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Hypergeometric Calculator

Calculate exact, cumulative, and complementary hypergeometric probabilities — with a full PMF chart, distribution table, and presets for card games, quality control, and biology.

P(X=k) = C(K,k)·C(N−K,n−k) / C(N,n)  ·  Sampling without replacement

Distribution Parameters

Define the population, success states, sample size, and observed successes

Total items in the population

Items with the desired property

Number of draws (without replacement)

Number of successes to evaluate

Quick Presets

Real-world hypergeometric scenarios

Summary

P(X = k) Exact
P(X = k) exact
P(X ≤ k) CDF
P(X ≥ k) CCDF
P(X < k)
P(X > k)

Distribution Stats

Mean (μ)
Variance (σ²)
Std Dev (σ)
Mode

Parameters