Percentile Formula: Rank, Value, Calculation and Solved Examples

The Percentile Formula is used to find the percentage of observations below a given value or to find the value at a given percentile position.
For percentile rank, use Percentile = (Number of values below x ÷ Total number of values) × 100.

The Percentile Formula helps students understand the position of a value in a dataset. If a student is at the 90ᵗʰ percentile, it means their score is higher than the scores of 90% of the students in that dataset. Percentile questions often appear in statistics, exam scores, entrance test results, growth charts and data interpretation.

In Class 10, Class 11 and Class 12 Maths or Statistics, percentile is used to compare values based on relative position. CBSE, ICSE, state board, CUET foundation, JEE foundation and NEET foundation questions may ask students to calculate percentile rank, find a percentile value, arrange data in ascending order or use interpolation when the rank has a decimal value.

Key Takeaways

• Percentile Formula: Percentile rank shows the percentage of values below a given value.
• Rank Formula: R = (P ÷ 100) × (N + 1) gives the position of a percentile value.
• Percentile Rank: It shows how a value compares with the rest of the dataset.
• Percentile Value: It gives the actual value at a selected percentile position.
• Data Order: Values must be arranged from smallest to largest before calculation.
• Interpolation: Decimal rank values are calculated between two nearby positions.

Percentile Formula Structure 2026

What is Percentile Formula?

The Percentile Formula gives the relative position of a value in a dataset. It shows the percentage of observations that fall below a given value.

Formula for percentile rank:

Percentile = (Number of values below x ÷ Total number of values) × 100

Where:

• x = value whose percentile rank is required
• Number of values below x = count of observations less than x
• Total number of values = total observations in the dataset
• Percentile = percentage position of x

Example:

Dataset:

3, 5, 7, 9, 12

Value:

x = 9

Values below 9:

3, 5, 7

Number of values below 9:

3

Total number of values:

5

So:

Percentile = (3 ÷ 5) × 100

Percentile = 60

The value 9 is at the 60ᵗʰ percentile.

Percentile Formula

The Percentile Formula has two common uses in school-level statistics. One finds the percentile rank of a given value, and the other finds the value at a given percentile.

Formula 1: Percentile rank of a value

Percentile = (Number of values below x ÷ N) × 100

Formula 2: Rank of a percentile value

R = (P ÷ 100) × (N + 1)

Where:

• R = rank or position of the percentile value
• P = required percentile
• N = total number of observations

If R is a whole number, use the value at that position. If R is a decimal, interpolate between the two nearest positions.

Percentile Rank Formula

The Percentile Rank Formula tells how many values in a dataset are below a specific value. It is useful in exam scores, marks, test performance and ranking-based comparison.

Formula:

Percentile Rank = (Number of values below x ÷ N) × 100

Where:

• x = given value
• N = total number of observations

Example:

Marks of students:

40, 50, 60, 70, 80, 90

Find the percentile rank of 80.

Values below 80:

40, 50, 60, 70

Number of values below 80:

4

Total values:

6

So:

Percentile Rank = (4 ÷ 6) × 100

Percentile Rank = 66.67

The score 80 is at approximately the 66.67ᵗʰ percentile.

Percentile Value Formula

The Percentile Value Formula is used to find the actual value corresponding to a percentile such as the 25ᵗʰ, 50ᵗʰ, 75ᵗʰ, 90ᵗʰ or 95ᵗʰ percentile.

Formula:

R = (P ÷ 100) × (N + 1)

Where:

• R = rank position
• P = required percentile
• N = total number of values

Steps:

1. Arrange the data in ascending order.
2. Substitute P and N in the formula.
3. Find the rank R.
4. Use the value at position R.
5. Interpolate if R has a decimal.

Example:

Find the 75ᵗʰ percentile for:

10, 20, 30, 40, 50, 60, 70

Here:

P = 75

N = 7

Formula:

R = (P ÷ 100) × (N + 1)

Substitute:

R = (75 ÷ 100) × (7 + 1)

R = 0.75 × 8

R = 6

The 6ᵗʰ value is 60.

