ConductScienceConductScience
ToolsConductScience tool
Fagan NomogramFree in-browser calculator

Bayes Calculator.

Interactive Fagan nomogram for Bayesian post-test probability. Enter pretest probability and likelihood ratio — see the update instantly. Data never leaves your browser.

Run calculator Request a Quote
PrivateData stays in your browser
LiveNo sign-up required
Open methodFormula shown on this page
CitableMethods and citation included

Calculator

Results update in place

Try it out

Load example Bayes data to see the full workflow

When to use

  • Convert pretest probability to post-test probability using a known likelihood ratio
  • Visualize Bayesian diagnostic reasoning on an interactive Fagan nomogram
  • Determine how much a positive or negative test result shifts disease probability
  • Quantify diagnostic information gain in bits using Shannon entropy
  • Compute post-test probability from sensitivity, specificity, and a test result

Do not use for

  • Computing sensitivity, specificity, or likelihood ratios from raw data — use the Diagnostic Test Calculator
  • Finding the optimal threshold for a continuous-score test — use the ROC/AUC Calculator
  • Comparing two measurement methods — use the Method Comparison Analyzer

A positive test does not mean you have the disease

A positive result shifts probability by a factor determined by the likelihood ratio. A highly specific test (LR+ = 20) applied to a low-prevalence condition (pretest = 1%) still yields a modest post-test probability of about 17%. Always anchor to pretest probability.

Odds form makes Bayesian updates simple

Post-test odds = pretest odds x LR. This multiplicative form is far simpler than the full Bayes formula with normalizing denominators. Convert back to probability only at the end: probability = odds / (1 + odds).

An LR of 1 means the test is useless

A likelihood ratio of 1 means the test result is equally likely in diseased and non-diseased patients — it provides zero diagnostic information. LR+ > 10 or LR- < 0.1 represents strong evidence.

Sequential testing multiplies likelihood ratios

When applying multiple independent tests, multiply their LRs: post-test odds = pretest odds x LR1 x LR2. This is how clinicians combine evidence from history, exam, and lab tests in a stepwise fashion.

1

Method

Post-test probability is computed using Bayes' theorem in odds form: post-test odds = pretest odds ×\times likelihood ratio, then converted back to probability. The Fagan nomogram is rendered as an interactive SVG with draggable anchor points. Shannon entropy H(p)=−p⋅log⁡2(p)−(1−p)⋅log⁡2(1−p)H(p) = -p \cdot \log_2(p) - (1-p) \cdot \log_2(1-p) quantifies diagnostic uncertainty before and after testing. All calculations run client-side in the browser.

2

Published

Published 2026-04-05. Calculations support planning and documentation; verify procurement decisions against manufacturer specifications or institutional SOPs.

3

How to cite

How to Cite

ConductScience Bayes Calculator. ConductScience, Inc. 2026. Available at: https://conductscience.com/tools/bayes-calculator

Fagan TJ. Letter: Nomogram for Bayes theorem. N Engl J Med. 1975;293(5):257. doi:10.1056/NEJM197507312930513

Bayesian Reasoning in Diagnostics

Bayes' theorem connects prior beliefs to updated beliefs through evidence. In diagnostic testing:

Pretest probability — the probability of disease before the test, based on prevalence, clinical presentation, and prior tests.
Likelihood ratio — how much more likely the test result is in diseased vs non-diseased patients.
Post-test probability — the updated probability of disease after incorporating the test result.

The key insight: a positive test does NOT mean you have the disease. It shifts the probability by a factor determined by the likelihood ratio. A highly specific test (LR+ = 20) applied to a low-prevalence condition (pretest = 1%) still yields a modest post-test probability (~17%).

Information Theory Perspective

Shannon entropy H(p)=−p⋅log⁡2(p)−(1−p)⋅log⁡2(1−p)H(p) = -p \cdot \log_2(p) - (1-p) \cdot \log_2(1-p) measures diagnostic uncertainty in bits. Before testing, uncertainty is H(pretest). After testing, uncertainty drops to H(posttest).

The information gain — the drop in entropy — quantifies how useful the test is. A test that moves probability from 50% to 90% reduces uncertainty by more bits than one that moves it from 90% to 95%, even though the absolute change is larger in the second case.

This provides a principled way to compare tests: the test with higher expected information gain is more diagnostically useful, regardless of whether it is used for ruling in or ruling out.

Frequently asked

325
Free tools
1,200+
Institutions
100%
Client-side
0
Uploads required

Next steps

Equipment

Laboratory Equipment

Browse scientific equipment for your research

Browse Protocol

Diagnostic Test Calculator — Compute LR from 2×2 table

Reference protocol for the next planning step.

Read guide Protocol

ROC/AUC Calculator — Find optimal threshold

Reference protocol for the next planning step.

Read guide Protocol

Diagnostic Sample Size Calculator — Plan your study

Reference protocol for the next planning step.

Read guide