Sensitivity & Specificity Calculator
Enter true positives, false positives, false negatives and true negatives to get sensitivity, specificity, predictive values, likelihood ratios, the diagnostic odds ratio, accuracy, F1 and Youden's J — each proportion with a Wilson 95% confidence interval. A second mode starts from sensitivity, specificity and prevalence and shows, person by person, why a positive result means less when a condition is rare. Free, no sign-up, and it runs in your browser.
| Condition present | Condition absent | Total | |
|---|---|---|---|
| Test positive | 0 | ||
| Test negative | 0 | ||
| Total | 0 | 0 | 0 |
Enter TP, FP, FN and TN to see sensitivity, specificity, predictive values and likelihood ratios.
How to Use the Sensitivity & Specificity Calculator
- 1. Choose your starting point. Use A 2 × 2 table of counts when you have study data, or Sensitivity, specificity and prevalence when you know the test's characteristics and want predictive values for a particular population.
- 2. Enter the counts. Compare every test result with the reference standard: true positives (TP), false positives (FP), false negatives (FN) and true negatives (TN). Row and column totals fill in so you can check them.
- 3. Read the table of measures. Each proportion comes with a Wilson 95% confidence interval; likelihood ratios and the diagnostic odds ratio use the log method.
- 4. Explore prevalence. In the second mode, change the prevalence and watch the positive predictive value move while sensitivity and specificity stay fixed.
Formulas: What Each Measure Tells You
| Measure | Formula | Question it answers |
|---|---|---|
| Sensitivity | TP / (TP + FN) | Of people with the condition, what share test positive? |
| Specificity | TN / (TN + FP) | Of people without it, what share test negative? |
| Positive predictive value | TP / (TP + FP) | If the test is positive, how likely is the condition? |
| Negative predictive value | TN / (TN + FN) | If the test is negative, how likely is its absence? |
| Positive likelihood ratio | Sensitivity / (1 − specificity) | How much does a positive result raise the odds? |
| Negative likelihood ratio | (1 − sensitivity) / specificity | How much does a negative result lower the odds? |
| Diagnostic odds ratio | (TP × TN) / (FP × FN) | One-number summary of discrimination, LR+ / LR− |
| Youden's J | Sensitivity + specificity − 1 | How far above a useless test (J = 0)? |
| F1 score | 2TP / (2TP + FP + FN) | Harmonic mean of PPV and sensitivity |
Proportions get Wilson score intervals, which stay inside 0–100% and behave well when a value is near 100%, where the simple Wald interval fails. Likelihood ratios use the log method of Simel, Samsa and Matchar (1991): SE(ln LR+) = √(1/TP − 1/(TP + FN) + 1/FP − 1/(FP + TN)), with the mirror-image formula for LR−.
Worked Example: A Rapid Test in 1,000 People
A rapid test is checked against a laboratory reference in 1,000 people, 100 of whom have the infection. It is positive in 90 of the 100 (TP = 90, FN = 10) and in 40 of the 900 without it (FP = 40, TN = 860). Press Load example to enter these counts.
| Measure | Estimate | 95% CI |
|---|---|---|
| Sensitivity | 90.0% | 82.6% – 94.5% |
| Specificity | 95.6% | 94.0% – 96.7% |
| Positive predictive value | 69.2% | 60.8% – 76.5% |
| Negative predictive value | 98.9% | 97.9% – 99.4% |
| Positive likelihood ratio | 20.25 | 14.85 – 27.61 |
| Negative likelihood ratio | 0.10 | 0.06 – 0.19 |
Sensitivity is 90 / 100 = 90.0% and specificity 860 / 900 = 95.6%. Of the 130 positive results, 90 are correct, so PPV = 69.2%. A positive result multiplies the odds of infection by about 20 (LR+ = 0.900 / (40/900) = 20.25), and a negative result cuts them to about a tenth (LR− = 0.10). Youden's J is 0.856 and the diagnostic odds ratio 193.5.
