Post Test Probability Calculator
A positive test result is not a diagnosis, and a negative one is not a clean bill of health. Both are evidence, and the right question after either is: given this result, what is the chance the disease is actually present? That chance is the post-test probability, and this calculator works it out from the pre-test probability plus the test’s sensitivity and specificity, or directly from its likelihood ratios, for both a positive and a negative result at once.
Medical disclaimer: this is an educational tool, not medical advice. It shows how test accuracy and prior probability combine; real diagnostic decisions belong with a qualified clinician who knows the patient.
Quick Answer
With a 20% pre-test probability and a test that is 90% sensitive and 85% specific, a positive result raises the chance of disease to 60% (the PPV), while a negative result drops it to 2.86%, an NPV of 97.14%. The likelihood ratios behind the move are LR+ 6 and LR− 0.118. Those are the pre-filled values above, so one click on Calculate reproduces every figure.
Key takeaways
- Post-test probability is Bayes' theorem applied to a test result: pre-test odds × likelihood ratio, converted back to a probability.
- After a positive result, the post-test probability is the PPV. After a negative result, it is the residual risk, 1 − NPV. The calculator reports both on every run.
- Pre-test probability dominates the answer. The same 90%/85% test gives a PPV of 60% at 20% pre-test probability and only about 5.7% at 1%.
- Two input modes (sensitivity/specificity or published likelihood ratios), natural-frequency patient counts, and a second-test chaining step are all in the one tool.
- Quick Answer
- How to use the post-test probability calculator
- How the calculator works: Bayes' theorem in two forms
- Worked example, verified against the tool
- Reading the likelihood ratios: strength bands
- Why the pre-test probability dominates: the base-rate trap
- Estimating the pre-test probability honestly
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the post-test probability calculator
Pick the mode that matches the numbers you have, enter them, and click Calculate. The results stay hidden until you do, and both possible results (positive and negative) are updated in the same run.
- Test accuracy mode (default): enter the pre-test probability, the test's sensitivity, and its specificity, all as percents. The population field only sizes the patient-count table; it changes no probability, and blank is read as 10,000.
- Likelihood ratio mode: switch to the second tab when a paper or guideline reports LR+ and LR− directly. Enter the pre-test probability (this tab keeps its own field, pre-filled at 10%) and the two ratios.
- Read the two headline numbers: the post-test probability after a positive result (the PPV) and after a negative result (the residual risk), with NPV, both likelihood ratios, overall accuracy, the step-by-step odds calculation, and the patient counts underneath.
- Chain a second test, if there is one: inside the results, pick the first test's result, enter the second test's likelihood ratio and result, and apply it. The message states the independence assumption out loud.
- Copy or share the headline results with the buttons in the results box.
Out-of-range entries are rejected with a specific message rather than quietly clamped: a blank pre-test probability earns “Enter a pre-test probability between 0 and 100.”, a sensitivity above 100 earns “Sensitivity cannot be above 100.”, and a negative likelihood ratio earns “Likelihood ratios cannot be negative.” The one silent adjustment is the population field, which is held between 100 and 1,000,000 because it only scales the counts table. Converting between a probability and its odds by hand is the job of an odds calculator; this page does that conversion inside every calculation.
How the calculator works: Bayes' theorem in two forms
Three inputs drive everything. The pre-test probability is the chance of disease before the test: the population prevalence, or a clinical estimate from symptoms and risk factors. Sensitivity is the share of diseased people the test correctly flags, written as P(positive test | disease). Specificity is the share of healthy people the test correctly clears, written as P(negative test | no disease).
The probability form of Bayes' theorem gives the headline results directly. After a positive test, the post-test probability is the positive predictive value:
P(disease | negative) = ((1 − sensitivity) × pre-test probability) ÷ ((1 − sensitivity) × pre-test probability + specificity × (1 − pre-test probability)), with NPV = 1 − that residual risk.
