IQR & Outlier Calculator
Find the quartiles, interquartile range, and Tukey fences of any data set, and automatically flag the outliers.
Fence multiplier (k)
1 outlier(s) detected
- 1
Q1 — median of lower half
13For odd-length data the overall median is excluded from both halves (Tukey hinges). - 2
Q3 — median of upper half
22 - 3
IQR = Q3 − Q1
22 − 13 = 9 - 4
Lower fence = Q1 − k × IQR
13 − 1.5 × 9 = -0.5 - 5
Upper fence = Q3 + k × IQR
22 + 1.5 × 9 = 35.5
How does this calculator work?
The IQR is Q3 minus Q1, the spread of the middle half of your data. Tukey fences sit at Q1 − k·IQR and Q3 + k·IQR, where k is 1.5 for mild or 3.0 for extreme outliers. Any value outside those fences is flagged as an outlier. Enter at least four numbers to see results.
Formula
How this is calculated
Enter your numbers in any order separated by commas or spaces. The calculator sorts them, splits the set into a lower and upper half, and takes the median of each half to get the first quartile (Q1) and third quartile (Q3). When the count is odd the overall median is excluded from both halves (the standard Tukey/Moore method). The interquartile range is simply IQR = Q3 − Q1, the spread of the middle 50% of the data.
The fence multiplier k sets how aggressively values are flagged. With k = 1.5 the fences sit at Q1 − 1.5·IQR and Q3 + 1.5·IQR, marking "mild" outliers; with k = 3.0 they mark only "extreme" outliers. Any value below the lower fence or above the upper fence is reported as an outlier.
All outputs share the same units as your input data. At least four values are required so each half has a defined median; the IQR is unaffected by extreme values, which is why it is preferred over the range for skewed data. If every value falls inside the fences, no outliers are reported.
Frequently asked questions
Mild outliers fall beyond 1.5×IQR from the quartiles, while extreme outliers fall beyond 3×IQR. Use the multiplier selector to switch between the two thresholds.
The data is sorted and split in half. Q1 is the median of the lower half and Q3 the median of the upper half. For an odd number of values the central median is excluded from both halves (Tukey hinges).
The IQR measures the middle 50% of the data and is resistant to extreme values, making it a robust measure of spread for skewed or outlier-prone data sets.
Also known as
TG we-Calculate Editorial Team. (2026). IQR & Outlier Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/iqr-outlier-calculator
TG we-Calculate Editorial Team. "IQR & Outlier Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/iqr-outlier-calculator.
TG we-Calculate Editorial Team, "IQR & Outlier Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/iqr-outlier-calculator
@misc{wecalculate_iqr_outlier_calculator, title = {IQR & Outlier Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/iqr-outlier-calculator}}, year = {2026}, note = {TG we-Calculate} }
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