Post-Test Probability Calculator

What Post-Test Probability Means

Post-test probability tells you how likely a condition is after you receive a test result. It combines the starting probability of disease, often called prevalence or pre-test probability, with the test's likelihood ratio. This calculator helps you move from pre-test belief to post-test belief with one Bayesian workflow.

Core Formulas

The full calculation uses three steps:

$$\text{Pre-test odds} = \frac{p}{1-p}$$

$$\text{Post-test odds} = \text{Pre-test odds} \times LR$$

$$\text{Post-test probability} = \frac{\text{Post-test odds}}{1 + \text{Post-test odds}}$$

Here, $p$ is the pre-test probability and $LR$ is the likelihood ratio tied to the observed test result.

Likelihood Ratio Options

If you already know the likelihood ratio, enter it directly. If not, you can derive it from sensitivity and specificity:

$$LR^+ = \frac{\text{Sensitivity}}{1 - \text{Specificity}}$$

$$LR^- = \frac{1 - \text{Sensitivity}}{\text{Specificity}}$$

A strong positive test usually has a large $LR^+$. A strong negative test usually has a very small $LR^-$.

How To Use This Calculator

• Choose whether to enter prevalence directly or calculate it from TP, FN, FP, and TN.
• Select whether the observed result is positive or negative.
• Enter the likelihood ratio directly, or derive it from sensitivity and specificity.
• Read the pre-test odds, post-test odds, and final post-test probability.

When This Tool Helps

Post-test probability is common in medical diagnostics, screening programs, lab result interpretation, and any setting where you must combine base rates with test performance. If you want to work backward from sensitivity and specificity, also try our Sensitivity and Specificity Calculator, p-hat Calculator, and Sample Size Calculator.