Answer:

The 75ᵗʰ percentile is 60.

Percentile Calculation Formula

The Percentile Calculation Formula depends on whether the question asks for rank or value. Students should first identify the requirement from the wording of the question.

Use percentile rank formula when the question asks:

• What percentile is this value?
• Find the percentile rank of x.
• What percentage of values are below x?

Formula:

Percentile = (Values below x ÷ N) × 100

Use percentile value formula when the question asks:

• Find the 90ᵗʰ percentile.
• Find the value at the 75ᵗʰ percentile.
• Calculate P₂₅, P₅₀ or P₉₅.

Formula:

R = (P ÷ 100) × (N + 1)

For a decimal rank:

Percentile Value = Lower value + Decimal part × (Upper value − Lower value)

Example:

If R = 5.25, use the 5ᵗʰ and 6ᵗʰ values.

Percentile Value = 5ᵗʰ value + 0.25 × (6ᵗʰ value − 5ᵗʰ value)

Percentile Formula Statistics

In percentile formula statistics, percentile is used to describe the position of a value within a dataset. It helps compare individual scores, marks, heights, weights or observations with the remaining values.

Percentile in statistics is commonly used for:

• Exam score comparison
• Data interpretation
• Growth charts
• Ranking systems
• Entrance test results
• Grouped frequency distributions

A percentile does not always show the actual score directly. It shows the relative position of a value compared with other values in the dataset.

Percentile Formula for Ungrouped Data

Ungrouped data contains individual values listed separately. Percentile calculation starts by arranging these values in ascending order.

Formula for percentile rank:

Percentile = (Values below x ÷ N) × 100

Formula for percentile value:

R = (P ÷ 100) × (N + 1)

Example:

Data:

18, 12, 25, 30, 10, 22

Arrange in ascending order:

10, 12, 18, 22, 25, 30

Find the 50ᵗʰ percentile.

Here:

P = 50

N = 6

Rank:

R = (50 ÷ 100) × (6 + 1)

R = 0.5 × 7

R = 3.5

The 3ʳᵈ value is 18.

The 4ᵗʰ value is 22.

Interpolate:

P₅₀ = 18 + 0.5 × (22 − 18)

P₅₀ = 18 + 2

P₅₀ = 20

The 50ᵗʰ percentile is 20.

Percentile Formula for Grouped Data

The Percentile Formula for grouped data is used when observations are arranged in class intervals with frequencies. The percentile value is found using the percentile class and cumulative frequency.

Formula:

Pₖ = L + [(kN ÷ 100 − cf) ÷ f] × h

Where:

• Pₖ = kᵗʰ percentile
• L = lower boundary of the percentile class
• k = required percentile
• N = total frequency
• cf = cumulative frequency before the percentile class
• f = frequency of the percentile class
• h = class width

Steps:

1. Find total frequency N.
2. Calculate kN ÷ 100.
3. Locate the class containing this value.
4. Identify L, cf, f and h.
5. Substitute values in the formula.

This method is common in statistics questions with class intervals.

90th Percentile Formula

The 90th percentile formula finds the value below which 90% of observations fall. It is widely used in scores, performance comparison and data analysis.

For ungrouped data:

R = (90 ÷ 100) × (N + 1)

So:

R = 0.90 × (N + 1)

For grouped data:

P₉₀ = L + [(90N ÷ 100 − cf) ÷ f] × h

or

P₉₀ = L + [(0.90N − cf) ÷ f] × h

Example:

Data:

10, 20, 30, 40, 50, 60, 70, 80, 90

Here:

N = 9

Rank:

R = 0.90 × (9 + 1)

R = 0.90 × 10

R = 9

The 9ᵗʰ value is 90.

Answer:

The 90ᵗʰ percentile is 90.

95th Percentile Formula

The 95th percentile formula finds the value below which 95% of observations fall. It is often used in reports, performance data and large datasets.

