How to Use the Percentile Calculator
This percentile calculator can find either the value at a given percentile or the percentile rank of a value in a dataset.
To use the calculator:
- Under Find, select Value at a Percentile or Percentile Rank.
- Enter your data values separated by commas, spaces, or line breaks.
- If you selected Value at a Percentile, enter the percentile you want to find, such as 25, 50, 75, or 90.
- Choose the percentile method. The calculator uses the Nearest Rank method by default, but you can switch to Linear Interpolation.
- However, if you selected Percentile Rank, enter the value, x, whose percentile rank you want to find. You do not need to choose a percentile method for this calculation.
- Select the number of decimal places you want in the answer
- Click Calculate.
The calculator will instantly return the percentile or percentile rank depending on your inputs and also show you exactly how the value was obtained, using a step-by-step approach.
What Is a Percentile?
A percentile shows the position of a value relative to the other values in a dataset. For example, the 75th percentile, written as P75, represents a value near which 75% of the observations are at or below it.
Some commonly used percentiles also have special names. The table below shows the relationship between these percentiles and their equivalent quartiles.
| Percentile | Name |
|---|---|
| P25 | First quartile, Q1 |
| P50 | Median or second quartile, Q2 |
| P75 | Third quartile, Q3 |
| P90 | 90th percentile |
As shown in the table, P25, P50, and P75 correspond to Q1, Q2, and Q3, respectively. These three values divide an ordered dataset into four parts. P90 does not have a quartile name, but it is another commonly used percentile for describing the position of a value within a dataset.
If you only need Q1, Q2, and Q3, you can use our Quartile Calculator.
Percentile Formula
There is more than one accepted method for calculating percentiles. As a result, different textbooks, calculators, and statistical programs may sometimes give slightly different answers for the same dataset.
This calculator supports two common methods: Nearest Rank and Linear Interpolation.
1. Nearest Rank Percentile Formula
The Nearest Rank method uses:
r = (P / 100) × n
where:
- P is the percentile you want to find.
- n is the number of observations.
- r is the rank or position of the percentile in the ordered dataset.
If r is not a whole number, round it up to the next whole number. The percentile is then the value at that position in the sorted dataset. For example, if r = 7.5, you use the 8th value.
This method always returns one of the values contained in the dataset.
2. Linear Interpolation Percentile Formula
The Linear Interpolation method used by this calculator follows the same position rule as Excel’s PERCENTILE.INC function. The formula is:
r = 1 + (P / 100)(n − 1)
where:
- P is the required percentile.
- n is the number of observations.
- r is the percentile position.
If r is a whole number, use the value at that position. However, if r falls between two positions, interpolate between the corresponding values.
For instance, suppose the percentile position is: r = 7.75. In this case, the required percentile falls 75% of the way between the 7th and 8th values.
Therefore, the interpolated value can be calculated as:
Percentile = lower value + decimal part × (upper value − lower value)
The two methods may return different values because they use different rules for locating a percentile.
How to Calculate a Percentile by Hand Using the Nearest Rank Method
To calculate a percentile manually using the Nearest Rank method:
- Arrange the data from smallest to largest.
- Count the number of values to find n.
- Calculate the rank using r = (P / 100) × n. If r is not a whole number, round it up to the next whole-number position.
- Find the value at that position in the ordered dataset.
Example 1: Find the 80th Percentile
Find P80 for the following dataset: 12, 28, 17, 35, 21, 42, 30, 25, 39
Solution
P80 is the 80th percentile. To find the 80th percentile for the above dataset by hand, follow these steps:
Step 1: Arrange the data in ascending order.
Sorting the values from smallest to largest gives:
12, 17, 21, 25, 28, 30, 35, 39, 42
Step 2: Count the number of values.
There are 9 observations. Therefore, n = 9
Step 3: Calculate the rank.
The Nearest Rank formula is: r = (P / 100) × n
Substituting P = 80 and n = 9:
r = (80 / 100) × 9
= 7.2
Since 7.2 is not a whole number, we round up to the next whole-number rank.
Therefore, r = 8
Step 4: Find the value at rank 8.
The 8th value in the ordered dataset is 39.
Therefore, P80 = 39
How to Calculate a Percentile by Hand Using Linear Interpolation
To calculate a percentile using Linear Interpolation:
- Arrange the values from smallest to largest.
- Count the number of observations to find n.
- Calculate the percentile position using r = 1 + (P / 100)(n − 1).
- If r is a whole number, use the value at that position. However, if r is not a whole number, identify the values immediately below and above the position.
- Interpolate between the two values using the decimal part of r.
Example 2: Find the 60th Percentile
Find P60 for the following dataset: 31, 14, 42, 25, 18, 36, 27, 22
Solution
P60 is the 60th percentile. To find the 60th percentile of the above data manually using the linear interpolation method, follow these steps:
Step 1: Arrange the data in ascending order.
Sorting the values from smallest to largest gives:
14, 18, 22, 25, 27, 31, 36, 42
Step 2: Count the number of values.
There are 8 observations. Therefore, n = 8.
Step 3: Calculate the percentile position.
Recall that the Linear Interpolation formula is: r = 1 + (P / 100)(n − 1)
Substituting P = 60 and n = 8, we get:
r = 1 + (60 / 100)(8 − 1)
= 1 + (0.60)(7)
= 5.2
Therefore, the percentile lies between the 5th and 6th positions.
