How does the Hypergeometric Calculator work?

K = successes in population, N = population size, n = sample size Then: P(k) = C(K,k) × C(N-K,n-k) / C(N,n) Then: Mean = n × K/N, Variance = n × (K/N) × (N-K)/N × (N-n)/(N-1) Then: Approaches binomial as N → ∞.

Can you give an example of how to use the Hypergeometric Calculator?

Example: Input N=50, K=10, n=5 gives a result of P(X=2).

Is the Hypergeometric Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Hypergeometric Calculator?

Our Hypergeometric Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Mathematics

Hypergeometric Calculator

Hypergeometric Distribution

N (population)

K (success states)

n (sample size)

k (successes)

Analyzes hypergeometric distribution modeling sampling without replacement from finite population.

Symbol	Name	Unit	Description
P	C(K	—	C(K
C	C value	—	Variable used in the calculation
K	n × (K/N) × (N-K)/N × (N-n)/(N-1)	—	n × (K/N) × (N-K)/N × (N-n)/(N-1)
N	n × (K/N) × (N-K)/N × (N-n)/(N-1)	—	n × (K/N) × (N-K)/N × (N-n)/(N-1)

Difficulty:advanced

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Did You Know?

Lottery odds calculated using hypergeometric; exact probability of matching k numbers.

References

›Hypergeometric Distribution

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Hypergeometric Calculator

Hypergeometric Distribution

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