Math

Binomial Probability Calculator

Find exact-count and cumulative probabilities for independent trials with a fixed success chance.

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How to use Binomial Probability Calculator

The binomial model assigns probability C(n,k) × p^k × (1−p)^(n−k) to k successes. Cumulative results sum the relevant outcomes.

Requires independent trials and constant probability. Whole counts satisfy 0 ≤ k ≤ n ≤ 1,000. Extreme tails can underflow to zero; displayed probabilities are numerical approximations.
Decimal inputs have at most 120 characters and magnitude from 1e-100 to 1e15, or zero. Floating-point results are rounded to 12 significant digits; extreme derived results may underflow or be rejected. Exact integer results are identified separately.

What calculation does Binomial Probability Calculator perform?

The binomial model assigns probability C(n,k) × p^k × (1−p)^(n−k) to k successes. Cumulative results sum the relevant outcomes.

Is p entered as a percentage?

No. Use 0.5 for 50%, 0 for an impossible success, or 1 for a certain success.

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