# False Positive Rate Calculator

Determines the rate of tests identified incorrectly with false positive and true negative values based on the prevalence and specificity.

You can read more about the formulas used and what the variables mean in the text below the form.

The false positive rate calculator is used to determine the of rate of incorrectly identified tests, meaning the false positive and true negative results.

In order to do so, the prevalence and specificity are taken in consideration. These can be input as fraction, % or ratio, depending on the way they are defined in the study.

There are three results, calculated based on the following formulas:

■ False Positive = (1 - Specificity) x (1 – Prevalence)

■ True Negative = Specificity x (1 - Prevalence)

■ False Positive Rate = 100 x False Positive / (False Positive + True Negative)

## Send Us Your Feedback

**Steps on how to print your input & results:**

1. Fill in the calculator/tool with your values and/or your answer choices and press Calculate.

2. Then you can click on the Print button to open a PDF in a separate window with the inputs and results. You can further save the PDF or print it.

Please note that once you have closed the PDF you need to click on the Calculate button before you try opening it again, otherwise the input and/or results may not appear in the pdf.

## Variables used

To calculate the false positive rate, the prevalence and specificity of the study in question have to be known.

They can be specified either as % (between 0 and 100%), fraction or as ratio (0 to 1):

■ Prevalence is defined as total disease divided by total and multiplied by 100. Its value is influenced by the study group dimension.

■ Specificity, or the True Negative Rate, represents the fraction of subjects without the disease and whose test is negative, therefore it quantifies the avoidance of false positive.

The Specificity can be extracted from true negative and false positive as follows:

Specificity = True Negative / (True Negative + False Positive) x 100

The following table explains the relationships between the types of results in an epidemiological study:

Test Result |
Disease |
Non-Disease |
Total Number |

Positive | True Positive | False Positive | Total Test Positive |

Negative | False Negative | True Negative | Total Test Negative |

Total Disease | Total Non-Disease | Total |

## Formulas and results

The results provided by the calculator and the way they are computed are presented below:

■ False Positive = (1 - Specificity) x (1 – Prevalence)

This is non-disease incorrectly identified through test as disease.

■ True Negative = Specificity x (1 - Prevalence)

This represents non-disease correctly identified as non-disease.

■ False Positive Rate = 100 x False Positive / (False Positive + True Negative)

This is the rate of incorrectly identified out of total non-disease.

It is important to note that sensitivity and specificity (as characteristics of test) are not influenced by the dimension of the population in the study.

## References

1. Jakobsdottir J, Weeks DE. Estimating Prevalence, False-Positive Rate, and False-Negative Rate with Use of Repeated Testing When True Responses Are Unknown. Am J Hum Genet. 2007; 81(5): 1111–1113.

2. Lalkhen AG, McCluskye A. Clinical tests: sensitivity and specificity. Contin Educ Anaesth Crit Care Pain. 2008; 8(6): 221-223.

Specialty: Research

Objective: Determination

Type: Calculator

No. Of Variables: 2

Article By: Denise Nedea

Published On: March 16, 2017

Last Checked: March 16, 2017

Next Review: March 10, 2023