The odds form says the same thing in three shorter steps, and it is the form most clinical teaching uses, following the likelihood-ratio method set out by Deeks and Altman in the BMJ. Convert the pre-test probability to odds (p ÷ (1 − p)), multiply by the likelihood ratio, and convert back with probability = odds ÷ (1 + odds). The ratios are LR+ = sensitivity ÷ (1 − specificity), how much more often a positive result occurs in diseased than in healthy people, and LR− = (1 − sensitivity) ÷ specificity, the same comparison for a negative result. The calculator runs both forms on every calculation and cross-checks them against each other, so a coding slip would surface as an error message instead of a wrong number. That cross-check is an application of the same conditioning logic a conditional probability calculator demonstrates in its general form.
Worked example, verified against the tool
A patient has a 20% pre-test probability of a disease, and the test is 90% sensitive and 85% specific. Those values are pre-filled. The calculator returns a post-test probability of 60% after a positive result, and the odds route it prints agrees step for step:
After a negative result the residual risk is (0.10 × 0.20) ÷ (0.10 × 0.20 + 0.85 × 0.80) = 0.02 ÷ 0.70 = 2.86%, giving an NPV of 97.14%, with LR− = 0.10 ÷ 0.85 = 0.118. In natural frequencies, out of 10,000 people at this pre-test probability, about 2,000 have the disease and 8,000 do not:
| Disease present | Disease absent | |
|---|---|---|
| Test positive | 1,800 true positives | 1,200 false positives |
| Test negative | 200 false negatives | 6,800 true negatives |
Among the 3,000 positive results, 1,800 are real: 1,800 ÷ 3,000 = 60%, the same PPV as the formula. Overall accuracy is (1,800 + 6,800) ÷ 10,000 = 86%, but accuracy flatters tests on imbalanced populations, which is why the PPV and NPV are the numbers that matter. Clinically, this positive result is only moderate support: the chance rose from 20% to 60%, so four in ten positives are false alarms and further testing is usually warranted. The negative result is far more decisive, dropping the risk to 2.86%.
The likelihood-ratio tab reproduces the same patient from published ratios instead: a 10% pre-test probability with LR+ 5 and LR− 0.2 (the second tab's pre-filled values) gives 35.71% after a positive result and 2.17% after a negative one, an NPV of 97.83%. And chaining works off the worked example directly: a positive first result (post-test odds 1.5) followed by a second positive test with LR 5 updates the odds to 7.5 and the final post-test probability to 88.24%.
Reading the likelihood ratios: strength bands
A likelihood ratio near 1 changes almost nothing, and the further it sits from 1, the harder the result pushes the probability. The calculator labels every LR+ and LR− it computes against these bands, which follow the conventional interpretation in the diagnostic-tests literature:
| LR+ | Reading for a positive result | LR− | Reading for a negative result |
|---|---|---|---|
| 10 or more | Strong evidence for disease | 0.1 or less | Strong evidence against disease |
| 5 to under 10 | Moderate evidence for disease | Above 0.1 to 0.2 | Moderate evidence against disease |
| 2 to under 5 | Small shift in probability | Above 0.2 to 0.5 | Small shift in probability |
| Above 1 to under 2 | Minimal shift in probability | Above 0.5 to under 1 | Minimal shift in probability |
| Exactly 1 | No diagnostic value | Exactly 1 | No diagnostic value |
Two odd cases are labelled honestly rather than smoothed over. An LR+ below 1 means a “positive” result would actually lower the probability, and an LR− above 1 means a “negative” result would raise it; the calculator says so and suggests checking the inputs, because swapped sensitivity and specificity figures are the usual cause. A perfect test is handled exactly: at 100% specificity LR+ is infinite and a positive result gives a post-test probability of 100%, and at 100% sensitivity LR− is 0 and a negative result leaves a residual risk of 0% for any pre-test probability below 100%.
