Math

Binomial Probability Calculator

Compute exact and cumulative binomial probabilities for n, k, p.

Last validated: 2026-02-14

Binomial Probability Calculator computes exact and cumulative probabilities for repeated independent trials. It is useful for acceptance testing, quality analysis, and probability homework. The tool gives fast probability outputs for chosen n, p, and k values. Use it to compare likely and unlikely event outcomes.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Binomial Inputs

Distribution Stats

P(X = k): 0.11718750

P(X <= k): 0.17187500

Expected value: 5.0000

Variance: 2.5000

How to use this tool

Enter number of trials, success probability, and target successes.
Run the calculator for exact/cumulative probabilities.
Interpret results in the context of your threshold decision.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

N: 10
K: 3
P: 0.5
Expected value: 5.0
Variance: 2.5

Expected Outputs

N: 10
K: 3
P: 0.5
Exact probability: 0.117188

Interpretation

N is 10. Use this as a decision input, not as a standalone conclusion.
K is 3. Use this as a decision input, not as a standalone conclusion.
P is 0.5. Use this as a decision input, not as a standalone conclusion.
Interpret this value alongside sample quality and assumptions to avoid overconfidence.

Scenario Compare (A vs B)

Use this to compare two input sets and quantify change in key outputs.

Scenario A

Expected value

Variance

Scenario B

Expected value

Variance

Confidence and limitations

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

Formula References

Algebra and arithmetic identities used by the selected formula.
Standard precision arithmetic; rounding shown for readability.

Assumptions

Outputs are deterministic formula results and depend entirely on input quality and units.
Results are for planning and learning; verify with domain standards before safety-critical use.
Rounding and finite precision can introduce small differences in edge cases.

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