To find a percentile, you use a simple idea: a percentile tells you what percentage of values fall below a certain number in a data set.

What “percentile” means

  • The Pth percentile is a value such that P percent of the data are below it.
  • Example: If your test score is at the 70th percentile, then 70% of people scored lower than you.

Two common tasks

There are two main “how to find percentile” problems:

  1. Find the percentile rank of a given value (e.g., “My score is 82, what percentile is that?”).
  1. Find the value at a given percentile (e.g., “What score is the 70th percentile?”).

1) Percentile rank of a value

This tells you “what percentile is this score?”.

Formula

Percentile=number of values less than xtotal number of values×100\text{Percentile}=\frac{\text{number of values less than }x}{\text{total number of values}}\times 100Percentile=total number of valuesnumber of values less than x​×100

Here xxx is your value.

Step-by-step

  1. List all data values.
  2. Count how many are less than your value xxx.
  3. Count the total number of values.
  4. Plug into the formula above and multiply by 100 to get a percentile.

Quick example

Data: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 (10 values).
Suppose x=80x=80x=80.

  • Values less than 80: 10, 20, 30, 40, 50, 60, 70 → 7 values.
  • Total values: 10.
  • Percentile P=710×100=70P=\frac{7}{10}\times 100=70P=107​×100=70.

So 80 is at the 70th percentile in this data set.

2) Value at a given percentile

This is “what score is the 70th percentile?” etc.

General idea

You first find the position (rank) in the ordered list that corresponds to the percentile, then read (or interpolate) the value there.

A common rank formula

One commonly used rank formula (similar to spreadsheet/online calculators) is:

r=p100×(n−1)+1r=\frac{p}{100}\times (n-1)+1r=100p​×(n−1)+1

  • ppp = desired percentile (e.g., 70 for the 70th percentile).
  • nnn = number of data points.
  • rrr = rank (position) in the ordered list.

Steps

  1. Order the data from smallest to largest.
  1. Let nnn be the total number of values.
  1. Choose the percentile ppp you want (e.g., 70).
  1. Compute the rank rrr using a formula such as r=p100×(n−1)+1r=\frac{p}{100}\times (n-1)+1r=100p​×(n−1)+1.
  1. If rrr is a whole number , take the value at that exact position in the ordered list.
  2. If rrr is a decimal , use the two surrounding positions and interpolate between them (or, in some simpler school methods, round up and take that position).

Example: 70th percentile of a small data set

Data: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 (already ordered, n=10n=10n=10).

Using rank based on (N+1)(N+1)(N+1), as shown in one common method:

R=70100×(10+1)=7.7R=\frac{70}{100}\times (10+1)=7.7R=10070​×(10+1)=7.7

  • Rank 7.7 lies between the 7th value (70) and the 8th value (80).
  • So the 70th percentile is between 70 and 80; with simple rounding you might choose 80, with interpolation you would compute a value between them.

HTML table: quick reference

Here is a quick-reference table in HTML, since you asked for tables in that format:

html

<table>
  <thead>
    <tr>
      <th>Task</th>
      <th>Key Formula / Idea</th>
      <th>Short Steps</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Find percentile rank of a value</td>
      <td>P = (number of values &lt; x / total values) × 100[web:3][web:5]</td>
      <td>Count values below x, divide by total, multiply by 100.[web:3][web:5]</td>
    </tr>
    <tr>
      <td>Find value at Pth percentile</td>
      <td>r = (p/100) × (n − 1) + 1 (rank); then read/interpolate value at rank r[web:1][web:7]</td>
      <td>Order data, compute rank, then take value at that position or interpolate.[web:1][web:7]</td>
    </tr>
  </tbody>
</table>

Why there are different formulas

Textbooks, exams, and tools sometimes use slightly different rank formulas (like using N+1N+1N+1 vs n−1n-1n−1) so percentiles can differ a bit between methods. In practice, they are usually very close, but if you must match a specific tool (like an exam board or Excel), use the same method they define.

Tiny story-style example

Imagine 10 students line up from lowest to highest test score, and you stand somewhere in that line. If you want to know “what percentile am I?”, you count how many students are behind you and turn that into a percentage. If instead the teacher says, “Tell me the score at the 80th percentile,” you would figure out which position in line corresponds to 80% of the way up and look at that student’s score.

TL;DR:

  • To find the percentile rank of a value: Percentile=values below xtotal values×100\text{Percentile}=\frac{\text{values below x}}{\text{total values}}\times 100Percentile=total valuesvalues below x​×100.
  • To find the value at a given percentile : order the data, compute the rank rrr from a percentile formula, then read or interpolate the value at that rank.

Information gathered from public forums or data available on the internet and portrayed here.