Post-Test Probability Calculator
Update a probability with a likelihood ratio — the odds form of Bayes' theorem, and the fastest way to see what a test result is actually worth.
Work in odds, not probabilities: post-test odds = pre-test odds × likelihood ratio.
How the post-test probability calculator works
Work in odds, not probabilities: post-test odds = pre-test odds × likelihood ratio. Convert the prior to odds, multiply, convert back. That is the whole calculation, and it is why likelihood ratios are the natural currency of diagnostic evidence.
A likelihood ratio of 1 changes nothing. Above 10 or below 0.1 is a decisive result; between 0.5 and 2 is barely worth the sample.
Formula: post-test odds = pre-test odds × LR; p = odds / (1 + odds)
Worked examples
| Inputs | Post-test probability | Note |
|---|---|---|
| 20% prior, LR 10 | 71.4286% | rises to 71.4% |
| A negative result: LR 0.1 | 2.439% | falls to 2.4% |
| An uninformative test: LR 1 | 20% | unchanged at 20% |
FAQFrequently asked questions
What is a likelihood ratio?
How many times more likely this result is in someone with the condition than without. LR+ = sensitivity ÷ (1 − specificity).
Why work in odds?
Because Bayes' theorem is a plain multiplication in odds and a messy fraction in probabilities.
What counts as a good test?
LR above 10 or below 0.1 shifts the probability decisively. Between 0.5 and 2, the result barely matters.
Can a test make something certain?
No. A finite likelihood ratio can never move a probability all the way to 0 or 100%.
Does the prior really matter that much?
Enormously. The same LR of 10 takes a 1% prior to 9% and a 50% prior to 91%. This is why testing a low-risk population produces mostly false positives.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.