Hardy-Weinberg Equilibrium Calculator
Carrier and affected rates from an allele frequency — where carriers outnumber affected people by exactly 2p/q, which is 198 to 1 at a 1% allele.
This is the Hardy-Weinberg equilibrium for a recessive condition: random mating, no selection, no migration, no new mutations, a large population. Real populations breach those assumptions to some degree, and founder effects in particular can push carrier rates far above this — treat the output as the baseline expectation rather than a measurement. Nothing is uploaded.
Carriers outnumber affected people by exactly 2p/q
2pq over q² cancels to 2p/q — nothing approximate about it. So a condition affecting 1 in 10,000 comes from an allele carried by about 1 in 51 people: a ratio of 198 to 1. And the gap widens as the allele gets rarer, reaching 1998:1 by one in a million. That is the whole reason carrier screening finds so many more people than the condition itself does.
| Allele q | Affected | Carriers | 1 in … affected | 1 in … carry | Ratio |
|---|---|---|---|---|---|
| 50.0% | 25.0% | 50.00% | 4 | 2.0 | 2:1 |
| 20.0% | 4.00% | 32.00% | 25 | 3.1 | 8:1 |
| 10.0% | 1.00% | 18.00% | 100 | 5.6 | 18:1 |
| 5.0% | 0.250% | 9.50% | 400 | 10.5 | 38:1 |
| 1.0% | 0.0100% | 1.98% | 10,000 | 50.5 | 198:1 |
| 0.1% | 0.000100% | 0.20% | 1,000,000 | 500.5 | 1998:1 |
Read backwards it is just as blunt: the allele frequency is the square root of the affected rate, so one in ten thousand affected implies an allele a hundred times commoner than that. Even at an even split the carriers still outnumber the affected, two to one.
But carriers can never be more than half the population
The heterozygote curve has a maximum, and it sits at exactly 50%, where the two alleles are equally common. Push the frequencies either way and the figure falls — symmetrically, so p = 0.4 and p = 0.6 give the same answer. However you arrange a two-allele gene, most people are not carriers of it.
| Common allele p | Carriers (2pq) |
|---|---|
| 10% | 18.00% |
| 25% | 37.50% |
| 40% | 48.00% |
| 50% | 50.00% |
| 60% | 48.00% |
| 75% | 37.50% |
| 90% | 18.00% |
The two ends of the curve are the sanity check: an allele that has vanished and an allele that has taken over both give zero carriers, because everybody is homozygous for something. The three genotype frequencies always sum to one — they are (p + q)² written out.
How to use
- Enter how many people share one case of the condition.
- Optionally enter a population to count over.
- Read the allele frequency, carrier rate and affected rate.
- Compare the carrier-to-affected ratio across the table.
Frequently asked questions
How many carriers are there for each affected person?
Exactly 2p/q, because 2pq divided by q squared cancels. At a 1% allele that is 198 carriers per affected person, and it keeps growing as the allele gets rarer — about 1,998 to 1 at one in a thousand.
How do I get the allele frequency from a prevalence?
Take the square root. A condition affecting one in 10,000 comes from an allele carried at 1%, which is a hundred times commoner than the condition itself. The square root is why rare conditions have surprisingly common alleles.
What fraction of people are carriers?
Two times p times q, where p and q are the two allele frequencies. At a 1% recessive allele that is 1.98% of people — roughly one in fifty, none of whom show any sign of it.
Can carriers ever be most of a population?
No. The 2pq curve peaks at exactly 50%, where both alleles are equally common, and falls away symmetrically in both directions. Whatever the frequencies, at least half of any population is homozygous for something.
What does Hardy-Weinberg assume?
Random mating, no selection, no migration, no new mutations and a large population. Real populations breach all of these to some degree, and founder effects in particular can push carrier rates well above the baseline this gives.
Why does carrier screening find so many more people?
Because it is looking for the 2pq group rather than the q squared one, and 2pq is enormously larger when q is small. A screening programme and a prevalence figure describe the same allele and sound like different conditions.
What do p and q actually mean?
They are the frequencies of the two alleles, and they sum to one. The three genotype frequencies are p squared, 2pq and q squared, which is (p + q) squared written out — so they always sum to one as well.
Does this send anything anywhere?
No. Every figure is computed in your browser, and nothing is uploaded or stored.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.