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Bayes' Theorem Calculator

Online Bayes' tool: infer the cause probability P(A|B) from evidence.

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P(A|B)=P(B|A)P(A)/P(B)
Likelihood
Prior
Total

📖 Tutorial | Bayes'

1. Definition
Bayes' theorem: P(A|B)=P(B|A)P(A)/P(B), with the denominator from total probability.
2. Formula & Notation
Prior, likelihoodPosterior
3. Properties & Laws
  • From effect to cause;
  • Denominator total probability;
  • Typical testing and diagnosis;
  • P(B)>0.
4. Steps
  1. Enter three probabilities;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: prevalence 1%, detection 90%, P(positive)=10.8%: ≈0.0833.
6. Common Pitfalls
Denominator is total probability;
Include the prior;
Posterior can be counterintuitive.

❓ FAQ | Bayes'

Use?
Inverse.
Denominator?
Total.
Typical?
Testing.
Conditional?
Same form.
Example?
0.0833.
Prior?
P(A).