Sensitivity & Specificity Calculator

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Walk-through

How to Use This Calculator

4 steps

1

Enter the confusion matrix

Fill in the four counts from your test results: true positives (TP, test positive and condition present), false positives (FP, test positive but condition absent), false negatives (FN, test negative but condition present), and true negatives (TN, test negative and condition absent).

2

Read sensitivity and specificity

The Sensitivity/Specificity tab shows the true positive rate and true negative rate together, plus all six rates in one stat grid so you can scan everything at once.

3

Check PPV and NPV for your population

The PPV/NPV tab shows how trustworthy a positive or negative result actually is, plus a live comparison of how those numbers shift if the same test were used on a higher- or lower-prevalence population.

4

Review overall accuracy

The Accuracy tab shows the share of all tests that were correct. Watch for the accuracy trap: a test can score very high accuracy on a rare condition while still missing almost every true case — the calculator flags this automatically.

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Reference

Formula & Methodology

4 formulas

Sensitivity (true positive rate)

Sensitivity = TP / (TP + FN)

Of everyone who actually has the condition, the fraction the test correctly flags as positive. Also called recall or the true positive rate.

Specificity (true negative rate)

Specificity = TN / (TN + FP)

Of everyone who does not have the condition, the fraction the test correctly clears as negative.

PPV and NPV

PPV = TP / (TP + FP) · NPV = TN / (TN + FN)

PPV (positive predictive value, also called precision) is the probability a positive result is a true positive. NPV is the probability a negative result is a true negative. Unlike sensitivity and specificity, both depend heavily on how common the condition is in the population being tested (prevalence).

Accuracy and prevalence

Accuracy = (TP + TN) / (TP + FP + FN + TN) · Prevalence = (TP + FN) / (TP + FP + FN + TN)

Accuracy is the share of all test results that were correct. Prevalence is the share of the tested population that actually has the condition — it is a property of the population, not the test, and it's the reason PPV and NPV can look very different across settings even for the exact same test.

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Glossary

Key Terms Explained

8 terms

Sensitivity The true positive rate — the proportion of people who actually have the condition that the test correctly identifies as positive. High sensitivity means few missed cases (few false negatives).

Specificity The true negative rate — the proportion of people who do not have the condition that the test correctly identifies as negative. High specificity means few false alarms (few false positives).

Positive predictive value (PPV) Also called precision — the probability that a person who tests positive actually has the condition. PPV rises with prevalence and with specificity.

Negative predictive value (NPV) The probability that a person who tests negative actually does not have the condition. NPV falls as prevalence rises, even with a highly sensitive test.

Accuracy The overall proportion of test results — positive and negative combined — that match the true condition status: (TP + TN) divided by the total tested. Can be misleadingly high when one class is rare.

True positive / false positive A true positive is a positive test result in someone who actually has the condition. A false positive is a positive result in someone who does not — a false alarm.

Prevalence The proportion of the tested population that actually has the condition: (TP + FN) divided by the total. A property of the population being tested, not of the test itself — and the main reason the same test can have very different PPV in different settings.

Confusion matrix The 2×2 table of TP, FP, FN, and TN counts that summarizes how a test's predictions line up against the true condition status. Every rate on this page is derived from these four numbers.

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Scenarios

Real-World Examples

3 worked examples

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Basic 2×2 → all rates

TP=40, FP=10, FN=5, TN=45 (N=100)

TP 40 FP 10 FN 5 TN 45

Sensitivity = 40/45 = 88.9%. Specificity = 45/55 = 81.8%. PPV = 40/50 = 80.0%. NPV = 45/50 = 90.0%. Accuracy = 85/100 = 85.0%. Prevalence = 45/100 = 45.0%. With a round total of 100, every rate reads directly off the counts.

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PPV depends on prevalence

Same 90% sensitivity / 95% specificity test, two populations

High-prevalence: TP 450 High-prevalence: FP 25 High-prevalence: FN 50 High-prevalence: TN 475

In a symptomatic clinic population where 50% actually have the condition (N=1000: 500 with, 500 without), this test gives PPV = 450/475 = 94.7% and NPV = 475/525 = 90.5%. Applied to a general-population screening setting where only 1% have the condition (N=10,000: 100 with, 9,900 without), the same 90%-sensitive, 95%-specific test gives TP=90, FN=10, FP=495, TN=9,405 — PPV collapses to 90/585 = 15.4%, even though sensitivity and specificity haven't changed at all. NPV moves the other way, rising to 9,405/9,415 = 99.9%.

