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Statistics

Bayes Theorem Calculator

Compute posterior probability from prior, sensitivity, and false positive rate.

Last validated: 2026-02-14

Use this free online Bayes Theorem Calculator to compute posterior probability from prior, sensitivity, and false-positive/base-rate inputs. It is useful for analysis, reporting, coursework, and experiment planning when you need quick statistical evidence without building a spreadsheet. The form focuses on Prior P(A), Likelihood P(B|A), False positive P(B|¬A) and returns Bayes Inputs, Result, 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.

Bayes Inputs

All values are percentages.

Result

Evidence P(B): 5.9000%

Posterior P(A|B): 16.1017%

How to use this tool

  1. Enter Prior P(A), Likelihood P(B|A), False positive P(B|¬A) for the bayes theorem 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 Bayes Inputs, Result 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

  • Prior a percent: 1.0
  • Likelihood b given a percent: 95.0
  • Likelihood b given not a percent: 5.0
  • Evidence b percent: 5.9
  • Posterior percent: 16.101694915254235

Expected Outputs

  • Prior a percent: 1
  • Likelihood b given a percent: 95
  • Likelihood b given not a percent: 5
  • Evidence b percent: 5.9

Interpretation

Confidence and limitations

Formula References

Assumptions

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