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Binomial Distribution PMF & CDF Calculator

P(X=k) = C(n,k)·p^k·(1−p)^(n−k) — binomial probability.

Calculates the binomial probability mass function P(X = k) and cumulative distribution P(X ≤ k) from trials n, success probability p, and k.

Priya Venkatesan By Priya Venkatesan
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

P(X=k) = C(n,k) × p^k × (1−p)^(n−k)

In depth

Calculates the binomial probability mass function P(X = k) and cumulative distribution P(X ≤ k) from trials n, success probability p, and k.