Calculate post-test probability using Bayes' theorem—essential for medical diagnosis and risk assessment.
Last updated: March 2026
True positive rate
True negative rate
Post-test probability is the probability that a patient has a disease after receiving a test result. It updates the pre-test probability (prevalence or clinical suspicion) based on the test's performance characteristics (sensitivity and specificity) using Bayes' theorem.
This calculation is fundamental in medical decision-making. A positive test doesn't guarantee disease, and a negative test doesn't guarantee absence of disease. The post-test probability quantifies the actual risk, accounting for both the test's accuracy and how common the condition is in the population.
The calculation uses likelihood ratios, which indicate how much a test result changes the odds of disease. LR+ shows how much a positive test increases disease probability, while LR− shows how much a negative test decreases it. Tests with LR+ > 10 or LR− < 0.1 are considered highly informative.
A patient tests positive for COVID-19:
Tests aren't perfect. False positives occur, especially when disease prevalence is low. A positive test increases your probability, but the actual chance depends on sensitivity, specificity, and how common the disease is in your population.
LR+ > 10 or LR− < 0.1 are considered strong evidence. LR+ between 5-10 or LR− between 0.1-0.2 are moderate. LR+ between 1-5 or LR− between 0.2-1 provide weak evidence. LR = 1 means the test is useless.
Use prevalence (population rate) when you have no other information. Use higher pre-test probability if the patient has symptoms or risk factors. Clinical judgment can adjust the pre-test probability above or below population prevalence.
Likelihood ratios combine sensitivity and specificity into a single number that directly indicates how much the test changes disease probability. They work regardless of prevalence and can be easily chained for multiple tests.
Yes! Simply select the test result (Positive or Negative). The calculator automatically uses the appropriate likelihood ratio (LR+ for positive, LR− for negative) to compute the correct post-test probability.
For independent tests, use the post-test probability from the first test as the pre-test probability for the second test. Multiply likelihood ratios together: post-test odds = pre-test odds × LR₁ × LR₂ × ...
Probability ranges from 0 to 1 (or 0% to 100%). Odds range from 0 to infinity. Probability = Odds / (1 + Odds). Odds = Probability / (1 − Probability). Odds are used in the middle steps of calculations.
Yes! This is a practical application of Bayes' theorem, specifically the likelihood ratio form. It updates prior beliefs (pre-test probability) with new evidence (test result) to get posterior beliefs (post-test probability).
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