Why the pre-test probability dominates: the base-rate trap
Predictive values track prevalence, not just test quality, and the calculator makes the effect impossible to miss. Run the screening case: a 1% pre-test probability with a test that is 95% sensitive and 90% specific. The PPV comes out at 8.76%, the residual risk after a negative at 0.06%, and the NPV at 99.94%, with LR+ 9.5 and LR− 0.056.
The counts show why. In 10,000 people, 100 have the disease and the test catches 95 of them, but the 10% false-positive rate applies to 9,900 healthy people and flags 990. True positives are outnumbered roughly ten to one, so a positive result is wrong far more often than it is right, despite a test that sounds excellent. This is the base-rate fallacy in arithmetic form, and it is the reason screening programs confirm positives with a second, different test. The same test in a high-risk clinic, where the pre-test probability might be 50%, gives a PPV of 90% instead. Nothing about the test changed; the starting probability did. If converting between percent and probability forms trips you up while comparing published figures, a probability percentage calculator covers that single conversion.
Estimating the pre-test probability honestly
The output is only as honest as this one input, and there are three routes to it, from most to least rigorous. Published prevalence for the population being tested is the firmest starting point when the patient resembles that population. Validated clinical prediction rules come next: scores such as the Wells score for pulmonary embolism or the HEART score for chest pain convert findings into a calibrated probability band. A clinician's estimate from history and examination is the third route, and it is the one most prone to drift.
Whichever route you use, test the sensitivity of the conclusion to the estimate: run the calculator at your estimate, then at half and double it. If the clinical decision flips across that range, the honest answer is that the pre-test probability needs more work (or a better test) before the result can carry the decision. The CDC's epidemiology teaching on screening for disease makes the same point from the population side: predictive value is a property of the test in a population, never of the test alone.
What competing calculators miss
The highest-ranking post-test and diagnostic-accuracy pages each do something well, and each leaves a real gap:
- Natural-frequency specialists (Worth the Test): a clean 2×2 table, a probability tree, and a Fagan nomogram, with a strong base-rate warning. The gap: no likelihood-ratio input mode and no way to chain a second test onto the result.
- Step-by-step odds calculators (OnlyCalculators' post-test page): a full eight-step odds working with a direct-Bayes verification, close to this page's method. The gap: no patient counts, so the base-rate effect stays abstract, and no sequential testing.
- Counts-in diagnostic tools (ConductScience, MedCalc-style): you enter TP, FP, FN, TN from a study and get sensitivity, specificity, predictive values, and confidence intervals. That is study appraisal, not bedside updating: if all you have is a pre-test probability and a published sensitivity, there is nothing to type in.
- Wrong likelihood-ratio definitions (found on a ranking page): one popular page defines LR+ as “the chances that a sick person will test positive” and LR− as “the chances that a healthy person will test negative.” Those are sensitivity and specificity. A likelihood ratio always compares the two groups, and this page's definitions, bands, and step printout keep that straight.
- The gap this page fills: both input modes in one tool, both Bayes forms cross-checked on every run, natural-frequency counts, LR strength labels, second-test chaining with its independence assumption stated, and the perfect-test edges (100% sensitivity or specificity) computed exactly instead of returning an error or a blank.
Frequently asked questions
After a positive result, yes: post-test probability equals the positive predictive value, the chance that a person with a positive test actually has the disease. After a negative result, post-test probability equals 1 minus the NPV, the residual chance of disease despite the negative test. The calculator shows both.
This is the base-rate fallacy, and the pre-test probability is the culprit. Take a disease with 1% prevalence tested with 95% sensitivity and 90% specificity: PPV = (0.95 × 0.01) ÷ (0.95 × 0.01 + 0.10 × 0.99) = 0.0095 ÷ 0.1085 ≈ 8.8%. The small false-positive rate applies to the huge healthy majority, so false positives swamp true positives. Try 1% pre-test in the calculator and watch it happen.
