Post-Test Probability Calculator
Enter how likely a condition is before testing, then describe the test by its likelihood ratio or by its sensitivity and specificity and the result you got. You get the post-test probability and odds, a step-by-step table, the working, and a Fagan nomogram you can download. Add up to five tests to chain them. For study and practice, not for clinical decisions. Free, no sign-up, and nothing leaves your browser.
How likely the condition is before the test: the prevalence in people like this patient, or your clinical estimate. Between 0 and 100, exclusive.
Enter a pre-test probability and a test result to get the post-test probability.
How to Use the Post-Test Probability Calculator
- 1. Enter the pre-test probability. How likely the condition is before the test, as a percentage: the prevalence among people like this patient, or a reasoned estimate.
- 2. Describe the test. Either give its sensitivity and specificity and pick the result (positive or negative), or type the likelihood ratio that applies — LR+ for a positive result, LR− for a negative one.
- 3. Chain more tests if you have them. Add up to five. Each result updates the odds in turn.
- 4. Read the answer. The post-test probability comes with the odds at every step, a plain-language reading and a Fagan nomogram with your line drawn on it.
How a Test Result Changes the Probability
A test result does not tell you the probability of disease by itself; it tells you by what factor to change the odds you started with. That factor is the likelihood ratio: LR+ = sensitivity / (1 − specificity) for a positive result and LR− = (1 − sensitivity) / specificity for a negative one. Bayes' theorem in odds form (Fagan, 1975) is then three steps:
Odds form of Bayes' theorem
Pre-test odds = p / (1 − p)
Post-test odds = pre-test odds × LR
Post-test probability = odds / (1 + odds)
Unlike predictive values, likelihood ratios do not depend on prevalence, so the same LR works for every patient; only the starting probability changes. That is why a positive result for a rare condition in a low-risk person can still leave the probability low.
Rule of Thumb for Likelihood Ratios
McGee (2002) showed that, for pre-test probabilities between about 10% and 90%, a likelihood ratio moves the probability by a roughly fixed number of percentage points:
| Likelihood ratio | Approximate change in probability |
|---|---|
| 2 | +15 points |
| 5 | +30 points |
| 10 | +45 points |
| 0.5 | −15 points |
| 0.2 | −30 points |
| 0.1 | −45 points |
Use the calculator, not the shortcut, near 0% or 100%, where the approximation fails.
Worked Example: Two Positive Tests
Load example starts from a pre-test probability of 20% — odds of 0.25. Test 1 has sensitivity 90% and specificity 80%, so LR+ = 0.90 / 0.20 = 4.5; the odds become 0.25 × 4.5 = 1.125, a probability of 52.9%. Test 2 (sensitivity 85%, specificity 95%) has LR+ = 0.85 / 0.05 = 17; the odds become 1.125 × 17 = 19.125, a probability of 95.0%. The combined likelihood ratio is 4.5 × 17 = 76.5. If test 1 had come back negative instead, LR− = 0.10 / 0.80 = 0.125 and the probability would have fallen from 20% to 3.0%.
- Ignoring the pre-test probability. The same positive result means very different things in a high-risk and a low-risk patient.
- Taking a likelihood ratio from the wrong population. LRs measured in a hospital referral clinic may not hold in primary care, where the mix of cases differs.
- Chaining tests that are not independent. Two blood markers of the same process share information; multiplying their LRs counts it twice and overstates the probability.
- Treating sensitivity as the chance of disease after a positive test. That is the positive predictive value, which depends on the pre-test probability.
For learning, not for diagnosis
This calculator illustrates Bayesian reasoning with the numbers you supply. It does not know whether those numbers fit your patient, and it is not a substitute for clinical judgment.
Frequently Asked Questions
- What is post-test probability?
- It is the probability that a person has the condition after the result of a test is known. It is calculated by converting the pre-test probability to odds, multiplying by the likelihood ratio for the result, and converting back to a probability.
- How do I calculate post-test probability from sensitivity and specificity?
- First compute the likelihood ratio: LR+ = sensitivity / (1 − specificity) for a positive result, LR− = (1 − sensitivity) / specificity for a negative one. Then multiply the pre-test odds, p / (1 − p), by that ratio, and convert the odds back with odds / (1 + odds). The calculator does all three steps and shows them.
- What is a Fagan nomogram?
- It is a chart with three vertical scales that does the odds calculation by drawing a straight line: from the pre-test probability on the left through the likelihood ratio in the middle, to the post-test probability on the right. Fagan published it in 1975 so clinicians could apply Bayes' theorem at the bedside.
- How is post-test probability different from the positive predictive value?
- They are the same number for a positive result when the pre-test probability equals the prevalence in the study that measured the predictive value. The post-test approach is more flexible because you can start from a different pre-test probability, which a fixed predictive value cannot do.
- Can I use more than one test?
- Yes: multiply the likelihood ratios, or let the calculator chain the tests. This is valid only if the tests are conditionally independent — if knowing one result tells you nothing more about the other once you know the true disease status. Tests that overlap in what they measure overstate the combined evidence.
- Where do I get the pre-test probability?
- Common sources are the prevalence of the condition in a population like the patient's, a validated clinical prediction rule, or a documented clinical estimate. It is usually the least certain number in the calculation, so try a range of values and see whether the conclusion changes.