Binomial Distribution Calculator

Find the probability of a number of successes in a fixed number of independent yes/no trials.

What Do You Want to Find?
p is a decimal between 0 and 1.
–
Probability
Mean (np)
Standard deviation
P(X = k)
As a percent
Work

Saved Calculations

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Binomial Distribution Formulas

P(X = k) = C(n, k) × pᵏ × (1 − p)ⁿ⁻ᵏ   Mean = np   SD = √(np(1 − p))

Use it when there are a fixed number of independent trials, each with the same chance of success (coin flips, pass/fail inspections, free throws).

Worked Example

Tips

The bar chart (shown for 30 trials or fewer) gives P(X = j) for each j. Large n is handled with logarithms to avoid overflow.