Sensitivity Calculator

Compute a diagnostic test's sensitivity (true positive rate) from the number of true positives and false negatives: Sensitivity = TP / (TP + FN).

Quick Facts

Formula
Sensitivity = TP / (TP + FN)
The share of true cases the test correctly flags positive. TP + FN is the total number of people who actually have the condition.

Your Results

Calculated
Sensitivity
-
TP / (TP + FN), as a percentage
Sensitivity (proportion)
-
Same value on a 0–1 scale
False negative rate
-
1 − sensitivity: true cases missed
Actual positives
-
TP + FN (people who have the condition)

Ready

Enter true positives and false negatives, then calculate.

What sensitivity measures

Sensitivity — also called the true positive rate (TPR), recall, or the hit rate — is the proportion of people who genuinely have a condition that a test correctly identifies as positive. It answers a single question: of everyone who actually has the disease, how many does the test catch?

The formula is:

Sensitivity = TP / (TP + FN)

Here TP (true positives) is the number of diseased people who test positive, and FN (false negatives) is the number of diseased people the test wrongly clears. The denominator TP + FN is the total number of people who actually have the condition. Sensitivity is always a value between 0 and 1 (0% to 100%), and it depends only on the diseased group — it says nothing about people who are healthy.

Worked example

Suppose 100 people in a study truly have a disease. A screening test flags 90 of them as positive and misses 10. Then TP = 90, FN = 10, and sensitivity = 90 / (90 + 10) = 90 / 100 = 0.90, or 90%. The 10 missed cases are false negatives, giving a false negative rate of 1 − 0.90 = 10%.

Why sensitivity matters

A highly sensitive test is good at ruling a condition out: because it rarely misses true cases, a negative result is trustworthy. This is captured by the mnemonic SnNout — a highly Snsensitive test with a Nnegative result rules the disease out. Screening tests (for cancer, infectious disease, or newborn conditions) are deliberately built for high sensitivity, because the cost of missing a real case is severe.

Sensitivity versus specificity

Sensitivity has a mirror-image partner, specificity = TN / (TN + FP), the true negative rate. Sensitivity uses only sick people; specificity uses only healthy people. The two are usually in tension: lowering a test's positivity threshold catches more true cases (higher sensitivity) but also raises false alarms (lower specificity). A complete evaluation of a test reports both, often alongside predictive values, which — unlike sensitivity — also depend on how common the disease is (prevalence).

Typical reference values

  • A rapid antigen test for a respiratory virus might have sensitivity around 70–85% (it misses some genuine infections).
  • A well-run PCR or laboratory reference test often reaches 95–99% sensitivity.
  • Mammography screening sensitivity is commonly cited near 85%, varying with breast density.
  • Sensitivity of 100% means the test never misses a true case (FN = 0); sensitivity of 0% means it catches none.

Frequently Asked Questions

What is sensitivity in a diagnostic test?
Sensitivity is the proportion of people who actually have the condition that the test correctly identifies as positive. It equals TP / (TP + FN), where TP is true positives and FN is false negatives. A test with 95% sensitivity misses 5% of true cases as false negatives.
What is the difference between sensitivity and specificity?
Sensitivity measures how well a test detects people who have the disease: TP / (TP + FN), using only the diseased group. Specificity measures how well it clears people who do not have it: TN / (TN + FP), using only the non-diseased group. A test can be high in one and low in the other; raising sensitivity by lowering the positivity threshold usually lowers specificity.
Is sensitivity the same as recall or the true positive rate?
Yes. In machine learning and information retrieval the same quantity — TP / (TP + FN) — is called recall or the true positive rate (TPR). Whether you call it sensitivity, recall, or TPR, the arithmetic is identical.
Does sensitivity depend on how common the disease is?
No. Sensitivity is a property of the test measured within the diseased group only, so it does not change with prevalence. Positive and negative predictive values do depend on prevalence — that is why a very sensitive test can still produce many false positives when a disease is rare.

Related calculators