Recombination Frequency and Map Distance Calculator

Background.

This recombination frequency calculator turns the offspring counts from a genetic cross into a map distance. Enter how many offspring fell into the parental (non-recombinant) classes and how many fell into the recombinant classes, and it returns the recombination frequency together with three map distances: the uncorrected map units, the Kosambi-corrected distance, and the Haldane-corrected distance.

The basic quantity is simple. The recombination frequency is the proportion of offspring that carry a new combination of the two parental alleles, which can only have arisen from a crossover between the two loci during meiosis. A testcross yielding 892 parental and 108 recombinant offspring out of 1,000 gives a recombination frequency of 108 ÷ 1,000 = 10.8 %. NHGRI defines the unit that follows directly: one centimorgan is equal to a 1 % chance that two markers on a chromosome will become separated from one another by a recombination event during meiosis. So 10.8 % recombination is 10.8 centimorgans — 10.8 map units — of uncorrected distance.

The complication, and the reason there are three answers rather than one, is that a double crossover between two loci restores the parental arrangement and is therefore invisible. Every double crossover you fail to count makes the loci look closer together than they are, and the effect grows with distance. Mapping functions correct for this. Haldane's 1919 function assumes crossovers occur independently with no interference at all, and gives the largest correction: for our 10.8 % example it returns 12.1673 cM. Kosambi's 1944 function assumes partial interference — one crossover partly suppresses another nearby — and gives a smaller correction, 10.9728 cM. The uncorrected 10.8 cM implicitly assumes complete interference, that double crossovers never happen. The three always fall in that order, and the gap widens as loci get further apart: at 1 % recombination Haldane gives 1.0101 cM, barely a 1 % uplift, while at 40 % recombination it gives 80.47 cM, more than double the uncorrected figure.

**Two caveats belong here rather than further down.** First, the calculator refuses a recombination frequency of 50 % or more, and the refusal is the answer rather than an error: at 50 % the two loci assort independently — they are on different chromosomes, or too far apart on the same one to track together — and both mapping functions diverge to infinity. There is no finite map distance for unlinked loci, and returning a capped 50 cM would be a wrong answer that looks right. Second, the map-distance mode runs the calculation backwards, converting a distance into an expected recombination frequency, and that direction is known to be unreliable: Kivikoski, Rastas, Löytynoja and Merilä showed in 2022 that the inverse Kosambi and Haldane functions systematically underpredict real recombination frequencies, because the Kosambi interference model does not reflect the underlying biology. Use the counts direction wherever you have data.

Below the calculator you will find the derivation of both mapping functions from their published inverse forms, the reason map distances add while recombination frequencies do not, the numerical limits where the calculation is refused, and a note on why a map distance measured in one sex or one species cannot be compared with one measured in another.

What is recombination frequency calculator?

A recombination frequency is the proportion of offspring from a cross that carry a combination of alleles neither parent had, arising because a crossover occurred between the two loci during meiosis. Two loci very close together are almost never separated, so their recombination frequency is near zero; two loci far apart, or on different chromosomes, are separated half the time, so their recombination frequency reaches a ceiling of 50 % and cannot exceed it. That ceiling is the signature of independent assortment, and it is why a recombination frequency is a measure of linkage rather than of physical distance. The unit derived from it is the centimorgan, named for Thomas Hunt Morgan and equivalent to the older term 'map unit'. NHGRI's definition is direct: one centimorgan is equal to a 1 % chance that two markers on a chromosome will become separated from one another due to a recombination event during meiosis. NHGRI also notes that on average one centimorgan corresponds to roughly one million base pairs in the human genome — an average for one species, not a conversion factor, since recombination rate varies enormously along a chromosome and between species and sexes. A map distance is not the same thing as a recombination frequency, even though they are numerically equal for small values. Map distance is defined as the expected number of crossovers between two loci, and it is ADDITIVE: if A to B is 20 cM and B to C is 20 cM, then A to C is 40 cM. Recombination frequency is not additive, because a double crossover between A and C leaves the parental arrangement intact and goes uncounted. Working through this calculator: 20 cM of Haldane distance implies a recombination frequency of 16.4840 %, and 40 cM implies 27.5336 % — not the 32.97 % you would get by adding the two frequencies. The mapping functions exist precisely to convert between the additive quantity and the observable one.

How to use this calculator.

1. 01Score your cross and sort the offspring into parental and recombinant classes. In a standard two-locus testcross there are four phenotype classes: the two most common are the parental types, and the two rarest are the recombinants.
2. 02Add the two parental classes together and enter the sum, then add the two recombinant classes together and enter that. Do not enter the four classes separately — the calculator needs only the two totals.
3. 03Read the recombination frequency first, then decide which map distance to quote. Below about 10 % the three values barely differ and the uncorrected map units are fine. Above that, state which mapping function you used, because the numbers diverge.
4. 04If the recombination frequency comes out at or above 50 %, the calculator will stop and tell you the loci are unlinked. That is a real result, not a failure — it means the two loci assort independently and no map distance applies.
5. 05Do not read more precision than your cross supports. A frequency measured from 1,000 offspring has a standard error of about one percentage point, so 10.8 cM is good to about three significant figures and the Haldane value should be reported as 12.2 cM, not 12.1673129315 cM.
6. 06Treat the map-distance mode as a rough prediction rather than a measurement. Converting a distance back into an expected recombination frequency is the direction that Kivikoski and colleagues showed to be systematically biased downwards.

The formula.

