Interquartile Range Calculator
The interquartile range (IQR) measures the spread of the middle 50% of your data and is one of the most useful statistics for understanding variability and identifying outliers. This calculator computes Q1 and Q3, calculates the IQR, and applies the standard 1.5 * IQR rule to identify lower and upper fences. Any data point falling outside these fences is flagged as a potential outlier. IQR is more robust than standard deviation because it ignores extreme values, making it ideal for datasets with unusual or extreme observations.
Interquartile range formula
IQR = Q3 - Q1
Lower Fence = Q1 - 1.5 * IQR
Upper Fence = Q3 + 1.5 * IQR
Outliers: values < Lower Fence or > Upper Fence
Understanding the 1.5 IQR rule
- The lower fence defines the boundary below which a value is considered an outlier.
- The upper fence defines the boundary above which a value is considered an outlier.
- The 1.5 multiplier is a standard choice in statistics that works well for most distributions.
- Outliers detected by this rule are often worth investigating for data entry errors or special cases.
- The 1.5 * IQR rule is used in box plots, where outliers are shown as individual points beyond the whiskers.
IQR calculator: frequently asked questions
What is the interquartile range (IQR)?
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1): IQR = Q3 - Q1. It represents the spread of the middle 50% of your data.
How do you use IQR to find outliers?
The 1.5 * IQR rule is standard: lower fence = Q1 - 1.5 * IQR, upper fence = Q3 + 1.5 * IQR. Any value below the lower fence or above the upper fence is considered an outlier.
What do the quartile fences represent?
The lower and upper fences are boundaries beyond which values are considered outliers. These fences define the expected range of normal data. Values outside the fences are unusual or extreme.
Why is IQR useful?
IQR is robust to extreme values and gives a clear picture of data spread. It is used for box plots, outlier detection, and understanding the consistency or variability of your data.
Can IQR be zero?
Yes. If Q1 and Q3 are the same (because more than 50% of your data has the same value), IQR will be zero. This indicates very little variability in the middle 50% of the data.
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: NIST Handbook.
- American Statistical Association: ASA.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.