✓ Effortless Math · Free Tool

Binomial Probability Calculator

Enter the number of trials n, the number of successes k, and the success probability p to get P(X = k), the cumulative probabilities, the mean, variance, standard deviation, and full step-by-step working.

P(X = k) = C(n, k) · p^k · (1 − p)^{n − k}

Results

P(X = k)

—

P(X = k)

—

P(X ≤ k)

—

P(X ≥ k)

—

P(X < k)

—

P(X > k)

—

Mean — np

—

Variance — np(1−p)

—

Std. deviation

—

C(n, k)

—

Results

Step-by-step