Hypergeometric Calculator: Quick & Accurate Probability Results

Our hypergeometric calculator helps you quickly determine the probability of a specific number of successes in a sequence of draws from a finite population without replacement.

Hypergeometric Probability Calculator

Use this calculator to find the hypergeometric probability based on population size, number of successes in population, sample size, and number of successes in the sample.

How to Use the Hypergeometric Calculator

Input the following information:

  • Population Size (N): The total number of items or people.
  • Successes in Population (K): The number of items labeled as ‘successes’ within the population.
  • Sample Size (n): The number of items you will randomly select from the population.
  • Successes in Sample (k): The number of items from your sample you wish to be ‘successes’.

After inputting these values, click the “Calculate” button to get the hypergeometric probability.

How the Calculator Works

The calculator uses the hypergeometric distribution formula to determine the probability. The formula is:

P(X = k) = [C(K, k) * C(N – K, n – k)] / C(N, n)

where C(n, k) is the combination of n items taken k at a time and P(X = k) is the probability of k successes in the sample.


The calculator assumes a finite population without replacement. The values for population size, successes in population, sample size, and successes in sample should be positive integers with sensible relationships (e.g., N ≥ K, n ≤ N, and k ≤ K).

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