Statistics

Bayes Theorem Calculator

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

Last validated: 2026-02-14

Bayes Theorem Calculator computes posterior probability from prior, sensitivity, and false-positive/base-rate inputs. It is useful for diagnostic reasoning and risk interpretation tasks. The tool makes base-rate effects explicit in one step. Use it to avoid intuition errors in conditional probability.

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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

Enter prior probability and conditional likelihood terms.
Run calculation to get posterior probability.
Compare posterior against decision thresholds for your use case.

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

Prior a percent is 1.0. Use this as a decision input, not as a standalone conclusion.
Likelihood b given a percent is 95.0. Use this as a decision input, not as a standalone conclusion.
Likelihood b given not a percent is 5.0. 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

Prior a percent

Likelihood b given a percent

Likelihood b given not a percent

Evidence b percent

Posterior percent

Scenario B

Prior a percent

Likelihood b given a percent

Likelihood b given not a percent

Evidence b percent

Posterior percent

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.
Interpretation depends on assumptions (distribution, independence, sample quality).

Formula References

Frequentist estimation and hypothesis-test formulas used in standard textbooks.
Interpretation depends on sample quality and assumptions.

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.
Interpretation depends on assumptions (distribution, independence, sample quality).

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