Binomial Distribution Calculator

Calculate binomial probabilities P(X=k), P(X≤k), P(X≥k), plus mean and variance.

Total number of independent trials (e.g., 20 coin flips).
The specific number of successes you want to calculate probability for.
Probability of success on each individual trial (0 to 1).

Results

P(X = k) — Exact
P(X ≤ k) — Cumulative
P(X ≥ k)
P(X < k)
P(X > k)
Mean (μ = np)
Variance (σ² = npq)
Std Dev (σ)

Formula

P(X=k) = C(n,k) × p^k × (1-p)^(n-k)
References: Binomial distribution: P(X=k) = C(n,k)p^k(1-p)^(n-k). Mean = np. Variance = np(1-p). Uses log-space computation to avoid overflow.