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Binomial Probability Calculator

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

Last validated: 2026-02-14

Use this free online Binomial Probability Calculator to compute exact and cumulative probabilities for repeated independent trials. It is useful for analysis, reporting, coursework, and experiment planning when you need quick statistical evidence without building a spreadsheet. The form focuses on Trials (n), Successes (k), Success probability (p) and returns Binomial Inputs, Distribution Stats, so you can move from input to answer without setting up a spreadsheet or custom script. Run one realistic example, adjust the inputs, and compare how the result changes before you copy or share it. Treat the result as a statistical aid: sample quality, independence, distribution assumptions, and context still determine whether the conclusion is valid.

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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

  1. Enter Trials (n), Successes (k), Success probability (p) for the binomial probability calculator, keeping units, dates, or text format consistent with the form labels.
  2. Confirm sample size, ordering, and distribution assumptions before relying on the calculated result.
  3. Click "Run the tool" and review Binomial Inputs, Distribution Stats for the primary output.
  4. Check the statistical assumptions and sample context before using the result in a report or 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

Confidence and limitations

Formula References

Assumptions

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