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Likelihood Ratio Calculator

Find diagnostic likelihood ratios.

How it is calculated

Enter sensitivity and specificity as percentages from 0 to 100. The tool converts them to fractions, Se = sensitivity ÷ 100 and Sp = specificity ÷ 100, and returns two ratios with four decimals: LR+ = Se ÷ (1 − Sp) and LR− = (1 − Se) ÷ Sp. LR+ says how much more often a positive result occurs in people with the condition than in people without it; LR− says the same for a negative result. A ratio of 1 means the result changes nothing. Sensitivity may be 0 to 100, but specificity must be strictly between 0 and 100, because a specificity of 100% would make LR+ a division by zero and the tool returns no result. The ratios do not use prevalence; to get a probability you must combine them with a pre-test probability yourself.

Worked example

A test has 90% sensitivity and 80% specificity. Convert to fractions: Se = 0.90 and Sp = 0.80. For the positive ratio, 1 − Sp = 0.20, so LR+ = 0.90 ÷ 0.20 = 4.5000. For the negative ratio, 1 − Se = 0.10, so LR− = 0.10 ÷ 0.80 = 0.1250. A positive result is therefore 4.5 times as likely in a person with the condition as in one without, and a negative result is only 0.125 times as likely, which lowers suspicion considerably.

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Common mistakes

  • Typing sensitivity and specificity as fractions such as 0.9 and 0.8; the fields are percentages, so those entries are read as 0.9% and 0.8% and give nonsense (LR+ 0.0091).
  • Swapping sensitivity and specificity, which exchanges the roles of the two ratios.
  • Treating an LR as a probability; it is a multiplier on the odds, not a percentage chance of disease.
  • Ignoring the pre-test probability; the same LR+ of 4.5 means very different things in a screening population and in a clinic with symptomatic patients.
  • Entering 100% specificity or 0% specificity to represent a perfect or useless test; the tool rejects those values.

Sources

About this calculator

A diagnostic likelihood ratio tells you how much a test result should shift your belief about whether a patient has a condition. The positive likelihood ratio is LR+ = sensitivity / (1 − specificity), showing how much more likely a positive result is in someone with the disease versus without it; the negative likelihood ratio is LR− = (1 − sensitivity) / specificity, showing how much a negative result should lower suspicion. An LR+ above 10 or LR− below 0.1 is generally considered strong evidence.

Clinicians combine LR with a patient's pre-test probability (based on prevalence and clinical presentation) — often via a Fagan nomogram or Bayes' theorem — to compute the post-test probability of disease, making it central to evidence-based diagnostic reasoning. Epidemiologists use likelihood ratios to evaluate how useful a screening or diagnostic test actually is beyond its raw sensitivity and specificity, and medical students learn LR as a core tool for interpreting lab and imaging results in context.

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Comments (1)

  • Editorial team

    Likelihood ratios act on odds, not on percentages, and the tool stops at the ratios themselves. With the default 90 percent sensitivity and 80 percent specificity, LR+ is 4.5. Start from a 20 percent chance, which is odds of 0.25; multiply to get 1.125, which is about 53 percent after a positive result. That last step you do by hand. This is for learning, not for interpreting your own test. Would a pre-test probability box help you?

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