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Accuracy can mislead

TP=0, FP=0, FN=20, TN=980 (N=1000)

TP 0 FP 0 FN 20 TN 980

A test that always reports negative, used where only 2% of the population has the condition, scores 98.0% accuracy — but its sensitivity is 0.0%: it catches none of the 20 true cases. PPV is undefined here too (there were zero positive test results to be right or wrong about). This is why accuracy alone is a poor summary for rare conditions, and why sensitivity and specificity are reported separately.

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Deep Dive

Understanding Sensitivity, Specificity, PPV, and NPV

3 chapters · 3 min read

Sensitivity and specificity describe how well a diagnostic test performs against the true condition status — but they don't tell you what a single positive or negative result means for the person who got it. That's what PPV and NPV are for, and why the same test can look very different depending on the population it's used on.

How the calculator works

Enter the four counts from your confusion matrix — true positives, false positives, false negatives, true negatives — and the calculator derives sensitivity, specificity, PPV, NPV, accuracy, and prevalence directly from those counts. Each rate has its own denominator (sensitivity and specificity look only at the true condition status; PPV and NPV look only at the test result), so a zero count in one denominator doesn't stop the other rates from being computed.

Why PPV and NPV move with prevalence, but sensitivity and specificity don't

Sensitivity and specificity are properties of the test itself — how well it distinguishes sick from healthy, holding for any population it's used on. PPV and NPV are properties of a test in a given population, because they answer a different question: given a result, what's the chance it's right? At low prevalence, even a small false-positive rate produces far more false alarms than true catches, dragging PPV down sharply — the same math behind why universal screening for rare conditions produces so many false alarms, and why doctors weigh pre-test probability before ordering a test.

Reading accuracy carefully

Accuracy folds everything into one number, which makes it easy to over-trust. On a rare condition, a test (or even a rule that always predicts 'negative') can score high accuracy while being clinically useless — it simply benefits from the condition being uncommon. Always check accuracy alongside sensitivity and specificity, not instead of them.

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Questions

Frequently Asked Questions

6 questions

What is sensitivity?+

Sensitivity is the true positive rate — the proportion of people who actually have the condition that the test correctly identifies as positive. Sensitivity = TP / (TP + FN).

What is specificity?+

Specificity is the true negative rate — the proportion of people who don't have the condition that the test correctly identifies as negative. Specificity = TN / (TN + FP).

What is PPV?+

PPV (positive predictive value) is also called precision — the probability that someone who tests positive actually has the condition. PPV = TP / (TP + FP), and unlike sensitivity, it depends on how common the condition is in the tested population.

How does prevalence affect PPV and NPV?+

Lower prevalence pulls PPV down and pushes NPV up, even with the exact same sensitivity and specificity, because at low prevalence false positives outnumber true positives among all positive results. See the worked example above comparing 50% vs 1% prevalence with the same test.

What is accuracy?+

Accuracy is the overall share of correct results: (TP + TN) divided by the total tested. It can be misleadingly high on rare conditions — check sensitivity and specificity too, not accuracy alone.

What about F1 score — is it related?+

F1 is the harmonic mean of PPV (precision) and sensitivity (recall): F1 = 2 × (PPV × Sensitivity) / (PPV + Sensitivity). You can compute it from the PPV and Sensitivity values shown here.

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Sensitivity and Specificity Calculator

Confusion Matrix

Same test, different prevalence

Methodology, sources, and limitations

How to Use This Calculator

Enter the confusion matrix

Read sensitivity and specificity

Check PPV and NPV for your population

Review overall accuracy

Formula & Methodology

Key Terms Explained

Real-World Examples

Basic 2×2 → all rates

PPV depends on prevalence

Accuracy can mislead

Understanding Sensitivity, Specificity, PPV, and NPV

How the calculator works

Why PPV and NPV move with prevalence, but sensitivity and specificity don't

Reading accuracy carefully

Frequently Asked Questions

Get a branded PDF of your results

Sensitivity and Specificity Calculator

Confusion Matrix

Sensitivity and Specificity Result

PPV and NPV Result

Same test, different prevalence

Accuracy Result

Methodology, sources, and limitations

How to Use This Calculator

Enter the confusion matrix

Read sensitivity and specificity

Check PPV and NPV for your population

Review overall accuracy

Formula & Methodology

Key Terms Explained

Real-World Examples

Understanding Sensitivity, Specificity, PPV, and NPV

How the calculator works

Why PPV and NPV move with prevalence, but sensitivity and specificity don't

Reading accuracy carefully

Frequently Asked Questions

Get a branded PDF of your results

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