# Sensitivity and Specificity Calculator

URL: https://speedycalculator.com/calculators/statistics/sensitivity-specificity/
Last updated: 2026-10-25

> This calculator evaluates a diagnostic or classification test from true and false positives and negatives. It gives sensitivity, specificity, predictive values, accuracy and likelihood ratios.

## Inputs

- True positives
- False positives
- False negatives
- True negatives

## Results

- Sensitivity (recall)
- Specificity
- Positive predictive value (precision)
- Negative predictive value
- Accuracy
- F1 score
- Positive likelihood ratio

## Formula

```
Sensitivity = TP ÷ (TP + FN)
Specificity = TN ÷ (TN + FP)
PPV = TP ÷ (TP + FP)
```

## Explanation

A test can be very sensitive yet produce many false positives if the condition is rare, which is why predictive values matter.

### How to use the Sensitivity and Specificity Calculator

- **True positives**
- **False positives**
- **False negatives**
- **True negatives**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Each metric is a ratio of counts from the confusion matrix.

### Inputs explained

FieldWhat to enterTrue positivesA numberFalse positivesA numberFalse negativesA numberTrue negativesA number

### What each result means

- **Sensitivity (recall)** = [True positives]÷([True positives] + [False negatives])×100
- **Specificity** = [True negatives]÷([True negatives] + [False positives])×100
- **Positive predictive value (precision)** = [True positives]÷([True positives] + [False positives])×100
- **Negative predictive value** = [True negatives]÷([True negatives] + [False negatives])×100
- **Accuracy** = ([True positives] + [True negatives])÷([True positives] + [False positives] + [False negatives] + [True negatives])×100
- **F1 score** = 2×[True positives]÷(2×[True positives] + [False positives] + [False negatives])
- **Positive likelihood ratio** = ([Sensitivity (recall)]÷100)÷(1 - [Specificity]÷100)

### Example values

How the main result changes when **True positives** changes and everything else stays at the example values above:

True positivesSensitivity (recall) (%)4581.8267.587.19090112.591.8413593.118094.74

## Worked example

Inputs — True positives: 90; False positives: 40; False negatives: 10; True negatives: 860.

Results — **Sensitivity (recall) = 90 %**; Specificity = 95.56 %; Positive predictive value (precision) = 69.23 %; Negative predictive value = 98.85 %; Accuracy = 95 %; F1 score = 0.7826; Positive likelihood ratio = 20.25.

## FAQ

**Why is PPV low for rare diseases?**
Even a small false-positive rate produces many false positives when most people are healthy.

**What is the F1 score?**
The harmonic mean of precision and recall.

**What formula does the Sensitivity and Specificity Calculator use?**
Sensitivity = TP ÷ (TP + FN).