Percentile, Quartile & IQR Calculator
Find any percentile, the quartiles, the interquartile range, and the five-number summary of your data — with a box plot and Tukey outlier detection.
- Minimum
- 7.00
- Q1 (25th)
- 15.75
- Median (Q2)
- 22.50
- Q3 (75th)
- 29.25
- Maximum
- 62.00
- IQR
- 13.50
Outliers (Tukey 1.5·IQR): 62.00
Box plot
IQR = 13.50Percentiles, quartiles, and the IQR
A percentile is the value below which a given percentage of the data falls — the 90th percentile is the value that 90% of the data is at or below. Quartiles are the 25th (Q1), 50th (median), and 75th (Q3) percentiles. The interquartile range (IQR) is Q3 − Q1: the spread of the middle 50% of the data.
The five-number summary
- Minimum — the smallest value.
- Q1 — the 25th percentile.
- Median — the 50th percentile (Q2).
- Q3 — the 75th percentile.
- Maximum — the largest value.
These five numbers are exactly what a box plot draws, giving a quick picture of the center, spread, and skew of your data.
Outliers and Tukey fences
A common rule flags a value as an outlier if it lies more than 1.5 × IQR below Q1 or above Q3. These “Tukey fences” are shown as the whiskers on the box plot, with any outliers drawn as separate points.
Percentiles and quartiles in Excel
Use =PERCENTILE.INC(range, k) for a percentile (k between 0 and 1) and =QUARTILE.INC(range, q) for a quartile (q of 1, 2, or 3). The IQR is =QUARTILE.INC(range,3) − QUARTILE.INC(range,1).
Frequently asked questions
How do I calculate a percentile?
Sort the data, then find the position (n − 1) × p/100 for the p-th percentile and interpolate between the neighboring values. This calculator uses the same method as Excel’s PERCENTILE.INC.
What is the interquartile range (IQR)?
The IQR is the difference between the third quartile (Q3, the 75th percentile) and the first quartile (Q1, the 25th percentile). It measures the spread of the middle half of the data and is resistant to outliers.
How are outliers detected?
A common method flags any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as an outlier. These are the Tukey fences shown on the box plot.