The recombination fraction r is a plain proportion: recombinant offspring divided by total offspring. With 108 recombinants among 1,000 offspring, r = 0.108. Multiplying by 100 gives both the percentage and, by the NHGRI definition of the centimorgan, the uncorrected map distance of 10.8 cM.

The two mapping functions are the algebraic inverses of the forms Kivikoski and colleagues print in their 2022 paper. Haldane's function is given there as r = ½(1 − e^−2d) with d in Morgans; rearranging for d gives d = −½ ln(1 − 2r), and multiplying by 100 converts to centiMorgans, so the Haldane distance is −50 ln(1 − 2r). For r = 0.108 that is −50 × ln(0.784) = 12.1673129315 cM. Kosambi's function is given as r = ½ tanh 2d; rearranging gives d = ¼ ln((1 + 2r) ÷ (1 − 2r)), so the Kosambi distance is 25 ln((1 + 2r) ÷ (1 − 2r)). For r = 0.108 that is 25 × ln(1.216 ÷ 0.784) = 10.9728262 cM.

Why three numbers and not one? Because each encodes a different assumption about crossover interference — the tendency of one crossover to suppress another nearby. The uncorrected map unit implicitly assumes complete interference: no double crossovers ever occur, so every crossover is visible. Haldane assumes no interference at all: crossovers are a Poisson process, so a great many double crossovers are invisible and the true distance must be much larger than the observed frequency suggests. Kosambi sits between them, with interference that weakens as the interval lengthens. The ordering uncorrected ≤ Kosambi ≤ Haldane holds for every recombination frequency in the domain, and the gap widens with distance: at r = 0.01 the Haldane distance is 1.0101 cM, an uplift of just 1 %; at r = 0.108 it is 12.1673 cM, an uplift of 12.7 %; at r = 0.40 it is 80.4719 cM, an uplift of 101 %.

ADDITIVITY is the reason mapping functions exist at all. Map distance is defined as the expected number of crossovers in an interval, so it adds along a chromosome; recombination frequency does not, because a double crossover restores the parental arrangement. Two adjacent 20 cM Haldane intervals sum to 40 cM, but their recombination frequencies of 16.4840 % each do not sum to the 27.5336 % implied by the 40 cM span. Adding the frequencies would give 32.97 %, which is too high — and would keep climbing past 50 % for longer chromosomes, which is impossible.

ROUNDING STAGE — FINAL ONLY. The division, both logarithms, the exponential in the reverse direction and the ×100 unit conversions are all carried in arbitrary-precision decimal arithmetic; each returned number is rounded exactly once, to ten decimal places, on return. The verdict sentence re-renders the frequency at two decimal places from the unrounded value.

WHAT IS REFUSED, AND WHY. A recombination frequency of 50 % or more is rejected, and the message is the scientific answer: the loci are unlinked, both mapping functions diverge, and no finite map distance exists. Note that Kivikoski and colleagues print the LINEAR function as capped at r = ½ for d > 0.5, which is correct for that mapping — but the Haldane and Kosambi distance functions genuinely have a pole at r = ½, so a capped output here would be a fabrication. Negative, fractional or zero offspring counts are rejected as data-entry errors. A supplied map distance above 1,000 cM is rejected for a numerical reason stated plainly on the page: beyond that, 1 − 2r underflows the working precision and the Kosambi logarithm would divide by zero. Loci that far apart are effectively unlinked anyway.

A worked example.

Frequently asked questions.

References& sources.

1. [1]National Human Genome Research Institute (NHGRI). Talking Glossary of Genomic and Genetic Terms — 'Centimorgan (cM)'. Source for the unit definition used by this calculator: one centimorgan is equal to a 1 % chance that two markers on a chromosome will become separated from one another due to a recombination event during meiosis; and for the note that one centimorgan corresponds on average to roughly 1 million base pairs in the human genome. Independent, free, US National Institutes of Health; retrieved 2026-07-29.
2. [2]Kivikoski, M., Rastas, P., Löytynoja, A. & Merilä, J. (2022). Predicting recombination frequency from map distance. Heredity (Edinburgh) 130(3):114–121, doi:10.1038/s41437-022-00585-3. PMC9981558. Source of the printed inverse mapping functions this calculator rearranges — Haldane r = ½(1 − e^−2d) and Kosambi r = ½ tanh 2d — and of the caveat displayed beside the map-distance output: the inverse Kosambi and Haldane functions systematically underpredict recombination frequencies, because the Kosambi interference model does not reflect the underlying biology. Independent, free via PubMed Central; retrieved 2026-07-29.
3. [3]Haldane, J. B. S. (1919). The combination of linkage values and the calculation of distance between the loci of linked factors. Journal of Genetics 8:299–309. The original no-interference mapping function. Independent; print-era publication, not freely available online — cited bibliographically, with the formula itself verified against the version printed by Kivikoski et al. (2022). Checked 2026-07-29.
4. [4]Kosambi, D. D. (1944). The estimation of map distance from recombination values. Annals of Eugenics 12:172–175, doi:10.1111/j.1469-1809.1943.tb02321.x. The original interference-aware mapping function. Independent; paywalled at the publisher — cited bibliographically, with the formula verified against the version printed by Kivikoski et al. (2022). Checked 2026-07-29.
5. [5]Sturtevant, A. H. (1913). The linear arrangement of six sex-linked factors in Drosophila, as shown by their mode of association. Journal of Experimental Zoology 14(1):43–59, doi:10.1002/jez.1400140104. The first genetic map, and the origin of the idea that the percentage of crossing over between two loci can serve as a measure of the distance between them. Independent; paywalled at the publisher — cited bibliographically for the historical origin only, and no number on this page is drawn from it. Checked 2026-07-29.