Likelihood Ratio Calculator

Calculate likelihood ratios, sensitivity, specificity, and post-test probability from test values or a 2×2 diagnostic table for disease testing.

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Likelihood ratio Formula

The following formulas are used to calculate likelihood ratios (LR). Sensitivity (Se) and specificity (Sp) can be written as proportions (0–1) or percentages (0–100) as long as you use the matching form.

Positive LR (LR+) = Se / (1 − Sp) = Se% / (100 − Sp%) 

Negative LR (LR−) = (1 − Se) / Sp = (100 − Se%) / Sp% 

• LR+ is the positive likelihood ratio
• LR− is the negative likelihood ratio
• Se is the sensitivity (true positive rate)
• Sp is the specificity (true negative rate)

To calculate a positive likelihood ratio (LR+), divide the sensitivity by (1 − specificity) when sensitivity and specificity are expressed as proportions (0–1). If they are expressed as percentages (0–100), divide sensitivity% by (100 − specificity%).

Likelihood ratios update odds: post-test odds = pre-test odds × LR. You can then convert odds back to probability (post-test probability = odds / (1 + odds)). In general, LR+ increases the post-test probability after a positive test result, and LR− decreases it after a negative test result.

References and review note

These definitions and formulas are standard in clinical epidemiology/biostatistics. For deeper context (including choosing pre-test probability and interpreting uncertainty), consult reputable clinical epidemiology texts and medical literature guides such as:

• Users’ Guides to the Medical Literature (diagnostic test interpretation and likelihood ratios).
• Clinical Epidemiology: The Essentials (diagnostic testing, Bayes’ theorem, and applying evidence to patients).
• Evidence-Based Medicine: How to Practice and Teach EBM (likelihood ratios and post-test probability concepts).

Last updated: 2026-01-01

Likelihood Ratio Definition

A likelihood ratio compares how likely a particular test result is in people with a disease versus people without the disease. Specifically:

• LR+ = P(test positive | disease) / P(test positive | no disease)
• LR− = P(test negative | disease) / P(test negative | no disease)

Likelihood Ratio Example

FAQ