Likelihood Ratio Calculator
One Number That Combines Both Error Types
Sensitivity and specificity each describe half of a test's behavior. Likelihood ratios combine both into a single figure that says how much a given result should shift your belief about whether a condition is present — a positive result with a high LR+ is strong evidence for the condition, while a negative result with a low LR− is strong evidence against it.
The Formula
LR− (Negative Likelihood Ratio) = (1 − Sensitivity) ÷ Specificity
Sensitivity and specificity can be entered as either a percentage (like 90) or a decimal (like 0.9) — the calculator converts automatically. Note that LR+ is undefined when specificity is 100% and LR− is undefined when specificity is 0%, since both would require dividing by zero.
General Interpretation Guide
| LR+ value | Effect on suspicion of condition |
|---|---|
| Above 10 | Large, often conclusive increase |
| 5 – 10 | Moderate increase |
| 2 – 5 | Small increase |
| 1 – 2 | Minimal increase |
The mirror logic applies to LR−: values below 0.1 are considered strong evidence against a condition, and values between 0.5 and 1 have minimal effect. These are general interpretive guidelines from the diagnostic testing literature, not fixed clinical rules.
Why Clinicians Prefer Likelihood Ratios
- Independent of prevalence — unlike PPV and NPV, likelihood ratios don't change based on how common the condition is in the tested population.
- Combining with pre-test probability — likelihood ratios are designed to be combined with a clinician's pre-test estimate (via Bayes' theorem, often using a nomogram) to produce a post-test probability.
- Comparing multiple tests — a single LR value makes it easier to rank competing diagnostic tests than comparing sensitivity and specificity pairs separately.
How to Use This Calculator
- Enter the test's sensitivity (as a percentage or decimal).
- Enter the test's specificity (as a percentage or decimal).
- Select Calculate to see LR+ and LR−.
Related Calculations
Compute sensitivity and specificity from raw counts with the Sensitivity/Specificity Calculator, or check predictive values with the PPV/NPV Calculator.