# Percentile Rank Calculator: Shows Work for 3 Different Formulas

This calculator will calculate the percentile rank of a data value within a data set using three different methods.

Plus, the calculator shows its work for solving all included methods, including the PERCENTRANK.INC Excel method.

Note if you wish to calculate a percentile, which is different from percentile rank, please visit the Percentile Calculator

Also on the page:

## Percentile Rank Calculator

Calculate the percentile rank of a value with a set of data.

Special Instructions

#### Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None

#### Load or Clear Example Entries:

To see how the Percentile Rank Calculator works, select one of the examples to load into the calculator. To clear example entries, select the "Clear Example" option.

Enter or paste data set:

#### Data set:

Enter each element of the data set (or paste a copied data set) into this text box. Be sure each number is separated by a space, a comma, a line return, or any combination of the three.

Data value:

#### Data value:

Enter a value from within the data set that you wish to calculate percentile rank for.

 # Data value
Dec places:Decimal places:Number of decimal places:Number of decimal places to round results to:

#### Number of decimal places:

Select how many decimal places you would like the results rounded to. Note that you can change the number of places before or after calculating the percentile.

# values (N):# of values (N):Number of values in set (N):Numbers of values in data set (N):

#### Number of values in data set (N):

This is the total number of values detected in the data set field.

Percentile Rank of x: Method Comparison
PR method #1:PR method #1:Percentile rank, method #1:Percentile rank, method #1:

#### Percentile rank, method #1:

This is the percentile rank of the entered data value based on method #1, which uses the following formula:

PR = (CF / N) * 100,

Where CF (Cumulative Frequency) is equal to the number of values in the data set that are less than or equal to the value of interest and where N is equal to the total number of values in the data set.

PR method #2):PR method #2:Percentile rank, method #2:Percentile rank, method #2:

#### Percentile rank, method #2:

This is the percentile rank of the entered data value based on method #2, which states the percentage of values within the data set that are less than the interest of value, and which uses the following formula:

PR = ((CF - (0.5 * F)) / N) * 100,

Where CF (Cumulative Frequency) equals the number of values in the data set that are less than or equal to the value of interest, F (Frequency) is equal to the number of times the value of interest is found within the data set, and where N is equal to the total number of values in the data set.

PR method #3:PR method #3:Percentile rank, method #3:Percentile rank, method #3:

#### Percentile rank, method #3:

This is the percentile rank of the entered data value based on method #3, which uses the following PERCENTRANK.INC Excel formula:

PR = CFE / (CFE + CFG) * 100,

Where CFE (Cumulative Frequency) equals the number of values in the data set that are less than the value of interest and where CFG is equal to the number of values in the data set that are greater than the value of interest.

Note that if the value of interest is not found within the data set, the PERCENTRANK.INC function interpolates one-quarter of the way between the PERCENTRANK.INC of the value below it and the PERCENTRANK.INC of the value above it ((PRn-1) + (0.25 * (PRn+1-PRn-1))).

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

## Learn

### What percentile rank means and how is it calculated

#### What is a Percentile Rank?

A Percentile Rank is the percentage of values in a data set that falls below a given point within a data set when sorted in ascending order.

#### Percentile Rank vs Percentile

While Percentile Rank and Percentile are related terms, they are not one in the same.

In the case of percentiles, a percentage is given, and a corresponding data value is calculated. Conversely, in the case of percentile ranks, a data value is given, and a percentage is calculated.

To illustrate the difference, suppose a teacher gave test to 10 students that resulted in the following test scores:

{16, 18, 20, 22, 18, 12, 19, 17, 23, 20}

As the teacher, you may want to generate a grade curve based on percentiles (90% = A, 80% = B, etc.), and then use percentile ranks to find the grade of each student based on their scores (score of 23 has a percentile rank of 95% so that student would get an A, score of 22 has a percentile rank of 85% so that student would get a B, etc.).

#### How to Calculate a Percentile Rank

Since there are several methods for calculating percentile rank, I will explain how to calculate percentile rank using three of the more common formulas.

#### Percentile Rank Example

Suppose you among a class of 20 students who take a test, which yields the following test scores:

{45, 65, 74, 82, 64, 91, 78, 87, 85, 79, 94, 59, 83, 86, 69, 84, 89, 78, 81, 77}

Further, suppose you want to see how your score of 84 compares to the scores achieved by your other 19 classmates.

Below, I have attempted to show my work for all three percentile rank methods used. Note that all inter-formula line results are rounded to 4 decimal places, while the final formula lines are rounded to a maximum of 3 places.

Method #1: For this method, we will need to solve the following percentile formula:

PR = (CFI / N) * 100,

Where CFI is equal to the number of values in the set that are less than or equal to the data value of interest and N is the total number of values in the set.

From the chart created earlier, we can see that CFI = 14 and N = 20. Substituting those values for the variables in the first percentile formula gives us the following:

PR = (14 / 20) * 100
PR = 0.7 * 100
PR = 70

So based on Method #1, 70% of the values in the entered data set are less than or equal to 84.

Method #2: For this method, we will need to solve the following percentile formula:

PR = ((CF - (0.5 * F)) / N) * 100,

Where CF is equal to the number of values in the set that are less than or equal to the data value of interest, F is the number of times the value of interest occurs in the data set, and N is the total number of values in the set.

From the chart created earlier we can see that CF = 14, F = 1, and N = 20. Substituting those values for the variables in the percentile formula gives us the following:

PR = ((14 - (0.5 * 1)) / 20) * 100
PR = ((14 - 0.5) / 20) * 100
PR = (13.5 / 20) * 100
PR = 0.675 * 100
PR = 67.5

So based on Method #2, 67.5% of the values in the entered data set are less than 84.

Method #3: For this method, we will need to solve the following percentile formula:

PR = (CFE / (CFE + CFG)) * 100,

Where CFE is equal to the number of values in the set that are less than the data value of interest, CFG is the number of values in the set that are greater than the data value of interest. Also, if the value of interest is not found within the data set, this method interpolates a percent rank between its nearest neighbors.

From the chart created earlier, we can see that CFE = 13 and CFG = 6. Substituting those values for the variables in the percentile formula gives us the following:

PR = ((13 / (13 + 6)) * 100
PR = (13 / 19) * 100
PR = 0.6842 * 100
PR = 68.421

So based on Method #3, 68.421% of the values in the entered data set are less than 84.

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".