For ruling disease in, LR+ of 10 or more is strong evidence (a large probability shift), 5 to under 10 is moderate, 2 to under 5 is small, and near 1 is nearly useless. For ruling disease out, LR− of 0.1 or less is strong, above 0.1 to 0.2 moderate, above 0.2 to 0.5 small. The calculator labels every LR+ and LR− it computes against these bands.
Three routes, from most to least rigorous: published prevalence for the population being tested, validated clinical prediction rules such as the Wells score for pulmonary embolism or the HEART score for chest pain, or a clinician's estimate from history and examination. A systematic estimate beats vague intuition; the calculator's output is only as honest as this input.
Sensitivity asks: given the disease is present, how often is the test positive? It is a property of the test alone and never changes with prevalence. PPV asks the reverse: given a positive test, how likely is the disease? PPV depends on both the test and the pre-test probability, which is why a highly sensitive test can still have a poor PPV in a low-prevalence population.
Yes, that is sequential Bayesian updating: the post-test probability after test one becomes the pre-test probability for test two. Use the chaining section above, which multiplies the post-test odds by the second test's likelihood ratio. This assumes the two tests are conditionally independent given the true disease status, which fails when both tests measure the same biological pathway.
Because predictive values track prevalence, not just test quality. In a high-risk clinic the pre-test probability is high, so positives are mostly true. In population screening the pre-test probability is low, so even a specific test generates a flood of false positives. One calculator on the web shows PPV swinging from about 15% at 1% prevalence to over 99% at 99% prevalence for the same test.
Use it when the source you trust reports likelihood ratios directly, as many diagnostic accuracy papers and guidelines do, or when a test has several result levels and each level carries its own published ratio. The two modes are mathematically identical: likelihood ratio mode simply skips the step of deriving LR+ and LR− from sensitivity and specificity.
At 100% specificity there are no false positives, LR+ is infinite, and a positive result gives a post-test probability of 100% at any non-zero pre-test probability. At 100% sensitivity there are no false negatives, LR− is 0, and a negative result leaves a residual risk of 0% for any pre-test probability below 100%. The calculator computes both edges exactly.
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References
- Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios, BMJ 2004;329:168–169 (the odds-form method this calculator uses, and the LR strength bands). Accessed October 24, 2026.
- Altman DG, Bland JM. Diagnostic tests 1: sensitivity and specificity, BMJ 1994;308:1552 (definitions of sensitivity and specificity as properties of the test). Accessed October 24, 2026.
- Akobeng AK. Understanding diagnostic tests 2: likelihood ratios, pre- and post-test probabilities and their use in clinical practice, Acta Paediatrica 2007;96(4):487–491. Accessed October 24, 2026.
- Fagan TJ. Nomogram for Bayes theorem, New England Journal of Medicine 1975;293:257 (the graphical form of the pre-test odds × LR update). Accessed October 24, 2026.
- Trevethan R. Sensitivity, Specificity, and Predictive Values: Foundations, Pliabilities, and Pitfalls in Research and Practice, Frontiers in Public Health 2017;5:307. Accessed October 24, 2026.
- Maxim LD, Niebo R, Utell MJ. Screening tests: a review with examples, Inhalation Toxicology 2014;26(13):811–828 (screening context, prevalence effects on predictive values). Accessed October 24, 2026.
- Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice, Lesson 3, Section 5: Screening for Disease (sensitivity, specificity and predictive value in population screening). Accessed October 24, 2026.
- Shreffler J, Huecker MR. Diagnostic Testing Accuracy, StatPearls, NCBI Bookshelf (definitions and formulas for sensitivity, specificity, predictive values and likelihood ratios). Accessed October 24, 2026.
- Penn State Eberly College of Science. STAT 509 Design and Analysis of Clinical Trials, Lesson 17.3: Estimating the Probability of Disease (Bayes updating for diagnostic testing, worked in probability form). Accessed October 24, 2026.
- Sox HC, Higgins MC, Owens DK. Medical Decision Making, 2nd edition, Wiley-Blackwell 2013 (pre-test probability estimation and sequential testing in clinical decisions). Accessed October 24, 2026.