How this calculator works
Convert the prior probability to odds, multiply by the likelihood ratio for the result, then convert back to probability. A positive-result likelihood ratio is sensitivity divided by one minus specificity; a negative-result ratio is one minus sensitivity divided by specificity. The implementation uses the equivalent Bayes expression to handle perfect-test boundaries without multiplying infinity by zero. In direct-ratio mode, enter the ratio that already corresponds to the observed result; the result label does not invert it. Use clinically relevant evidence and professional interpretation for real tests.
Formula
Prior odds = p/(1 - p). LR+ = sensitivity/(1 - specificity). LR- = (1 - sensitivity)/specificity. Posterior odds = prior odds × LR. Posterior probability = p LR / (1 - p + p LR).
Worked example
With prior probability 10%, sensitivity 80% and specificity 90%, a positive result gives 0.08/(0.08 + 0.09) = 47.06%. A negative result gives 0.02/(0.02 + 0.81) = 2.41%.
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Frequently asked questions
Which likelihood ratio should I enter?
Use LR+ for a positive result or LR- for a negative result. Direct-ratio mode treats the entered ratio as evidence for the observed result.
Can repeated tests be multiplied together?
Only when the required conditional-independence assumptions hold. Repeated or related tests often share errors, so simple multiplication can overstate evidence.
Does a negative result eliminate the condition?
Usually it reduces the modelled probability without making it zero. The effect depends on sensitivity, specificity and the prior, and requires clinical context.