Outlier Calculator (IQR Fences and Box Plot)
Paste your data to find the box-plot fences and count the outliers.
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Outlier Calculator (IQR Fences and Box Plot) by TheCalcTools
How the Outlier Calculator (IQR Fences and Box Plot) works
Tukey’s rule marks a value as an outlier if it lies more than 1.5 interquartile ranges below Q1 or above Q3. These limits are the “fences” drawn as whiskers on a box plot.
Using 3 × IQR instead flags only extreme outliers. An outlier is not automatically an error: check whether it is a typo, a measurement problem or a genuine unusual value before removing it.
The formula
Worked example
Using the default values shown in the calculator:
| Your data | 10, 12, 12, 13, 14, 15, 15, 16, 18, 45 |
|---|---|
| Fence multiplier | 1.5 × IQR (outliers) |
- Q1 = 12.25, Q3 = 15.75, so IQR = 3.50.
- Fences: 12.25 − 1.5 × 3.50 = 7.00 and 15.75 + 1.5 × 3.50 = 21.00.
- Only 45 lies outside, so 1 outlier is found.
Result:
| Outliers found | 1 |
|---|---|
| Lower fence | 7.0000 |
| Upper fence | 21.0000 |
| Q1 | 12.2500 |
| Q3 | 15.7500 |
| IQR | 3.5000 |
| Values below the lower fence | 0 |
| Values above the upper fence | 1 |
Frequently asked questions
Should I delete outliers?
Only if you can show they are errors. Genuine extreme values carry information. Report results with and without them if they change your conclusion.
Why 1.5?
John Tukey chose 1.5 × IQR as a practical rule for box plots. For normally distributed data it flags roughly 0.7% of values.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.