Percentile Calculator
Find the percentile or score at a percentile by entering the numbers in a data set in the calculator below. Continue reading below to learn the percentile formula and the steps to find it.
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Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.
How to Calculate a Percentile
A percentile is a value indicating the percent of a distribution less than or equal to it on a scale from 0 to 100. Percentiles are very similar to quartiles, with the difference being that quartiles divide the data into quarters rather than hundredths.
You might say that percentiles mark the divisions of a data set into one hundred equally sized groups.
Percentiles are used to find the relative standing of a value in a data set. Some common examples are child height and weight or IQ scores.
Given a data set, you can calculate the percentile for a score using the percentile formula:
p = n / N × 100
Thus, the percentile p is equal to the number of elements n that are less than or equal to the score divided by the total number of elements in the data set N, multiplied by 100.
How to Calculate the Score at a Percentile
You can find the score for a given percentile in a few easy steps.
Step One: Sort the Data
The first step is to sort the data set from smallest to largest. Of course, you can do this by hand, or you can use our least to greatest calculator for a larger data set.
Step Two: Calculate the Rank
Next, find the index, sometimes also called the rank, for a given percentile in the data. The formula to find the index is:
i = p / 100 × (N – 1) + 1
Where:
p = percentile
N = number of elements in the set
Step Three: Calculate the Score
To calculate the score, locate the element at rank i in the ordered data, assuming i is an even integer.
s = xi
If i is an even integer, then the score s is equal to the value at index i.
If i is not an even integer, then you’ll need to split the fraction portion from i into the variable rf and calculate the score using this formula:
s = xi + rf × (xi + 1 – xi)
The score s is equal to the element at index i plus the fractional portion of index i, which is rf times the element at index i + 1 minus the element at index i.