that raise the true F.

The repeated-generation buildup uses a simplified recursion that applies the same per-generation increment F at each step, which is a reasonable approximation for a fixed breeding scheme but does not capture changing relationships or selection across generations. The inbreeding-depression estimate of ten percent per unit F is a generic rule of thumb; actual depression depends heavily on the species, the trait, and the population's genetic load, so treat this figure as an indicative flag rather than a precise prediction.

Finally, the equivalent effective population size Ne = 1 / (2F) is an idealised relationship that links a single mating's F to a population concept; in a real population, Ne is shaped by many factors including sex ratio, variance in reproductive success, and fluctuating numbers. Use the coefficient of inbreeding calculator for teaching, pedigree screening, and quick comparative estimates, and complement it with dedicated pedigree software and field data for research-grade conservation or breeding programmes.