Statistics Calculators

Binomial Distribution Calculator

Calculate the probability of exactly k successes in n independent trials, each with the same probability of success.

P(X = k) —

P(X ≤ k) —

Mean (expected successes) —

Variance —

About the Binomial Distribution Calculator

The binomial distribution models the number of successes in a fixed number of independent trials, where each trial has the same probability of success — such as counting heads in coin flips or defective items in a batch.

Formula: P(X = k) = C(n, k) × pᵌ × (1 − p)ᵉ⁻ᵌ · Mean = np · Variance = np(1 − p)

Enter the number of trials, the probability of success on each trial, and a target number of successes to find both the exact and cumulative probability, along with the distribution's mean and variance.