statistics

Sensitivity Calculator

Sensitivity measures how well a diagnostic test catches true disease cases. Medical professionals, epidemiologists, and researchers use this metric to evaluate test reliability—especially when false negatives carry serious consequences. Calculate sensitivity by entering confirmed positive cases and missed diagnoses, then instantly see how your test performs at detecting actual disease.

Last updated: May 8, 2026

Creators Wojciech Sas, PhD

Reviewers Anna Szczepanek and Davide Borchia

7,518 people find this calculator helpful

Sensitivity Formula

Sensitivity quantifies the ability of a diagnostic test to correctly identify individuals who have the disease. It answers the question: of all people with the condition, what percentage will test positive?

Sensitivity = TP ÷ (TP + FN)

TP — True positives—the number of individuals with disease who tested positive
FN — False negatives—the number of individuals with disease who tested negative

Understanding Diagnostic Sensitivity

Sensitivity and specificity form the foundation of evaluating any diagnostic test's performance. Unlike predictive values, which depend on disease prevalence, sensitivity is an intrinsic property of the test itself—it remains constant regardless of how common the disease is in your population.

A test with high sensitivity (typically >90%) is excellent at ruling out disease when the result is negative. If someone tests negative on a highly sensitive test, clinicians can be confident they likely don't have the condition. Conversely, a positive result on a high-sensitivity test doesn't guarantee disease presence—it could still be a false positive.

This is why understanding both sensitivity and specificity matters. Sensitivity tells you about false negatives; specificity addresses false positives. In screening programs where missing cases is catastrophic (tuberculosis, cancer), clinicians prioritise high sensitivity. When false alarms are costly (confirming rare conditions), specificity becomes critical.

Key Pitfalls When Using Sensitivity

Common mistakes when interpreting or applying sensitivity in clinical or research contexts:

Confusing sensitivity with positive predictive value — A test can be highly sensitive yet have low positive predictive value if the disease is rare. High sensitivity means few people with disease are missed, not that a positive result confirms disease. Always consider disease prevalence and specificity together.
Ignoring prevalence when making clinical decisions — Sensitivity alone doesn't tell you the probability of disease given a positive test. That's positive predictive value, which incorporates prevalence. A 95% sensitive test for a disease affecting 1 in 10,000 people will still have many false positives.
Assuming sensitivity applies to all populations equally — Sensitivity is theoretically constant, but real-world variations in patient age, symptom severity, or test administration can shift results. Always validate test performance in your specific population, not just in published studies.
Using sensitivity to compare different test types — Only compare sensitivity when both tests operate on the same outcome definition. A blood test and imaging scan may define disease differently, making direct sensitivity comparison misleading.

Interpreting Test Results With Sensitivity

Knowing your test's sensitivity helps you understand what a negative result means—and what it doesn't mean about a positive one.

Negative result on a high-sensitivity test: Very reassuring. If sensitivity is 95% and you test negative, disease is unlikely (though never impossible).

Positive result on a high-sensitivity test: Doesn't confirm disease. Sensitivity only addresses false negatives. You still need specificity and prevalence to calculate the actual probability of having the disease given that positive result.

Negative result on a low-sensitivity test: Less reassuring. The test may have missed your disease. Further testing or clinical evaluation is warranted.

Positive result on a low-sensitivity test: May still indicate disease, but many cases slip through undetected. This test alone is insufficient for screening.

Likelihood ratios—derived from sensitivity and specificity—often communicate test utility more intuitively than sensitivity alone. A positive likelihood ratio >10 means a positive result substantially increases the probability of disease.

The sensitivity calculator derives several interconnected statistics from the confusion matrix. These values help construct a complete picture of test performance:

Specificity = TN ÷ (FP + TN)

Positive Likelihood Ratio = Sensitivity ÷ (1 − Specificity)

Negative Likelihood Ratio = (1 − Sensitivity) ÷ Specificity

Positive Predictive Value = (Sensitivity × Prevalence) ÷ [(Sensitivity × Prevalence) + ((1 − Specificity) × (1 − Prevalence))]

Accuracy = (TP + TN) ÷ (TP + TN + FP + FN)

TN — True negatives—individuals without disease who tested negative
FP — False positives—individuals without disease who tested positive
Prevalence — The proportion of the population that has the disease

Frequently Asked Questions

Why does a positive result on a sensitive test not guarantee I have the disease?

Sensitivity only measures how well a test detects disease in people who have it. It completely ignores false positives—people without disease who still test positive. If a disease is rare, even a 99% sensitive test will produce many false positives. To know the actual probability of disease given a positive result, you need positive predictive value, which combines sensitivity, specificity, and disease prevalence. Always ask your clinician for the positive predictive value or likelihood ratios rather than sensitivity alone.

When should clinicians prioritise sensitivity over specificity?

High sensitivity is critical in screening and rule-out scenarios where missing disease is dangerous. If undetected disease leads to serious harm—like screening for cancer, tuberculosis, or coronary artery disease—a sensitive test minimises missed cases. The downside is more false alarms, requiring additional confirmatory tests. Conversely, specificity matters most when confirming a suspected diagnosis or when false positives trigger unnecessary, harmful interventions. Many clinical pathways use high-sensitivity screening followed by high-specificity confirmatory testing to balance these competing concerns.

How do I calculate sensitivity if I only have test percentages, not raw numbers?

If you know sensitivity as a percentage (e.g., 92%), you already have the answer—percentages are equivalent to sensitivity values expressed as proportions. However, if you have sensitivity expressed as a ratio or percentage and need to find raw true positives or false negatives, rearrange the formula: true positives = sensitivity × (true positives + false negatives). You'll need additional information (total diseased individuals or the other cell count) to solve for unknowns. The sensitivity calculator automates this algebra if you provide raw numbers.

Does sensitivity change if I test different populations?

Theoretically, sensitivity is an intrinsic property of the test and should remain constant. In practice, real-world factors introduce variation: age, comorbidities, disease severity, sample quality, operator expertise, and even disease definition can shift results. A test validated in a hospital population with symptomatic disease may perform differently in asymptomatic screening or in a primary care setting. Always verify published sensitivity in your specific population context before relying on it for clinical decisions.

What's the relationship between sensitivity and false negatives?

They're inversely related. If sensitivity is 90%, then 10% of diseased individuals are false negatives—they have disease but tested negative. Higher sensitivity means fewer false negatives. A test with 99% sensitivity misses disease in only 1% of people who have it. This is why high-sensitivity tests are preferred for rule-out decisions: a negative result makes disease unlikely. However, sensitivity doesn't tell you about false positives, which depend on specificity instead.

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