Post-Test Probability Calculator — Likelihood Ratio Method
Enter the pre-test probability of a condition, plus the test sensitivity and specificity, to find the post-test probability — how likely the condition really is after a positive or negative result.
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Test result
Probability the condition is present given a positive test
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Pre-test odds
preTestProb ÷ (1 − preTestProb) = 0.1 ÷ 0.9 = 0.1111 - 2
LR+ (likelihood ratio)
Sensitivity ÷ (1 − Specificity) = 0.9 ÷ 0.05 = 18 - 3
Post-test odds
Pre-test odds × LR+ = 0.1111 × 18 = 2 - 4
Post-test probability (%)
postTestOdds ÷ (1 + postTestOdds) × 100 = 2 ÷ 3 × 100 = 66.7
How does this calculator work?
Post-test probability uses Bayes theorem in odds form: post-test odds = pre-test odds × LR, where LR+ = sensitivity / (1 − specificity) for a positive result and LR− = (1 − sensitivity) / specificity for a negative result. Convert back from odds: prob = odds / (1 + odds). High LR+ rules in a diagnosis; low LR− rules it out.
Formula
How this is calculated
The likelihood ratio (LR) method is the most concise way to update a pre-test probability with the result of a diagnostic test. It rests on Bayes theorem expressed in odds form: Post-test odds = Pre-test odds × Likelihood Ratio. Converting between probability and odds uses: odds = prob / (1 − prob) and prob = odds / (1 + odds).
For a positive test result, the positive likelihood ratio is LR+ = sensitivity / (1 − specificity). A high LR+ (above 10) strongly rules in a diagnosis; a low LR+ (below 2) adds little information. For a negative test result, the negative likelihood ratio is LR− = (1 − sensitivity) / specificity. A low LR− (below 0.1) strongly rules out a diagnosis.
The pre-test probability is usually the prevalence of the condition in the tested population, or a clinician's estimate based on symptoms and history. Key limitation: the method assumes the test is applied to the population for which its sensitivity and specificity were measured — applying test statistics outside that reference population can give misleading results. This calculator is for educational and planning purposes; clinical decisions require a qualified healthcare professional.
Frequently asked questions
A likelihood ratio summarises how much a test result changes the probability of a condition. LR+ above 10 is considered strong evidence in favour; LR+ below 2 is weak. LR− below 0.1 is strong evidence against; LR− above 0.5 is weak. Unlike sensitivity and specificity, LRs can be applied directly to any pre-test probability to compute the post-test probability.
The pre-test probability is the probability of the condition being present before the test result is known. It can come from published disease prevalence in a relevant population, or from a clinician's assessment based on history and physical examination. A higher pre-test probability (higher disease prevalence or higher clinical suspicion) yields a higher post-test probability for the same test result.
Yes, this calculator implements the same underlying calculation as the Fagan nomogram (1975), which is a graphical tool connecting pre-test probability, likelihood ratio and post-test probability on three parallel scales. This calculator computes the same values algebraically from the likelihood ratio odds formula.
Also known as
TG we-Calculate Editorial Team. (2026). Post-Test Probability Calculator — Likelihood Ratio Method [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/post-test-probability-calculator
TG we-Calculate Editorial Team. "Post-Test Probability Calculator — Likelihood Ratio Method." TG we-Calculate. 2026. https://we-calculate.com/calculator/post-test-probability-calculator.
TG we-Calculate Editorial Team, "Post-Test Probability Calculator — Likelihood Ratio Method," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/post-test-probability-calculator
@misc{wecalculate_post_test_probability_calculator, title = {Post-Test Probability Calculator — Likelihood Ratio Method}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/post-test-probability-calculator}}, year = {2026}, note = {TG we-Calculate} }
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