Free clinical calculator
The Fagan nomogram turns a pre-test probability and a test's likelihood ratio into a post-test probability. Enter how likely the diagnosis is before testing, then the likelihood ratios or the sensitivity and specificity, and the calculator shows the probability after a positive and after a negative result, the math and the nomogram.
Fagan nomogram: pre-test probability 30.0%. Positive result (LR+ 8.5): post-test probability 78.5%. Negative result (LR− 0.167): post-test probability 6.7%.
Pre-test probability: 30.0%
If the test is positive
78.5%
LR+ 8.5: moderate increase in probability
If the test is negative
6.7%
LR− 0.167: moderate decrease in probability
If the test is positive
If the test is negative
The Fagan nomogram is a graphical form of Bayes' theorem, published by T. J. Fagan as a one-page letter in the New England Journal of Medicine in 1975. It answers a daily clinical question: given how likely a diagnosis was before a test, how likely is it after the result?
It works with likelihood ratios (LRs). An LR says how many times more (or less) likely a test result is in people with the disease than in people without it. In odds form Bayes' theorem is a simple product, post-test odds = pre-test odds × LR, and the nomogram's log scales turn that multiplication into a straight line.
Find the pre-test probability on the left scale: your estimate of disease probability before the test, from prevalence, the clinical picture or a validated score.
Find the test's likelihood ratio on the middle scale: LR+ for a positive result, LR− for a negative one.
Draw a straight line from the left point through the middle point and extend it to the right scale.
Read the post-test probability where the line meets the right scale. Compare it with your treatment and testing thresholds.
A patient has a 30% pre-test probability of the disease. The test has 85% sensitivity and 90% specificity, the calculator's default values.
A positive result moves the probability from 30% to about 78%; a negative one drops it to about 7%. Whether either is enough to act on depends on your thresholds, not on the test alone.
The further an LR is from 1, the more a result changes the probability. Likelihood ratios above 10 or below 0.1 are considered strong evidence to rule a diagnosis in or out in most circumstances (Deeks & Altman, BMJ 2004). For pre-test probabilities between 10% and 90%, McGee's approximations estimate the change without a calculator.
| Likelihood ratio | Approximate change in probability | Interpretation |
|---|---|---|
| > 10 | +45 points or more | Large increase: strong evidence to rule in |
| 5 to 10 | +30 to +45 points | Moderate increase in probability |
| 2 to 5 | +15 to +30 points | Small increase in probability |
| 0.5 to 2 | Less than 15 points | Minimal change: rarely decisive on its own |
| 0.2 to 0.5 | -15 to -30 points | Small decrease in probability |
| 0.1 to 0.2 | -30 to -45 points | Moderate decrease in probability |
| < 0.1 | -45 points or more | Large decrease: strong evidence to rule out |
Approximate changes from McGee, J Gen Intern Med 2002 (LR 2 ≈ +15, 5 ≈ +30, 10 ≈ +45 percentage points; the inverses mirror them). An LR of 1 leaves the probability unchanged.
Convert the pre-test probability to odds with p / (1 − p), multiply by the likelihood ratio of the test result, then convert back with odds / (1 + odds). For a 30% pre-test probability and an LR of 8.5: 0.429 × 8.5 = 3.64 odds, which is a post-test probability of about 78.5%.
The positive likelihood ratio is sensitivity / (1 − specificity) and the negative likelihood ratio is (1 − sensitivity) / specificity, with both values as fractions. A test with 85% sensitivity and 90% specificity has LR+ = 0.85 / 0.10 = 8.5 and LR− = 0.15 / 0.90 ≈ 0.17. At exactly 100% specificity LR+ is undefined.
Use the best estimate for the patient in front of you: the prevalence of the disease in a similar setting, adjusted for the history and examination, or the output of a validated clinical prediction score. Pre-test probability varies by setting, so a test with fixed likelihood ratios can lead to very different post-test probabilities.
Yes. The nomogram is Bayes' theorem in odds form drawn on log scales: post-test odds equal pre-test odds times the likelihood ratio. Drawing the line gives a quick visual estimate, while calculating gives the exact value. This calculator does both, so you can check the drawing against the numbers.
It is only as good as its inputs. Likelihood ratios come from studies whose patients may differ from yours, pre-test probability is an estimate, and applying several tests in a row by multiplying their LRs assumes the tests are independent, which is often untrue. Use the result to support clinical judgement, not to replace it.
This calculator reads its inputs from the URL and has a free JSON version, no sign-up, with the same parameters:
Last reviewed: . This calculator is for education and clinical decision support by health professionals. It does not replace clinical judgement or local guidelines, and no data you enter leaves your browser.