Hardy-Weinberg — p² + 2pq + q² = 1
Allele frequencies p, q. Genotypes: p² (AA), 2pq (Aa), q² (aa). Carrier frequency 2pq for rare recessive.
Why This Biology Metric Matters
Why: Carrier frequency (2pq) is much higher than disease frequency (q²) for rare recessive diseases. Essential for genetic counseling.
How: From disease prevalence q², get q = √q², p = 1−q. Carrier frequency = 2pq. Cystic fibrosis 1:2500 → q², so q ≈ 0.02, 2pq ≈ 1:25.
- ●For rare diseases, 2pq ≈ 2q. Carriers far outnumber affected.
- ●Cystic fibrosis: 1:2500 affected, ~1:25 carriers (Caucasian).
- ●Assumes random mating, no selection, no migration, large population.
Hardy-Weinberg Equilibrium — Carrier Frequency Calculator
Calculate allele and carrier frequencies from disease prevalence. Essential for genetic counseling.
Disease Examples
Inputs
For educational use only. Always confirm dosages and care with a licensed veterinarian.
🧬 Biology Facts
p² + 2pq + q² = 1. p = freq(A), q = freq(a).
— Hardy-Weinberg
Carrier frequency 2pq. For rare: 2pq ≈ 2√(q²).
— Carriers
q² = disease frequency. q = √(q²). p = 1 − q.
— Allele freq
Assumes: random mating, no selection, large N.
— Assumptions
📋 Key Takeaways
- • p² + 2pq + q² = 1: Hardy-Weinberg equilibrium relates allele (p, q) and genotype frequencies.
- • Carrier frequency 2pq: For rare diseases, carriers (2pq) far outnumber affected (q²).
- • q = √(q²): Recessive allele frequency is the square root of disease frequency.
- • p = 1 - q: Dominant allele frequency completes the pair (p + q = 1).
💡 Did You Know?
Hardy and Weinberg independently derived the equilibrium in 1908.
Source: Population Genetics
For CF (1:2500), carrier frequency is ~4% — 1 in 25 people.
Source: Genetic Counseling
Carriers have one mutant allele but do not express the disease.
Source: Medical Genetics
Carrier frequencies vary by population due to founder effects.
Source: Human Genetics
2pq ≈ 2q for rare diseases when q is very small.
Source: Approximation
Two carriers mating have 25% risk of affected child.
Source: Inheritance
🔧 How It Works
Hardy-Weinberg equilibrium: (p + q)² = p² + 2pq + q². Given disease frequency q² (homozygous recessive), compute q = √(q²), then p = 1 - q. Carrier frequency = 2pq.
Step 1: Identify q² (e.g., 1:2500 = 0.0004)
Step 2: q = √(q²), p = 1 - q
Step 3: Carrier frequency = 2pq
Step 4: Verify p² + 2pq + q² = 1
🎯 Expert Tips
Population-Specific
Use ethnicity-specific prevalence when available (e.g., Tay-Sachs in Ashkenazi Jews).
X-Linked Caveat
Standard HW applies to autosomal traits. X-linked diseases (hemophilia) need different formulas.
Genetic Counseling
Always consult a certified genetic counselor for personalized risk assessment.
Input Formats
Enter as ratio (1:2500) or percentage (0.04%). Both work.
📊 Disease Comparison
| Disease | Prevalence | Carrier Frequency | Carrier Ratio |
|---|---|---|---|
| Cystic Fibrosis | 1:2500 | 3.92% | 1 in 26 |
| Sickle Cell | 1:600 | 7.83% | 1 in 13 |
| PKU | 1:15000 | 1.62% | 1 in 62 |
| Tay-Sachs | 1:3600 | 3.28% | 1 in 31 |
| Albinism | 1:10000 | 1.98% | 1 in 51 |
❓ FAQ
Why is carrier frequency higher than disease frequency?
Carriers (2pq) have one copy of the recessive allele. For rare diseases, 2pq ≈ 2q, which is ~2√(q²) — much larger than q².
Can HW be used for X-linked diseases?
Standard HW applies to autosomal traits. For X-linked (hemophilia, DMD), disease frequency in males = q; carrier frequency in females = 2pq.
What if the population deviates from HW?
Deviations indicate selection, drift, or inbreeding. For rare autosomal recessive diseases, HW often gives good approximations.
How accurate for genetic counseling?
Population-level estimates are generally accurate. Individual risk should consider family history and genetic testing. Consult a genetic counselor.
Why do carrier frequencies vary by population?
Founder effects, genetic drift, and selection (e.g., sickle cell and malaria resistance) cause variation.
What input format should I use?
Ratio (1:2500 or 1 in 2500) or percentage (0.04%). Both are supported.
📈 Key Stats
📚 Sources
- • Hardy, G.H. (1908). Mendelian proportions in a mixed population. Science.
- • Weinberg, W. (1908). Über den Nachweis der Vererbung beim Menschen.
- • ACMG/ACOG — Carrier screening guidelines
⚠️ Disclaimer
Educational only. For clinical genetic counseling and personalized risk, consult a certified genetic counselor or medical geneticist.
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