Binomial Distribution Calculator
Enter the number of trials n and success probability p, then choose what to calculate and enter a score or probability.
Example: Flip a fair coin 20 times — what is the probability of getting at most 8 heads? Set n = 20, p = 0.5, choose P(X ≤ x), enter x = 8, click Calculate.
The Binomial Distribution Calculator computes probabilities for the binomial distribution B(n, p), where n is the number of independent trials and p is the probability of success on each trial. X counts the number of successes.
How to use: Enter the number of trials (n) and the success probability (p), then enter either a score (number of successes) or a target probability, and click Calculate.
- P(X ≤ 𝑥) — cumulative probability: at most 𝑥 successes.
- P(X ≥ 𝑥) — upper-tail probability: at least 𝑥 successes.
- P(𝑥₁ ≤ X ≤ 𝑥₂) — probability of successes between 𝑥₁ and 𝑥₂ (inclusive).
- P(X ≤ 𝑥₁) + P(X ≥ 𝑥₂) — probability of successes outside the range 𝑥₁ to 𝑥₂.
- PMF: P(X = 𝑥) — exact probability of exactly 𝑥 successes.
- Score 𝑥 from P(X ≤ 𝑥) — find the number of successes for a given cumulative probability.
- Score 𝑥 from P(X ≥ 𝑥) — find the number of successes for a given upper-tail probability.
- Scores 𝑥₁, 𝑥₂ — find both tail scores from two probabilities.
Because the binomial is a discrete distribution, P(X < 𝑥) ≠ P(X ≤ 𝑥). Use the “≤ / ≥” toggle (visible after calculating) to switch between strict and non-strict inequalities.