For ungrouped data:

R = (95 ÷ 100) × (N + 1)

So:

R = 0.95 × (N + 1)

For grouped data:

P₉₅ = L + [(95N ÷ 100 − cf) ÷ f] × h

or

P₉₅ = L + [(0.95N − cf) ÷ f] × h

Example:

If N = 19, then:

R = 0.95 × (19 + 1)

R = 0.95 × 20

R = 19

The 95ᵗʰ percentile is the 19ᵗʰ value in the ordered dataset.

Percentile Formula with Interpolation

Interpolation is used when the percentile rank position is a decimal. It estimates the value between two neighbouring observations.

Formula:

Percentile Value = Lower value + d × (Upper value − Lower value)

Where:

• Lower value = value at the lower position
• Upper value = value at the next position
• d = decimal part of the rank

Example:

Data:

10, 20, 30, 40, 50, 60

Find the 25ᵗʰ percentile.

Here:

P = 25

N = 6

Rank:

R = (25 ÷ 100) × (6 + 1)

R = 0.25 × 7

R = 1.75

The 1ˢᵗ value is 10.

The 2ⁿᵈ value is 20.

Decimal part:

d = 0.75

Interpolate:

P₂₅ = 10 + 0.75 × (20 − 10)

P₂₅ = 10 + 7.5

P₂₅ = 17.5

Answer:

The 25ᵗʰ percentile is 17.5.

Difference Between Percentage and Percentile

Percentage and percentile both use 100 as a base, but they measure different things. Percentage measures a part of a total, while percentile shows position in a dataset.

Example:

A student scoring 80% got 80 marks out of 100.

A student at the 80ᵗʰ percentile scored higher than 80% of students in the dataset.

Difference Between Percentile and Quartile

Percentiles divide data into 100 equal parts, while quartiles divide data into 4 equal parts. Quartiles are special percentiles.

The 50ᵗʰ percentile is also the median.

Example:

If P₅₀ = 45, then 50% of observations lie below 45.

Percentile Formula Class 10

In Class 10, percentile questions usually focus on basic rank and data comparison. Students may be asked to arrange data, count values below a number, and calculate percentile rank.

Useful formula:

Percentile = (Values below x ÷ N) × 100

Example:

If 18 students scored below a student in a group of 30 students:

Percentile = (18 ÷ 30) × 100

Percentile = 60

So, the student is at the 60ᵗʰ percentile.

Percentile Formula Class 11

In Class 11, percentile questions may include grouped data, cumulative frequency and interpolation. Students may need to calculate P₂₅, P₅₀, P₉₀ or P₉₅ from class intervals.

Grouped data formula:

Pₖ = L + [(kN ÷ 100 − cf) ÷ f] × h

This formula is used when the data is given in class intervals such as 0-10, 10-20 and 20-30.

How to Find Percentile

To find percentile, first decide whether the question asks for percentile rank or percentile value. Then arrange the data in ascending order if individual values are given.

Case 1: Finding percentile rank of a value

Use:

Percentile = (Values below x ÷ N) × 100

Example:

Dataset:

3, 5, 7, 9, 12

Find percentile rank of 9.

Values below 9:

3, 5, 7

Count:

3

Total values:

5

So:

Percentile = (3 ÷ 5) × 100

Percentile = 60

Answer:

9 is at the 60ᵗʰ percentile.

Case 2: Finding value at a percentile

Use:

R = (P ÷ 100) × (N + 1)

Example:

Dataset:

2, 4, 6, 8, 10, 12, 14

Find 50ᵗʰ percentile.

Here:

P = 50

N = 7

Rank:

R = (50 ÷ 100) × (7 + 1)

R = 0.5 × 8

R = 4

The 4ᵗʰ value is 8.

Answer:

The 50ᵗʰ percentile is 8.

Case 3: Finding percentile for grouped data

Use:

Pₖ = L + [(kN ÷ 100 − cf) ÷ f] × h

Example:

Find P₅₀.

