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Bayesian Calculator
Bayesian CalculatorBayesian
Probabilistic Inference Intelligence
Initial prevalence (%)
True Positive Rate (%)
True Negative Rate (%)
About the Bayesian Calculator
Bayes' theorem updates a probability when new evidence arrives. It is used to interpret medical tests, spam filters and risk assessments.
How to use the Bayesian Calculator
- Enter the Prior P(A), the probability that the condition is present before testing.
- Enter the test's Sensitivity (true positive rate) and Specificity (true negative rate).
- Press Calculate to see the probability after a positive result.
Formula and method
P(A | positive) = (Sensitivity × Prior) ÷ (Sensitivity × Prior + (1 − Specificity) × (1 − Prior))
Worked example
A condition affects 1% of people. A test has 99% sensitivity and 95% specificity. After a positive result the probability of having the condition is only 16.7%, because false positives outnumber true positives when the condition is rare.
Tips
- Enter percentages as decimals if the tool asks for values between 0 and 1.
- Rare conditions produce many false positives even with accurate tests.
Frequently Asked Questions
Because the prior probability is small. Most positives come from the large healthy group.