This Percentile, Quartile, and IQR Calculator helps you analyze the distribution and spread of your data. It calculates percentiles (values below which a given percentage of observations fall), quartiles (values that divide data into four equal parts), and the interquartile range (IQR, a measure of statistical dispersion). For example, you can analyze test scores to find the 75th percentile, determine salary quartiles, or use the IQR to identify outliers in any numerical dataset.
Quick Calculator
Need a quick calculation? Enter your numbers below:
Calculator
1. Load Your Data
2. Select Column & Enter Percentile
Related Calculators
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What is a Percentile?
Percentile Meaning
A percentile shows where a value ranks compared to all other values in a dataset. If you're in the 75th percentile for height, you're taller than 75% of people in your comparison group. Percentiles help you understand relative position rather than absolute values.
High Percentile Meanings
98th Percentile Meaning
You scored higher than 98% of people. Only 2% performed better than you.
99th Percentile Meaning
You outperformed 99% of people. You're in the top 1%.
Percentile vs Percentage
Percentile:
Your rank position (90th percentile = better than 90% of people)
Percentage:
Portion of total (90% correct answers on a test)
Types of Percentile Calculators
Baby Percentile Calculator
Track your child's growth compared to other children of the same age and gender.
IQ Percentile Calculator
Convert IQ scores to percentile ranks to understand cognitive ability position.
Net Worth & Income Percentiles
Compare your financial position to others in your age group or region.
Test Score Percentiles
Understand standardized test performance relative to all test-takers.
Real-World Example: Net Worth Percentiles by Age
US household net worth distribution showing how wealth varies by age group (2024 data).
Net Worth Percentile by Age
| Age Range | 25th Percentile | 50th Percentile (Median) | 75th Percentile | 90th Percentile |
|---|---|---|---|---|
| 25-29 | $4,000 | $23,000 | $75,000 | $177,000 |
| 30-34 | $8,000 | $50,000 | $142,000 | $285,000 |
| 35-39 | $20,000 | $91,000 | $225,000 | $424,000 |
| 40-44 | $35,000 | $141,000 | $350,000 | $644,000 |
| 45-49 | $46,000 | $190,000 | $473,000 | $875,000 |
| 50-54 | $75,000 | $266,000 | $740,000 | $1,580,000 |
Key Insights:
- Net worth typically increases significantly with age due to compound growth
- At age 30, the median net worth is $50,000 - half of people have more, half have less
- The 75th percentile shows substantial wealth gaps - top 25% accumulate much more
- 90th percentile households represent the top 10% of wealth in each age group
How to use this: Find your age group and see which percentile your net worth falls into. This helps with financial planning and goal setting.
How to Calculate Percentile (Step-by-Step)
Method 1: Find a Specific Percentile Value
- Sort your data: Arrange all values from smallest to largest
- Calculate position: Position = (Percentile ÷ 100) × (n - 1) + 1
- Find the value: If position is whole number, use that data point
- Interpolate if needed: If position is decimal, interpolate between neighboring values
Example: Find 25th Percentile
Data: [10, 15, 20, 25, 30, 35, 40, 45, 50]
Method 2: Find Percentile Rank of a Value
- Count values below: How many values are less than your target
- Add half of equal values: Add 0.5 × (number of equal values)
- Divide by total: Divide result by total number of values
- Convert to percentage: Multiply by 100
Example: Find percentile rank of 30 in [10, 15, 20, 25, 30, 35, 40, 45, 50]
Key Formulas
Quartiles:
Outlier Detection:
Interactive Percentile Visualization
Explore how percentiles divide data using this interactive histogram and box plot.
Understanding Percentiles and Quartiles
This visualization shows 1,000 exam scores. Hover over the percentile buttons to see how they divide the data.
Distribution of Exam Scores (Histogram)
Box Plot Representation
25th Percentile (Q1)
67.0
25% scored below this
50th Percentile (Median)
75.0
50% scored below this
75th Percentile (Q3)
83.0
75% scored below this
Interquartile Range (IQR)
16.0 points
The range containing the middle 50% of scores (from 67.0 to 83.0)
Understanding the Visualization
Histogram Colors:
Key Insight:
Each histogram bar represents a score range (e.g., 70-75), not a single score. The box plot summarizes the same data by showing the key percentiles and the IQR.
Creating Percentile Calculators in Different Tools
Examples of how to calculate percentiles in R, Python, and Excel.
R
# Calculate percentiles in R
library(tidyverse)
data <- c(10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60)
# Using quantile() function
percentiles <- quantile(data, probs = c(0.25, 0.50, 0.75, 0.90, 0.95))
print(percentiles)
# 25% 50% 75% 90% 95%
# 22.5 35.0 47.5 55.0 57.5
# Specific percentile
p25 <- quantile(data, 0.25)
p75 <- quantile(data, 0.75)
iqr <- p75 - p25
print(str_glue("IQR: {iqr}"))
# IQR: 25
# Find percentile rank of a value
value <- 35
percentile_rank <- (sum(data < value) + 0.5 * sum(data == value)) / length(data) * 100
print(str_glue("Value {value} is at the {percentile_rank} percentile"))
# Value 35 is at the 50 percentile
# Create percentile table
percentile_table <- tibble(
percentile = c(10, 25, 50, 75, 90, 95, 99),
value = quantile(data, probs = percentile/100)
)
print(percentile_table)
# percentile value
# 0 10 15.0
# 1 25 22.5
# 2 50 35.0
# 3 75 47.5
# 4 90 55.0
# 5 95 57.5
# 6 99 59.5Python (NumPy/Pandas)
import numpy as np
import pandas as pd
data = [10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60]
# NumPy percentiles
percentiles = np.percentile(data, [25, 50, 75, 90, 95])
print("Percentiles:", percentiles)
# Pandas quantiles
df = pd.Series(data)
q25, q50, q75 = df.quantile([0.25, 0.50, 0.75])
iqr = q75 - q25
# Find percentile rank
from scipy import stats
value = 35
percentile_rank = stats.percentileofscore(data, value)
print(f"Value {value} is at the {percentile_rank}th percentile")
# Create comprehensive percentile table
percentile_df = pd.DataFrame({
'percentile': [10, 25, 50, 75, 90, 95, 99],
'value': [np.percentile(data, p) for p in [10, 25, 50, 75, 90, 95, 99]]
})Excel
Method 1: PERCENTILE Function
=PERCENTILE(A1:A100, 0.25) # 25th percentile
=PERCENTILE(A1:A100, 0.50) # 50th percentile (median)
=PERCENTILE(A1:A100, 0.75) # 75th percentileMethod 2: PERCENTRANK Function
=PERCENTRANK(A1:A100, B1) # Find percentile rank of value in B1
=PERCENTRANK(A1:A100, B1, 3) # With 3 decimal placesStep-by-step Excel Guide:
- Put your data in column A (A1:A100)
- In cell C1, type
=PERCENTILE(A:A,0.25)for 25th percentile - In cell C2, type
=PERCENTILE(A:A,0.5)for median - In cell C3, type
=PERCENTILE(A:A,0.75)for 75th percentile - For IQR:
=C3-C1
Common Questions & Limitations
Frequently Asked Questions
What's a good percentile?
Depends on context. For standardized tests, 75th+ is good. For baby growth, 3rd-97th percentile can be normal.
Can percentiles exceed 100?
No. Percentiles range from 0-100. The 100th percentile would mean you outperformed everyone.
Limitations & Considerations
- Different calculation methods may yield slightly different results
- Small sample sizes (n < 30) can affect reliability
- Outliers can significantly impact percentile ranks