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+ (Positive Likelihood Ratio) = Sensitivity ÷ (1 − Specificity)
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

Commonly cited likelihood ratio interpretation ranges
LR+ valueEffect on suspicion of condition
Above 10Large, often conclusive increase
5 – 10Moderate increase
2 – 5Small increase
1 – 2Minimal 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

  1. Enter the test's sensitivity (as a percentage or decimal).
  2. Enter the test's specificity (as a percentage or decimal).
  3. 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.