**Try this Sensitivity and Specificity Calculator in medical diagnostics, scientific research, and data analysis to evaluate the performance of binary classification tests. **

The calculator typically requires input of four key values:

**True Positives (TP)**: Correctly identified positive cases**False Positives (FP)**: Incorrectly identified positive cases**True Negatives (TN)**: Correctly identified negative cases**False Negatives (FN)**: Incorrectly identified negative cases

## Sensitivity and Specificity Calculator

This calculator helps you determine the sensitivity and specificity of a test.

Sensitivity (True Positive Rate) is calculated as: TP / (TP + FN)

Specificity (True Negative Rate) is calculated as: TN / (TN + FP)

Scenario | True Positives (TP) | False Positives (FP) | True Negatives (TN) | False Negatives (FN) | Sensitivity | Specificity |
---|---|---|---|---|---|---|

Test A | 90 | 10 | 180 | 20 | 81.82% | 94.74% |

Test B | 75 | 5 | 195 | 25 | 75.00% | 97.50% |

Test C | 95 | 15 | 175 | 15 | 86.36% | 92.11% |

Test D | 50 | 2 | 198 | 50 | 50.00% | 99.00% |

Test E | 99 | 30 | 160 | 11 | 90.00% | 84.21% |

**Calculations:**

**Test A**- Sensitivity = 90 / (90 + 20) = 81.82%
- Specificity = 180 / (180 + 10) = 94.74%

**Test B**- Sensitivity = 75 / (75 + 25) = 75.00%
- Specificity = 195 / (195 + 5) = 97.50%

**Test C**- Sensitivity = 95 / (95 + 15) = 86.36%
- Specificity = 175 / (175 + 15) = 92.11%

**Test D**- Sensitivity = 50 / (50 + 50) = 50.00%
- Specificity = 198 / (198 + 2) = 99.00%

**Test E**- Sensitivity = 99 / (99 + 11) = 90.00%
- Specificity = 160 / (160 + 30) = 84.21%

**These are some key points from these sample calculations:**

**Trade-off between Sensitivity and Specificity**: Notice how tests with high sensitivity often have slightly lower specificity, and vice versa. For example, Test E has the highest sensitivity (90.00%) but the lowest specificity (84.21%) among all tests.**Balanced Performance**: Test A and Test C show relatively balanced performance, with both sensitivity and specificity above 80%. These tests might be preferred in situations where both false positives and false negatives are equally concerning.**High Specificity Test**: Test D shows very high specificity (99.00%) but low sensitivity (50.00%). This type of test would be good at ruling in a condition when positive but might miss many positive cases.**High Sensitivity Test**: Test E has the highest sensitivity (90.00%) but the lowest specificity (84.21%). This test would be good at ruling out a condition when negative but might have more false positives.**Impact of False Results**: Test B and Test D have the same number of total tests (300) but different distributions of false results.

## How to Calculate Sensitivity and Specificity

Calculating sensitivity and specificity involves a step-by-step process:

**Gather data**: Collect the results of your diagnostic test and the true condition status for each subject.**Categorize results**: Sort the data into four categories:

- True Positives (TP)
- False Positives (FP)
- True Negatives (TN)
- False Negatives (FN)

**Calculate Sensitivity**:

- Use the formula: Sensitivity = TP / (TP + FN)
- This measures the test’s ability to correctly identify positive cases.

**Calculate Specificity**:

- Use the formula: Specificity = TN / (TN + FP)
- This measures the test’s ability to correctly identify negative cases.

**Interpret results**:

- Sensitivity and specificity are expressed as percentages or decimal values between 0 and 1.
- Higher values indicate better test performance.

**More Calculators : – Mean Absolute Deviation Calculator – Binomial Probability Distribution Calculator**

## Sensitivity and Specificity Calculation Formula

The formulas for calculating sensitivity and specificity are straightforward:

**Sensitivity Formula**:

`Sensitivity = TP / (TP + FN)`

Where:

- TP = True Positives
- FN = False Negatives

**Specificity Formula**:

`Specificity = TN / (TN + FP)`

Where:

- TN = True Negatives
- FP = False Positives

## What is Sensitivity and Specificity?

**Sensitivity** and **specificity** are two fundamental measures used to assess the performance of diagnostic tests, particularly in medical and scientific fields.

**Sensitivity**, also known as the **true positive rate** or **recall**, measures the proportion of actual positive cases that are correctly identified by a test. It answers the question: “Of all the subjects who have the condition, how many were correctly identified by the test?” A highly sensitive test will rarely miss positive cases, making it useful for **ruling out** a condition when the result is negative.

**Specificity**, also called the **true negative rate**, measures the proportion of actual negative cases that are correctly identified by a test. It answers the question: “Of all the subjects who do not have the condition, how many were correctly identified by the test?” A highly specific test will have few false positives, making it useful for **confirming** a condition when the result is positive.

Understanding both sensitivity and specificity is crucial because they often involve a trade-off. Increasing one may decrease the other, depending on how the test’s threshold is set. This relationship is often visualized using a **Receiver Operating Characteristic (ROC) curve**.