Here:

N = 20

kN ÷ 100 = 50 × 20 ÷ 100

kN ÷ 100 = 10

The 10ᵗʰ value lies in class 10-20.

So:

L = 10

cf = 5

f = 8

h = 10

Formula:

P₅₀ = L + [(kN ÷ 100 − cf) ÷ f] × h

Substitute:

P₅₀ = 10 + [(10 − 5) ÷ 8] × 10

P₅₀ = 10 + (5 ÷ 8) × 10

P₅₀ = 10 + 6.25

P₅₀ = 16.25

Answer:

The 50ᵗʰ percentile is 16.25.

Solved Examples on Percentile Formula

Percentile Formula questions usually test rank, ordered position, interpolation or grouped data. Always arrange raw data in ascending order before finding a percentile value.

Example 1: Find the percentile rank of 9 in [3, 5, 7, 9, 12]

Given:

Dataset:

3, 5, 7, 9, 12

Value:

x = 9

Values below 9:

3, 5, 7

Number of values below 9:

3

Total values:

N = 5

Formula:

Percentile = (Values below x ÷ N) × 100

Substitute:

Percentile = (3 ÷ 5) × 100

Percentile = 60

Answer:

The value 9 is at the 60ᵗʰ percentile.

Example 2: Find the 75ᵗʰ percentile of 6, 8, 10, 12, 14, 16, 18

Given:

Data is already ordered:

6, 8, 10, 12, 14, 16, 18

Here:

P = 75

N = 7

Formula:

R = (P ÷ 100) × (N + 1)

Substitute:

R = (75 ÷ 100) × (7 + 1)

R = 0.75 × 8

R = 6

The 6ᵗʰ value is 16.

Answer:

The 75ᵗʰ percentile is 16.

Example 3: Find the 40ᵗʰ percentile of 10, 20, 30, 40, 50

Given:

Data:

10, 20, 30, 40, 50

Here:

P = 40

N = 5

Rank:

R = (40 ÷ 100) × (5 + 1)

R = 0.40 × 6

R = 2.4

The 2ⁿᵈ value is 20.

The 3ʳᵈ value is 30.

Decimal part:

d = 0.4

Interpolation:

P₄₀ = 20 + 0.4 × (30 − 20)

P₄₀ = 20 + 4

P₄₀ = 24

Answer:

The 40ᵗʰ percentile is 24.

Example 4: Find P₅₀ for grouped data

Add cumulative frequency:

Here:

k = 50

N = 20

Find position:

kN ÷ 100 = 50 × 20 ÷ 100

kN ÷ 100 = 10

The 10ᵗʰ value lies in 10-20.

So:

L = 10

cf = 5

f = 8

h = 10

Formula:

Pₖ = L + [(kN ÷ 100 − cf) ÷ f] × h

Substitute:

P₅₀ = 10 + [(10 − 5) ÷ 8] × 10

P₅₀ = 10 + 6.25

P₅₀ = 16.25

Answer:

The 50ᵗʰ percentile is 16.25.

Common Mistakes in Percentile Formula

Many percentile mistakes happen when students use the data without arranging it in ascending order. Percentile value calculation always needs ordered data.

Important checks:

• Arrange raw data from smallest to largest.
• Count values below x for percentile rank.
• Use N + 1 in the rank formula when that method is specified.
• Interpolate when the rank is a decimal.
• Use cumulative frequency for grouped data.
• Identify the percentile class before applying the grouped formula.
• Write percentile notation properly, such as P₂₅, P₅₀, P₉₀ and P₉₅.

For percentile rank, count values below the given value carefully. For percentile value, find the rank position first.

Applications of Percentile Formula

The Percentile Formula is used in Statistics, education, health, entrance exams and data analysis. It compares one value with the rest of a dataset.

Main applications:

• It shows a student’s position in exam scores.
• It helps compare entrance test performance.
• It is used in growth charts for height and weight.
• It helps analyse income and population data.
• It is used in statistics and data science.
• It supports quartile and median calculations.
• It helps compare large datasets through rank positions.