# Post-Test Probability Calculator URL: https://speedycalculator.com/calculators/statistics/post-test-probability/ Last updated: 2026-10-30 > The post-test probability calculator updates the chance that a patient has a condition after a test result. Start from a pre-test probability (or prevalence) and a likelihood ratio, from sensitivity and specificity, or from a 2 × 2 table of counts, for a positive or a negative result. ## Inputs - What do you know? - Pre-test probability (prevalence) (%) - Likelihood ratio - Sensitivity (%) - Specificity (%) - True positives (TP) - False positives (FP) - False negatives (FN) - True negatives (TN) - Test result ## Results - Post-test probability - Pre-test probability used - Sensitivity - Specificity - Positive likelihood ratio (LR+) - Negative likelihood ratio (LR−) - Likelihood ratio used - Pre-test odds - Post-test odds - Change in probability ## Formula ``` Pre-test odds = pre-test probability ÷ (1 − pre-test probability) Post-test odds = pre-test odds × likelihood ratio Post-test probability = post-test odds ÷ (1 + post-test odds) LR+ = sensitivity ÷ (1 − specificity) · LR− = (1 − sensitivity) ÷ specificity ``` ## Explanation A test result does not tell you on its own whether someone has a condition; it shifts the probability you had before the test. The post-test probability combines that pre-test probability – often the prevalence in similar patients, adjusted for symptoms – with the strength of the test, summarised by its likelihood ratio. The calculation is easiest in odds. Convert the pre-test probability to odds, multiply by the likelihood ratio and convert back. A positive result uses the positive likelihood ratio LR+ = sensitivity ÷ (1 − specificity); a negative result uses LR− = (1 − sensitivity) ÷ specificity. LR+ above 10 or LR− below 0.1 are usually considered strong evidence; values near 1 barely change anything. The calculator offers three starting points: a known pre-test probability and likelihood ratio, a pre-test probability with the test’s sensitivity and specificity, or a 2 × 2 table of true and false positives and negatives, in which case the prevalence, sensitivity and specificity are taken from the table. It is an educational tool – clinical decisions also depend on context and should be made with a clinician. ### How to use the Post-Test Probability Calculator - **What do you know?** - **Pre-test probability (prevalence)** - **Likelihood ratio** - **Sensitivity** - **Specificity** - **True positives (TP)** - **False positives (FP)** - **False negatives (FN)** - **True negatives (TN)** - **Test result** Results update as you type, and everything is calculated in your browser. ### How it works The pre-test probability p is turned into odds p/(1 − p), multiplied by the likelihood ratio for the result observed, and converted back with odds/(1 + odds). When a table is entered, prevalence = (TP + FN)/N, sensitivity = TP/(TP + FN) and specificity = TN/(TN + FP). ### Worked example Pre-test probability 20% and a positive test with sensitivity 85% and specificity 90%. LR+ = 0.85 ÷ 0.10 = 8.5. Pre-test odds = 0.2 ÷ 0.8 = 0.25; post-test odds = 0.25 × 8.5 = 2.125; post-test probability = 2.125 ÷ 3.125 = 68%. A negative result instead uses LR− = 0.15 ÷ 0.90 = 0.1667, giving odds 0.0417 and a probability of 4%. ### Rough guide to likelihood ratios LR+LR−Effect on probability> 10< 0.1Large, often conclusive5–100.1–0.2Moderate2–50.2–0.5Small1–20.5–1Rarely important ### Inputs explained FieldWhat to enterWhat do you know?Choose one: Pre-test probability and likelihood ratio, Pre-test probability, sensitivity and specificity, 2 × 2 table of test resultsPre-test probability (prevalence)In %Likelihood ratioA numberSensitivityIn %SpecificityIn %True positives (TP)A numberFalse positives (FP)A numberFalse negatives (FN)A numberTrue negatives (TN)A numberTest resultChoose one: Positive, Negative ### What each result means - **Post-test probability** = [o1]÷(1 + [o1])×100 - **Pre-test probability used** = [p0] - **Sensitivity** = [se] - **Specificity** = [sp] - **Positive likelihood ratio (LR+)** = [Sensitivity]÷(100 - [Specificity]) - **Negative likelihood ratio (LR−)** = (100 - [Sensitivity])÷[Specificity] - **Likelihood ratio used** = [lr] - **Pre-test odds** = [Pre-test probability used]÷(100 - [Pre-test probability used]) - **Post-test odds** = [o1] - **Change in probability** = [Post-test probability] - [Pre-test probability used] ## Worked example Inputs — What do you know?: Pre-test probability and likelihood ratio; Pre-test probability (prevalence): 20 %; Likelihood ratio: 6. Results — **Post-test probability = 60 %**; Pre-test probability used = 20 %; Likelihood ratio used = 6; Pre-test odds = 0.25; Post-test odds = 1.5; Change in probability = 40 percentage points. ## Key terms - **Pre-test probability**: The probability of the condition before the test, often the prevalence. - **Likelihood ratio**: How many times more likely a result is in people with the condition than without it. - **Post-test probability**: The updated probability after taking the test result into account. - **Odds**: Probability ÷ (1 − probability). ## FAQ **How do you calculate post-test probability?** Convert the pre-test probability to odds, multiply by the likelihood ratio and convert back. 20% → odds 0.25; × 6 = 1.5; 1.5 ÷ 2.5 = 60%. **What is the difference between pre-test odds and pre-test probability?** Probability is cases ÷ everyone; odds are cases ÷ non-cases. A 29% prevalence is odds of 0.29 ÷ 0.71 = 0.41 (or about 2.4 to 1 against). **What is a good likelihood ratio?** LR+ above 10 or LR− below 0.1 make large, often decisive changes; 2–5 and 0.2–0.5 make small changes; values near 1 are useless. **Can a likelihood ratio be negative?** No. It is a ratio of two probabilities and is always 0 or more. **Is the post-test probability the same as the positive predictive value?** Yes, when the pre-test probability equals the prevalence in the population where PPV was measured. **Why does the same test mean different things for different patients?** Because the pre-test probability differs. A positive result moves 2% to about 15% but 50% to about 89% with LR+ = 8.5. **Can I apply several tests in a row?** Yes, if they are independent: the post-test probability of one test becomes the pre-test probability of the next. ## Sources - [NCBI Bookshelf – Diagnostic testing accuracy: sensitivity, specificity, predictive values and likelihood ratios](https://www.ncbi.nlm.nih.gov/books/NBK557491/) - [CDC – Sensitivity, specificity and predictive values (Principles of Epidemiology)](https://www.cdc.gov/csels/dsepd/ss1978/lesson5/section1.html) - [Penn State STAT 414 – Introduction to Probability Theory](https://online.stat.psu.edu/stat414/)