Statistics

Binomial Distribution Calculator

Calculate probabilities and cumulative probabilities for binomial distribution

Number of Trials (n)*

Success Probability (p)*

Target Successes (k)*

P(X = k)

0.246094

P(X ≤ k)

0.623047

P(X ≥ k)

0.623047

Mean (μ)

5.0000

Expected number of successes

Standard Deviation (σ)

1.5811

Spread of the distribution

P(X = k) = C(n,k) × pᵏ × (1−p)^(n−k)
Mean μ = n × p
Variance σ² = n × p × (1−p)
Std Dev σ = √(n × p × (1−p))

Supported inputs

Input	Description
Number of Trials (n)	Total number of independent trials
Success Probability (p)	Probability of success on a single trial (0–1)
Target Successes (k)	Number of successes to compute probability for

Formula

P(X = k) = C(n,k) × pᵏ × (1−p)^(n−k)
Mean μ = n × p
Variance σ² = n × p × (1−p)
Std Dev σ = √(n × p × (1−p))

More calculators selected by category and topic.

Related Tags: