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Likelihood Ratio Calculator

Calculate positive and negative likelihood ratios for a diagnostic test.

About Likelihood Ratio Calculator

Likelihood ratios convert a test result into a change in odds, which is why they combine so cleanly with pre-test probability. An LR+ above 10 substantially raises the probability of disease. A test with excellent sensitivity can still be nearly useless if specificity is poor, and the likelihood ratio is what exposes that.

Formula

Likelihood Ratio

LR+ = sensitivity ÷ (1 − specificity); post-test odds = pre-test odds × LR

likelihood ratio
How much a result shifts the odds of disease
post-test probability
Bayesian update of the pre-test probability

Worked example

With the default values below, Likelihood Ratio Calculator returns Positive Likelihood Ratio of 6.00000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sensitivityaccepts 0–100 %
90 %
Specificityaccepts 0–100 %
85 %
Pre-test probabilityaccepts 0–100 %
20 %

Results

Positive Likelihood Ratio
6.00000
Negative Likelihood Ratio
0.11765
Post-Test Probability After a Positive
60.000%
Post-Test Probability After a Negative
2.857%
Test Usefulness
Moderate diagnostic value

Step by step

  1. 1Values used
  2. 2Likelihood Ratio
  3. 3Positive Likelihood Ratio= 6.00000
  4. 4Negative Likelihood Ratio= 0.11765
  5. 5Post-Test Probability After a Positive= 60.000
  6. 6Post-Test Probability After a Negative= 2.857
  7. 7Test Usefulness= Moderate diagnostic value

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Likelihood Ratio calculated?

LR+ = sensitivity ÷ (1 − specificity); post-test odds = pre-test odds × LR Likelihood ratios convert a test result into a change in odds, which is why they combine so cleanly with pre-test probability. An LR+ above 10 substantially raises the probability of disease.

Why does Likelihood Ratio matter?

A test with excellent sensitivity can still be nearly useless if specificity is poor, and the likelihood ratio is what exposes that.

What values do I need to enter?

This calculator takes 3 inputs: Sensitivity, Specificity, Pre-test probability. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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