Post-Test Probability Calculator

After a test result, Bayes' theorem updates the probability of disease.

How the Math Works

This calculator uses Bayes' theorem to compute post-test probability, which updates the likelihood of a condition after a diagnostic test result. The formula combines disease prevalence (prior probability), test sensitivity (true positive rate), and specificity (true negative rate). Mathematically, post-test probability = (prevalence × sensitivity) / [(prevalence × sensitivity) + ((1 - prevalence) × (1 - specificity))]. This adjusts the initial probability by weighing the test's accuracy against the background rate of the condition in the population.

Practical Applications

To use the calculator, input the prevalence of the condition in your population, the test's sensitivity (ability to correctly identify those with the condition), and its specificity (ability to correctly exclude those without it). The calculator processes these values to determine the probability you truly have the condition after receiving a positive or negative test result. For example, in medical diagnosis, this helps clinicians decide whether to pursue additional testing or treatment based on the test's reliability and disease frequency in their patient population.

Day-to-Day Use

This tool empowers individuals to interpret test results more accurately in everyday scenarios, from health screenings to security checks. By factoring in how common a condition is and how dependable the test is, it prevents overreaction to false positives or complacency with false negatives. For instance, a positive HIV test result becomes more meaningful when you understand your risk profile and the test's precision, reducing unnecessary anxiety or missed diagnoses in real-world decision-making.

Worked example

5% prevalence, 95% sensitivity, 90% specificity → a positive means only ~33% chance of disease.

FAQ