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Binomial Distribution Calculator

Calculate exact, cumulative, and complementary binomial probabilities. Get mean, variance, standard deviation, and a full probability distribution chart instantly.

Distribution Parameters

Enter trials, successes, and probability of success

Number of independent trials

Target number of successes

Success probability (0 – 1)

Distribution Chart

Enter values to see chart
All k Selected k
Probability
P result
Mean (μ = np)
expected successes
Variance (σ²)
np(1−p)
Std Deviation (σ)
√variance

Binomial Distribution Formulas

PMF — Exact Probability

P(X=k) = C(n,k) · pᵏ · (1-p)ⁿ⁻ᵏ

Mean

μ = n × p

Variance

σ² = n × p × (1 − p)

Std Deviation

σ = √(np(1 − p))