Updated Statistics

Binomial Distribution Calculator

Compute binomial probabilities for exact outcomes, cumulative totals, upper tails, and ranges. Generate a full probability table with CSV export and view key distribution moments instantly.

PMF: P(X=k) CDF: P(X≤k) Tail: P(X≥k) Range: P(a≤X≤b) Table + CSV

Assumes n independent Bernoulli trials with constant success probability p (0 ≤ p ≤ 1). Results are mathematical probabilities, not guarantees.

Binomial Probability, Cumulative, Tail & Table

Enter trials (n) and success probability (p), then choose a mode to compute exact probability, cumulative totals, tails, ranges, or a full table.

Number of Trials (n)

Success Probability (p)

Successes (k)

Decimals

Number of Trials (n)

Success Probability (p)

k for P(X ≤ k)

Decimals

Computation Method

Number of Trials (n)

Success Probability (p)

k for P(X ≥ k)

Decimals

Computation Method

Number of Trials (n)

Success Probability (p)

Lower Bound (a)

Upper Bound (b)

Decimals

Range Type

Number of Trials (n)

Success Probability (p)

k From

k To

Include CDF Column

Decimals

Export

Max Table Rows

Binomial Distribution Calculator

Binomial Probability, Cumulative, Tail & Table

P(X = k)

Mean (μ = np)

Variance (σ² = np(1−p))

Std. Dev. (σ)

P(X ≤ k)

Mean (μ = np)

Variance (σ²)

Std. Dev. (σ)

P(X ≥ k)

P(X ≤ k−1)

Mean (μ)

Std. Dev. (σ)

Range Probability

Lower Tail (≤ a−1)

Upper Tail (≥ b+1)

Mean / Std. Dev.

Mean (μ)

Variance (σ²)

Std. Dev. (σ)

Most Likely k (Mode)

Binomial Distribution Calculator

Binomial Probability, Cumulative, Tail & Table

P(X = k)

Mean (μ = np)

Variance (σ² = np(1−p))

Std. Dev. (σ)

P(X ≤ k)

Mean (μ = np)

Variance (σ²)

Std. Dev. (σ)

P(X ≥ k)

P(X ≤ k−1)

Mean (μ)

Std. Dev. (σ)

Range Probability

Lower Tail (≤ a−1)

Upper Tail (≥ b+1)

Mean / Std. Dev.

Mean (μ)

Variance (σ²)

Std. Dev. (σ)

Most Likely k (Mode)

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