# Percentile Rank Calculator

Created by Bogna Szyk
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Jul 13, 2023

Our percentile rank calculator helps you find the percentile for any data value in a set of up to 30 values. It will tell you roughly whether your value is low or high in this particular dataset.

In essence, a percentile rank is obtained by dividing the data into ranks using percentiles. This article will explore the definition and applications of the percentile rank and give you a handy percentile rank formula to use in your calculations. Keep reading to learn more about how to find percentile rank.

💡 For a more thorough statistical analysis of a dataset, check out our 5-number summary calculator!

## What is a percentile rank?

The end of the school year is approaching. You start wondering which college to pick. You know you're not the top student in your class, but you're doing pretty well. You found a great college with low tuition (to minimize those pesky student loans) and are now looking at their entry requirements. They are saying you need an SAT score of at least 1500.

You haven't practiced for your SATs yet, so you start wondering "How good is this result, really? Is it possible to score 1500?" Somehow, you get your hands on last year's SAT percentile chart and check what percentage of all students got a result of 1500 or lower.

What you're looking for is precisely the percentile rank of the value 1500. You find out that the percentile rank is 60. It means that 60% of all students got a result equal to or lower than 1500. It means that you need to beat 60% of all students on SATs to get to your dream school. That sounds doable - at least if you start studying now!

Below, we'll talk about the term percentile rank more deeply so you can understand how to find the percentile for the data value. Keep reading!

## Percentile rank formula

Now that you have a better idea of what the percentile rank actually is, let's try putting it in a neat mathematical equation. We'll be using a set of values A = {x₁, x₂, x₃, ..., xn} with N values and try to determine the percentile rank of the data point xₘ. In such a case:

PR = L / N × 100

where:

• PR — Percentile rank — it can take values from 0 to 100;

• L — Number of values from the set A that are lower than or equal to your data value xm; and

• N — Total number of values in the set A.

This formula looks simple, but finding the percentile rank by hand is actually quite a tedious task. It involves a lot of counting numbers. Check out the next section with an example showing how to find the percentile for the data value. Luckily, you can also use our percentile rank calculator to do it much faster!

## How to find the percentile rank for a data value? The percentile rank calculator

You have already learned how to calculate percentile rank, so let's move on to an actual example of calculations.

Let's say that your teacher gave back the tests from last week. You take a look at your grade (or use our test grade calculator) — it turns out that you scored 25 points, but the maximum is nowhere to be seen. You have no idea whether or not you did well on this paper. The teacher shoots you a smile and says that you need to calculate your own grade. He writes down all results on the board: 6, 12, 24, 33, 23, 17, 30, 18, 27, 17, 25, 23, 27, 20, 13, 32, 26.

The teacher also gives you the grading scale. Lo and behold, it is actually based on percentiles: grade A for percentiles 91-100, grade B for 71-90, grade C for 51-70, and D for 25-50. That's right; the teacher decided that 25% of the class would not pass the test. So, how to calculate percentile rank in this case?

1. The first thing you need to do is put the numbers in ascending order. You don't necessarily have to do it, but it will make your life much easier:

6, 12, 13, 17, 17, 18, 20, 23, 24, 24, 25, 26, 27, 27, 30, 32, 33, which is 17 numbers in total

We have 17 results, which means that N = 17.

2. Now, find your result. 25 points lies more or less in the final thirds of this dataset, so you start hoping for a good grade.

3. Count the results that are lower or equal to yours:

6, 12, 13, 17, 17, 18, 20, 23, 24, 24, 25 - which is 11 numbers in total

It means that the value of L = 11.

4. Now, all that's left to do is plug these numbers in the percentile rank formula:

PR = L / N × 100

PR = 11 / 17 × 100

PR = 64.7

5. This is how to find the percentile rank, which for you is 64.7. That translates to a solid C. It could've been better, but at least you passed!

## Applications of percentile rank

Knowing how to calculate the percentile rank can save you a lot of trouble in school, but it's also extremely useful in real life! When you become a parent, you tend to check how your child is developing by comparing them to other kids. For example, you measure your newborn's weight and see what their percentile rank is (we have a weight percentile calculator). If it's very low, your child is smaller and lighter than an average newborn; if it's high, your baby is bigger than the average (here, you can use our height percentile calculator).

## FAQ

### How do you calculate percentile rank?

To calculate percentile rank:

1. Write down the number X which you want to find the percentile rank of.
2. Count the total amount of numbers you will compare it against. We'll call this N.
3. Count how many of those numbers are less than or equal to X. We'll call this L.
4. Divide L by N and times the result by 100 to get the percentile rank of X.

### What is percentile in simple words?

A percentile is a number on a scale of 0-100 that indicates how a specific value compares against others within a particular context. It can represent grades, physical conditions, or any other quantifiable property.

### What is the highest percentile rank?

100th is the highest percentile rank. The 100th percentile represents the highest position when using percentiles to compare different values. It means that all other values are less than or equal to this number.

### What does a 95th percentile mean?

If a number is 95th percentile, it means that 95% of the values in the dataset are less than or equal to this number. The remaining 5% of the dataset is greater than this 95th percentile value.

Bogna Szyk
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