Why the Positive Predictive Value Collapses at Low Prevalence
Sensitivity and specificity belong to the test; predictive values belong to the test and the population. Switch to the second mode and enter a sensitivity of 90%, a specificity of 95% and a prevalence of 1%, as in community screening. Out of 10,000 people, 100 have the condition and 90 of them test positive. Of the 9,900 who do not, 5% — 495 people — also test positive. So only 90 of the 585 positive results are real, and PPV = 15.4%, even though the test is the same one.
| Prevalence | PPV | NPV |
|---|---|---|
| 0.1% | 1.8% | 100.0% |
| 1% | 15.4% | 99.9% |
| 5% | 48.6% | 99.4% |
| 10% | 66.7% | 98.8% |
| 20% | 81.8% | 97.4% |
| 50% | 94.7% | 90.5% |
This is Bayes' theorem at work: PPV = Se·π / (Se·π + (1 − Sp)(1 − π)), where π is the prevalence. When a condition is rare, the few true positives are swamped by false positives from the much larger healthy group, which is why screening programmes confirm positive results with a second, more specific test. (At 0.1% prevalence, NPV is 99.99%, shown rounded to 100.0%.)
Reporting and Common Mistakes
The STARD 2015 guidelines for diagnostic accuracy studies ask for the 2 × 2 table and estimates with 95% confidence intervals. A results sentence might read: "Sensitivity was 90.0% (95% CI 82.6–94.5%) and specificity 95.6% (95% CI 94.0–96.7%)." The Copy result button produces that line with the predictive values added.
- Quoting PPV and NPV from a case-control sample. If you recruited 100 patients and 100 controls, the sample prevalence is 50% by design and the predictive values do not apply to anyone. Recompute them at a realistic prevalence.
- Confusing sensitivity with PPV. Sensitivity is about people who have the condition; PPV is about people who test positive. They answer different questions.
- Treating accuracy as the headline. With a rare condition, a test that calls everyone negative scores high accuracy and is useless. Report sensitivity and specificity separately.
- Ignoring imperfect reference standards. If the reference test misses cases, every measure here is biased; say what the reference was.
Frequently Asked Questions
- What is the difference between sensitivity and specificity?
- Sensitivity is the share of people with the condition whom the test correctly calls positive; specificity is the share of people without it whom the test correctly calls negative. A highly sensitive test rarely misses cases, so a negative result helps rule the condition out. A highly specific test rarely raises false alarms, so a positive result helps rule it in.
- Why do positive and negative predictive values change with prevalence?
- Because they depend on how many people in the tested group have the condition. At low prevalence, even a small false-positive rate applied to the large healthy group produces more false positives than there are true positives, so PPV falls; NPV rises. Sensitivity and specificity, by contrast, do not change with prevalence in principle.
- What is a good likelihood ratio?
- A common guide treats LR+ above 10 and LR− below 0.1 as large, conclusive shifts in probability; 5–10 and 0.1–0.2 as moderate; 2–5 and 0.2–0.5 as small; and values near 1 as useless. Multiply the pre-test odds by the likelihood ratio to get the post-test odds, which is what makes likelihood ratios portable between populations.
- How are the confidence intervals calculated?
- Each proportion — sensitivity, specificity, PPV, NPV, accuracy and prevalence — uses the Wilson score interval. Likelihood ratios and the diagnostic odds ratio use the log method: the interval is built on the log scale and exponentiated. Intervals assume the cases are independent; clustered data, such as several lesions per patient, need wider ones.
- What happens if one of the cells is zero?
- Proportions still get a Wilson interval, which handles 0% and 100% gracefully. Likelihood ratios and the diagnostic odds ratio can become infinite or have undefined intervals: if FP is 0, LR+ is infinite and is shown as not estimable. Some researchers add 0.5 to each cell in that case; if you do, say so.
- Is sensitivity the same as recall, and PPV the same as precision?
- Yes. Machine-learning papers call sensitivity recall and PPV precision, and the F1 score is their harmonic mean. Specificity is sometimes called the true negative rate, and 1 − specificity the false positive rate.