Step 4: Identify the two surrounding values.
The 5th value is: 27 and the 6th value is: 31
Since the position is 5.2, the percentile lies 20% of the way from the 5th value to the 6th value.
Step 5: Interpolate between the two values.
When the percentile position falls between two values, we use the formula:
Percentile = lower value + decimal part of r × (upper value − lower value)
For this example:
- Lower value = 27
- Upper value = 31
- Decimal part of r = 0.2
Substituting these values into the formula gives:
Percentile = 27 + 0.2(31 − 27)
= 27 + 0.2(4)
= 27.8
Therefore, P60 = 27.8
In this example, 27.8 does not appear in the original dataset. This is expected because Linear Interpolation can return a value between two observed data values.
Which Percentile Method Should You Use?
Use the method required by your course, textbook, instructor, or statistical software.
The Nearest Rank method is useful when:
- Your problem uses the formula
r = (P/100) × n. - You are calculating percentiles by hand using a simple classroom method.
- You want the percentile to be one of the observed values in the dataset.
On the other hand, the Linear Interpolation method is appropriate when:
- Your instructions require interpolation.
- You need a percentile value that can fall between two observations.
- You want to follow the same approach used by Excel’s
PERCENTILE.INCfunction.
There is no need to convert between the methods. Simply select the one that matches the method required for your problem.
What Is Percentile Rank?
Percentile rank tells you where a particular value lies relative to the other observations in a dataset. This is different from finding a percentile.
When finding a percentile, you start with a percentile such as P75 and find its corresponding value. However, when finding percentile rank, you start with a value and determine its relative position in the dataset.
For example:
- Percentile question: What value is at the 75th percentile?
- Percentile rank question: What is the percentile rank of a score of 39?
Our calculator uses the midrank method when calculating percentile rank. This method accounts for values that are tied with the value being ranked.
Percentile Rank Formula
The percentile rank formula used by this calculator is:
PR = ((B + 0.5E) / n) × 100
where:
- PR is the percentile rank.
- B is the number of observations below the value.
- E is the number of observations equal to the value.
- n is the total number of observations.
The 0.5E term assigns half of the tied observations below the value and half above it. This prevents all tied values from being treated as though they occur completely below or completely above the target value.
How to Calculate Percentile Rank by Hand
To calculate the percentile rank of a value:
- Arrange the dataset from smallest to largest.
- Count the total number of observations to find n.
- Count the number of observations below the target value to find B.
- Count the number of observations equal to the target value to find E.
- Substitute the values into PR = ((B + 0.5E) / n) × 100.
Example 3: Find the Percentile Rank of 39
Consider the following dataset: 31, 18, 44, 22, 56, 27, 39, 14, 50, 35.
Find the percentile rank of 39.
Solution
To find the percentile rank of 39 for the above dataset manually, follow these steps:
Step 1: Arrange the data in ascending order.
The sorted data is: 14, 18, 22, 27, 31, 35, 39, 44, 50, 56
Step 2: Count the number of observations.
There are 10 observations. Therefore, n = 10
Step 3: Count the values below 39.
The values below 39 are: 14, 18, 22, 27, 31, 35. Counting this, we see that there are six values.
Therefore, B = 6
Step 4: Count the values equal to 39.
The value 39 appears once. Therefore, E = 1
Step 5: Apply the percentile rank formula.
PR = ((B + 0.5E) / n) × 100
Substituting B = 6, E = 1, and n = 10, we get:
PR = ((6 + 0.5(1)) / 10) × 100
= (6.5 / 10) × 100
= 65
Therefore, PR = 65%. This implies that a value of 39 is at approximately the 65th percentile using the midrank method.
Percentile vs. Percentile Rank
Both percentile and percentile rank describe position within a dataset. However, they answer different questions.
A percentile starts with a percentile, such as P75, and asks for the data value at that position. However, a percentile rank starts with a data value and asks where that value stands relative to the other observations.
The table below summarizes the main difference between the two.
| Percentile | Percentile Rank | |
|---|---|---|
| What you know | A percentile, such as P75 | A data value, such as 39 |
| What you find | The value at that percentile | The relative position of the value |
| Example question | What is the 75th percentile? | What is the percentile rank of 39? |
| Typical answer | A data value | A percentage |
As shown in the table, the main difference is the direction of the calculation. With a percentile, you start with a percentile and find the corresponding data value, whereas with a percentile rank, you start with a data value and find its position as a percentage.
A simple way to remember the difference is “A percentile gives you a value, while a percentile rank tells you where a value stands in the dataset.”
Frequently Asked Questions
A percentile calculator finds the value at a given percentile or the percentile rank of a value in a dataset. Our tool supports the Nearest Rank and Linear Interpolation methods and shows a step-by-step solution.
First, arrange the data from smallest to largest. Then calculate the percentile position using the required method. For the Nearest Rank method, r = (P / 100) × n. However, for Linear Interpolation: r = 1 + (P / 100)(n − 1)
A percentile gives the data value at a given percentile. On the other hand, a percentile rank shows where a specific value stands relative to the rest of the dataset.
Different methods use different rules for locating the percentile. The Nearest Rank method selects an observed value, while Linear Interpolation can return a value between two observations.
Yes. The 50th percentile, or P50, is the median.
No. Enter the values in any order. The calculator sorts the data automatically before performing the calculation.
