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Percentile Calculator

Calculate a percentile from a data set or find the percentile rank of a specific value. Enter your numbers and choose the calculation you need.

Calculate Percentiles

Enter a data set and calculate a percentile value or the percentile rank of a specific score.

Enter your data and choose the percentile you want to find.

Percentile Value
0
Data Points 0
Minimum 0
Maximum 0
Median 0

How to Calculate a Percentile

A percentile shows the value below which a given percentage of observations in a data set falls. To calculate a percentile, first sort the data from smallest to largest and then determine the position of the selected percentile.

This calculator uses linear interpolation between neighboring values when the percentile position falls between two data points.

Percentile Formula

Position = (n − 1) × p

Here, n is the number of values in the data set and p is the percentile written as a decimal. For example, the 75th percentile uses p = 0.75.

If the calculated position falls between two values, the calculator uses linear interpolation to estimate the percentile value.

Percentile Rank Formula

Percentile rank tells you what percentage of values in the data set fall below or are tied with a specific score.

Percentile Rank = (Values Below X + 0.5 × Values Equal to X) ÷ n × 100

This method assigns half of tied values to each side of the selected score.

Percentile Calculation Examples

Suppose the sorted data set is:

10, 20, 30, 40, 50

75th Percentile

With five data points:

(5 − 1) × 0.75 = 3

Position 3 corresponds to the value 40, so the 75th percentile is 40.

60th Percentile

(5 − 1) × 0.60 = 2.4

The position falls between 30 and 40. Linear interpolation gives:

30 + (40 − 30) × 0.4 = 34

The 60th percentile is 34.

Percentile vs. Percentile Rank

Percentile and percentile rank are closely related, but they answer different questions.

Measure Question It Answers Example
Percentile What value corresponds to a selected percentile? What is the 75th percentile of this data set?
Percentile Rank What percentage of the data is below a specific value? What percentile rank does a score of 30 have?

Use Percentile from Data when you know the percentile you want to find. Use Percentile Rank when you already have a score or value and want to see where it stands within the data set.

How to Read Percentiles

A percentile describes the relative position of a value within a data set. For example, a value at the 80th percentile is higher than about 80% of the observations in that data set.

Percentiles do not show how far apart values are. Two observations can be close together but still fall into different percentiles if the data is tightly grouped.

Percentile General Meaning
25thAbout 25% of values fall below this point
50thThe median of the data set
75thAbout 75% of values fall below this point
90thAbout 90% of values fall below this point

Common Uses of Percentiles

Percentiles are used whenever it is useful to compare a value with the rest of a group rather than looking only at the raw number.

  • Comparing test scores with other students.
  • Analyzing distributions in statistics and research.
  • Identifying unusually high or low observations.
  • Comparing performance across groups with different score ranges.
  • Summarizing large data sets with quartiles and percentile cutoffs.

If your calculation starts with a mean and standard deviation instead of a raw data set, the Z-Score Calculator is usually the better tool.

Related Calculators

Z-Score Calculator Calculate a z-score from a value, mean, and standard deviation and compare values within a distribution. Grade Calculator Calculate your current class grade from points, percentages, assignments, tests, and quizzes. SAT Score Calculator Estimate and calculate SAT scores from test performance and scoring inputs.

Frequently Asked Questions

How do I calculate a percentile?
Sort the data from smallest to largest, calculate the percentile position, and use linear interpolation if the position falls between two values.
How do I calculate percentile rank?
Count the values below your selected score, add half of the values equal to it, divide by the total number of observations, and multiply by 100.
What is the difference between percentile and percentile rank?
A percentile gives the data value associated with a selected percentage, while percentile rank shows the relative position of a specific score within the data set.
What does the 50th percentile mean?
The 50th percentile is the median. It represents the middle of the ordered data set, with about half of the values below it and half above it.
What does the 90th percentile mean?
The 90th percentile is a value near the upper end of the distribution. Approximately 90% of the observations fall below that percentile value.
Why can percentile calculators give different results?
Different calculators and statistical tools may use different percentile definitions or interpolation methods. This calculator uses linear interpolation based on the position formula (n − 1) × p.
Can I enter decimal or negative values?
Yes. The data set can contain positive numbers, negative numbers, integers, or decimals.
Does my data need to be sorted first?
No. You can enter the values in any order. The calculator automatically sorts the data before calculating percentiles and percentile ranks.
Should I use a percentile calculator or a z-score calculator?
Use this percentile calculator when you have a raw data set. Use a Z-Score Calculator when you want to compare a value with a distribution using its mean and standard deviation.