Binomial Distribution Calculator

Use our free binomial distribution calculator to find P(X=k), P(X≤k), and P(X≥k) with mean (np), variance (np(1-p)), and standard deviation.

Math

Probability Type

Number of trials (n)

Success probability (p)

Successes (k)

Formula

The binomial distribution models the number of successes in n independent Bernoulli trials with constant success probability p.

P(X=k) = C(n,k) × p^k × (1-p)^(n-k)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select exact, at-most, or at-least.
2Enter n (trials), p (probability), k (successes).
3Click Calculate.

Examples

n=10, p=0.5, k=5

1.P(X=5)=C(10,5)×0.5⁵×0.5⁵≈0.2461
2.Mean=5, Var=2.5, SD≈1.581

Result: 0.246094

n=10, p=0.5, k≤5

1.Sum P(0) through P(5)

Result: 0.623047

Frequently Asked Questions

Models number of successes in n independent trials with probability p.

C(n,k) × p^k × (1-p)^(n-k).

μ = np.

σ² = np(1-p).

Fixed n, independent trials, constant p, two outcomes.

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CalculateMe Team

Last updated: 2026-07-14

Binomial Distribution Calculator

Formula

How It Works

Examples

n=10, p=0.5, k=5

n=10, p=0.5, k≤5

Frequently Asked Questions

What is binomial distribution?

Formula for P(X=k)?

Mean?

Variance?

Requirements?

Related Calculators

Binomial Distribution Calculator

Formula

How It Works

Examples

n=10, p=0.5, k=5

n=10, p=0.5, k≤5

Frequently Asked Questions

What is binomial distribution?

Formula for P(X=k)?

Mean?

Variance?

Requirements?

Related Calculators