# Sensitivity Calculator

URL: https://speedycalculator.com/calculators/statistics/sensitivity/
Last updated: 2026-10-30

> The sensitivity calculator finds a test’s sensitivity (true positive rate, recall) from its true positives and false negatives, together with the miss rate, and – if you add true negatives and false positives – the specificity, predictive values, accuracy and likelihood ratios.

## Inputs

- True positives (TP)
- False negatives (FN)
- Additional parameters (needs TN and FP)
- True negatives (TN)
- False positives (FP)

## Results

- Sensitivity (true positive rate)
- False negative rate (miss rate)
- People with the condition (TP + FN)
- Specificity
- Positive predictive value
- Negative predictive value
- Accuracy
- Positive likelihood ratio
- Negative likelihood ratio

## Formula

```
Sensitivity = TP ÷ (TP + FN)
False negative rate (miss rate) = FN ÷ (TP + FN) = 1 − sensitivity
```

## Explanation

Sensitivity tells you how good a test is at finding the people who really have a condition. Of everyone who has it, what share does the test flag as positive? If 80 people with a disease are tested and 72 test positive, the sensitivity is 72 ÷ 80 = 90% and the remaining 10% are false negatives – cases the test misses.

Highly sensitive tests are used to rule conditions out: if a 99%-sensitive test is negative, the condition is unlikely ("SnNout"). But sensitivity says nothing about false alarms. A test that calls everyone positive has 100% sensitivity and is useless, so sensitivity should always be read together with specificity.

Enter the true positives and false negatives to get the sensitivity and miss rate. Switch on the additional parameters and enter the true negatives and false positives to see the specificity, the positive and negative predictive values for your sample, the accuracy and the likelihood ratios as well.

### How to use the Sensitivity Calculator

- **True positives (TP)**
- **False negatives (FN)**
- **Additional parameters (needs TN and FP)**
- **True negatives (TN)**
- **False positives (FP)**

Results update as you type, and everything is calculated in your browser.

### How it works

Sensitivity divides the true positives by everyone who truly has the condition (TP + FN). The other measures use the full 2 × 2 table when the negatives are entered.

### Worked example

Of 80 patients with a confirmed infection, 72 test positive and 8 negative. Sensitivity = 72 ÷ 80 = 90%; miss rate = 10%. Among 200 uninfected people, 180 test negative and 20 positive, so specificity = 90%, PPV = 72 ÷ 92 = 78.26%, NPV = 180 ÷ 188 = 95.74%, accuracy = 252 ÷ 280 = 90% and LR+ = 0.9 ÷ 0.1 = 9.

### Interpreting sensitivity

SensitivityCases missed per 10099%195%590%1080%2060%40

### Inputs explained

FieldWhat to enterTrue positives (TP)A numberFalse negatives (FN)A numberAdditional parameters (needs TN and FP)Choose one: Show, HideTrue negatives (TN)A numberFalse positives (FP)A number

### What each result means

- **Sensitivity (true positive rate)** = [True positives (TP)]÷([True positives (TP)] + [False negatives (FN)])×100
- **False negative rate (miss rate)** = 100 - [Sensitivity (true positive rate)]
- **People with the condition (TP + FN)** = [True positives (TP)] + [False negatives (FN)]
- **Specificity** = [True negatives (TN)]÷([True negatives (TN)] + [False positives (FP)])×100
- **Positive predictive value** = [True positives (TP)]÷([True positives (TP)] + [False positives (FP)])×100
- **Negative predictive value** = [True negatives (TN)]÷([True negatives (TN)] + [False negatives (FN)])×100
- **Accuracy** = ([True positives (TP)] + [True negatives (TN)])÷([True positives (TP)] + [False negatives (FN)] + [True negatives (TN)] + [False positives (FP)])×100
- **Positive likelihood ratio** = [Sensitivity (true positive rate)]÷(100 - [Specificity])
- **Negative likelihood ratio** = (100 - [Sensitivity (true positive rate)])÷[Specificity]

## Worked example

Inputs — True positives (TP): 72; False negatives (FN): 8; Additional parameters (needs TN and FP): Show; True negatives (TN): 180; False positives (FP): 20.

Results — **Sensitivity (true positive rate) = 90 %**; False negative rate (miss rate) = 10 %; People with the condition (TP + FN) = 80; Specificity = 90 %; Positive predictive value = 78.2609 %; Negative predictive value = 95.7447 %; Accuracy = 90 %; Positive likelihood ratio = 9; Negative likelihood ratio = 0.1111.

## Key terms

- **Sensitivity**: The proportion of true cases that test positive.
- **False negative**: A negative result in someone who has the condition.
- **Miss rate**: FN ÷ (TP + FN) = 1 − sensitivity.

## FAQ

**How do you calculate sensitivity?**
Divide the true positives by all people who have the condition: TP ÷ (TP + FN). 72 ÷ 80 = 90%.

**Is sensitivity the same as recall?**
Yes. Machine learning calls it recall or the true positive rate.

**What is a good sensitivity?**
It depends on the cost of missing a case. Screening tests for serious treatable diseases often aim for 95% or more.

**What does 100% sensitivity mean?**
No cases are missed – every person with the condition tests positive. It does not mean every positive is correct.

**Does sensitivity depend on prevalence?**
Not directly; it is calculated only among people who have the condition. Predictive values do depend on prevalence.

**How do sensitivity and specificity trade off?**
Lowering the positivity threshold catches more cases (higher sensitivity) but flags more healthy people (lower specificity).


## Sources

- [CDC – Sensitivity, specificity and predictive values (Principles of Epidemiology)](https://www.cdc.gov/csels/dsepd/ss1978/lesson5/section1.html)
- [NCBI Bookshelf – Diagnostic testing accuracy: sensitivity, specificity, predictive values and likelihood ratios](https://www.ncbi.nlm.nih.gov/books/NBK557491/)