True positive
True negative
False positive
False negative
Prevalence
%
Results
Sensitivity
%
Specificity
%
Positive likelihood ratio
Negative likelihood ratio
PPV
%
NPV
%
Accuracy
%

# Sensitivity And Specificity Calculator

By Łucja Zaborowska

Our sensitivity and specificity calculator is the quickest way to calculate all the necessary data needed for medical research statistics and test evaluation.

With our online sensitivity and specificity calculator you're able to compute PPV, NPV, the positive and negative likelihood ratio and the accuracy.

We'll show you how to calculate the negative predictive value from sensitivity and specificity, explain the sensitivity of a test, and describe all you need to know about the NPV and PPV in statistics.

## How to use the sensitivity and specificity calculator?

Calculating sensitivity, specificity, PPV, and NPV requires the same four pieces of information:

1. Number of true positive cases (TP) ✅✅

Number of people with the disease who tested positive.

2. Number of true negative cases (TN) ❌❌

Number of people without the disease who tested negative.

3. Number of false positive cases (FP) ❌✅

Number of people without the disease who tested positive.

4. Number of false negative cases (FN) ✅❌

Number of people with the disease who tested negative.

↓ Find these values with our 2x2 table method presented below. ↓

2x2 table for sensitivity and specificity

Take a longer look at the table - it's an easy, visual way to understand the meaning of all presented variables.

## How to calculate sensitivity and specificity?

1. How to calculate sensitivity?

Sensitivity - the proportion of people with the disease who tested positive compared to the number of all the people with the disease, regardless of their test result.

To calculate sensitivity, we'll need:

• Number of true positive cases (TP); and
• Number of false negative cases (FN).

And the following sensitivity equation:

`Sensitivity = TP / (TP + FN)`

1. How to calculate specificity?

Specificity - the proportion of healthy people that tested negative compared to the total number of people without the disease, no matter their test result.

To calculate specificity, we'll need:

• Number of true negative cases (TN); and
• Number of false positive cases (FP).

And the following specificity equation:

`Specificity = TN / (FP + TN)`

We have plenty of other statistics calculations ready for you:

 💡 TP + FN = Total number of people with the disease; and TN + FP = Total number of people without the disease.

## How to calculate positive predictive value? - PPV, NPV

Here we present the theoretical basis of our NPV and PPV calculator - this is how we can calculate the Negative Predictive Value from sensitivity and specificity.

You'll need:

• Sensitivity (also: true positive, false negative);
• Specificity (also: true negative, false positive); and
• Prevalence - the amount of the population affected by a particular disease at the time you are interested in, given in %.

Follow the Positive Predictive Value formula (PPV) presented below:

`PPV = (Sensitivity * Prevalence)/[(Sensitivity * Prevalence) + ((1 - Specificity) * (1 - Prevalence))]`

PPV depends on the prevalence - it measures the precision of a test, which is the probability that a positive test result is indeed correct.

Negative Predictive Value formula (NPV):

`NPV =(Specificity * (1 - Prevalence))/[((1 - Sensitivity) * Prevalence) + (Specificity * (1 - Prevalence))]`

NPV also depends on the prevalence of the disease - it describes the probability that a negative test result is indeed correct.

## Likelihood ratio calculators

In this section, we'll explain the principles behind our probability ratios calculator.

Both positive and negative likelihood ratios describe the value of a test. They represent the possibility that the person with the disease will test positive and that the healthy person will test negative, respectively.

1. Positive likelihood ratio

`Positive likelihood ratio = Sensitivity / (1 - Specificity)`

1. Negative likelihood ratio

`Negative likelihood ratio = (1 - Sensitivity) / Specificity`

## How to calculate the accuracy of a test?

Accuracy is just the ratio of correct results to all the results of a test.

The accuracy formula is one of the easiest ones to remember:

`Accuracy = (TP + TN) / (TP + TN + FP + FN)`

Have you already calculated everything for your test's statistical evaluation? Step up the game and try our probability calculator. 🎲

Łucja Zaborowska