Percentile Calculator

Find values at specific percentiles in your dataset. Understand distribution quartiles, rankings, and spread with ease.

Last updated: March 2026

Dataset (comma/space separated)

Percentile (0-100)

Results

P25 Value

38.7500

25% of values fall below this

Q1 (25th)

38.7500

Q2 / Median

57.5000

Q3 (75th)

76.2500

IQR

37.5000

Sample size (n)

Minimum

15.0000

Maximum

90.0000

What is a Percentile?

A percentile is a value in a dataset below which a certain percentage of observations fall. For example, the 25th percentile (P25 or Q1) is the value below which 25% of the data points lie. Percentiles are essential for ranking, benchmarking, and understanding data distributions without being affected by extreme outliers.

Quartiles are special percentiles that divide data into four equal parts: Q1 (25th percentile), Q2 (50th percentile or median), and Q3 (75th percentile). The interquartile range (IQR) is Q3 − Q1 and represents the spread of the middle 50% of data, commonly used for outlier detection using the 1.5×IQR rule.

Percentiles are robust to outliers unlike mean and standard deviation. They're widely used in standardized testing ("your score is in the 92nd percentile"), growth charts for children, income distribution analysis, and performance benchmarking. The median (P50) is particularly important as it represents the central value that divides the dataset in half.

How to Use This Calculator

Step-by-Step Guide

Enter your dataset: Input all data points separated by commas, spaces, or newlines. Order doesn't matter—the calculator will sort automatically. Need at least 1 value.

Specify percentile: Enter any percentile from 0 to 100. Common values: P25 (Q1), P50 (median), P75 (Q3), P90 (top 10% threshold), P99 (top 1%).

Automatic calculation: The calculator sorts your data, computes the requested percentile using linear interpolation, and displays all quartiles and IQR.

Interpret results: P75 = 80 means 75% of values ≤ 80, and 25% ≥ 80. Use quartiles for box plots and IQR for outlier detection (values beyond Q1−1.5×IQR or Q3+1.5×IQR).

Calculation Method

1. Sort data ascending: [x₁, x₂, ..., xₙ]

2. Calculate position: pos = (percentile/100) × (n−1)

3. If pos is integer k: value = xₖ

4. If pos is fractional: linearly interpolate between neighbors

Quartiles: Q1 = P25, Q2 = P50 (median), Q3 = P75

IQR: Interquartile Range = Q3 − Q1

Example Calculation

Test Score Distribution

Dataset:

[15, 20, 35, 40, 50, 55, 60, 70, 75, 80, 85, 90]
n = 12 students

Finding P25 (Q1):
Position = (25/100) × (12−1) = 2.75
→ Between index 2 (value 35) and index 3 (value 40)
→ Interpolate: 35 + 0.75×(40−35) = 35 + 3.75 = 38.75

All Quartiles:
Q1 (P25) = 38.75 ← 25% below this
Q2 (P50) = 57.50 ← Median, 50% below
Q3 (P75) = 77.50 ← 75% below this
IQR = Q3 − Q1 = 77.50 − 38.75 = 38.75

Outlier thresholds:
Lower fence: Q1 − 1.5×IQR = -19.375 (no outliers below)
Upper fence: Q3 + 1.5×IQR = 135.625 (no outliers above)

Interpretation:

25% of students scored below 38.75, the median score is 57.50, and 75% scored below 77.50. The IQR of 38.75 shows moderate spread in the middle 50% of scores. No outliers detected using the 1.5×IQR rule.

Frequently Asked Questions

What is a percentile?

Value below which a given percentage of observations fall. P25 means 25% of data is below this value. P50 = median (half below, half above). P100 = maximum. Essential for ranking and benchmarking without outlier sensitivity.

What are quartiles?

Percentiles that divide data into four equal parts: Q1 (P25, 25th percentile), Q2 (P50, median), Q3 (P75, 75th percentile). IQR = Q3−Q1 measures middle 50% spread. Used in box plots and outlier detection.

How to calculate percentile?

Sort data ascending. Position = (p/100)×(n−1). If position is integer, use that data point. If fractional, linearly interpolate between neighbors. Formula ensures consistent results across implementations.

Is P0 the minimum?

Yes. P0 = 0th percentile = minimum value. P100 = 100th percentile = maximum. P50 = median (middle value, divides data in half). These are special boundary cases.

Can percentiles be fractional?

Yes. Any percentile from 0 to 100 is valid. P33.33 (tertiles), P20 (quintiles), P10 (deciles), P90 (top 10% threshold). Provides flexible distribution analysis for various needs.

What if data has duplicate values?

Duplicates (ties) don't affect percentile calculation—handled naturally by the interpolation method. Multiple identical values are treated as separate points for sorting and position calculation.

Percentile vs. percentile rank?

Percentile: 'What value is at P75?' (answer: a specific number). Percentile rank: 'What percentile is value 85?' (answer: a percentage). They're inverse operations of each other.

Why use percentiles over mean±SD?

Percentiles are robust to outliers and don't assume normal distribution. Interpretable ('top 10%' = P90+). Used in benchmark scoring, clinical trials, growth charts, income analysis, and test standardization where outliers exist.