Lower Fence Calculator — Outlier Detection with Tukey Fences
Enter your dataset and instantly get the lower fence (Q1 − 1.5 × IQR), upper fence, quartiles, IQR, and a list of outliers — visualised on an annotated number line.
Values below this are flagged as potential outliers (Q1 − 1.5 × IQR)
- 1
Q1 (median of lower half)
8 - 2
Q3 (median of upper half)
18 - 3
IQR = Q3 − Q1
18 − 8 = 10 - 4
Lower fence = Q1 − 1.5 × IQR
8 − 1.5 × 10 = -7Values below this threshold are flagged as potential outliers by Tukey's rule.
How does this calculator work?
Sort the data, find Q1 (median of lower half) and Q3 (median of upper half), compute IQR = Q3 − Q1. Lower fence = Q1 − 1.5 × IQR; upper fence = Q3 + 1.5 × IQR. Any value outside these fences is a potential outlier by Tukey's box-plot rule (≈0.7% of data under normality).
Formula
How this is calculated
The lower fence is the boundary below which a data point is considered a potential outlier using Tukey's method, the standard technique behind box-and-whisker plots. First the dataset is sorted and split into halves: the first quartile Q1 is the median of the lower half, Q3 is the median of the upper half, and the interquartile range IQR = Q3 − Q1 captures the spread of the middle 50% of the data. The lower fence is then Q1 − 1.5 × IQR and the upper fence is Q3 + 1.5 × IQR.
Any observation outside those fences is labelled a mild outlier (values beyond Q1 − 3 × IQR or Q3 + 3 × IQR are sometimes called extreme outliers — this calculator marks anything beyond 1.5 × IQR). The 1.5 multiplier is a convention introduced by John Tukey in 1977 that works well for roughly normal distributions; it corresponds to roughly ±2.7 standard deviations and flags about 0.7% of data as outliers under normality.
This calculator uses Tukey's hinges method: when n is odd the median itself is excluded from both halves when computing Q1 and Q3. Results may differ slightly from software that uses a different interpolation rule (e.g. Excel's QUARTILE function uses linear interpolation).
Frequently asked questions
The lower fence is Q1 − 1.5 × IQR, where Q1 is the first quartile and IQR is the interquartile range (Q3 − Q1). Any data point below the lower fence is considered a potential outlier by Tukey's box-plot method.
The 1.5 multiplier was chosen empirically by John Tukey because it works well for normally distributed data — flagging about 0.7% of values as outliers, which is statistically meaningful without being too aggressive. The factor 3 × IQR is sometimes used for "extreme" outliers.
Not necessarily. The fence flags data points that deserve investigation, not automatic removal. Extreme values can be real measurements, data-entry errors, or members of a different subpopulation. Always examine outliers in context before deciding whether to keep, correct, or remove them.
Also known as
TG we-Calculate Editorial Team. (2026). Lower Fence Calculator — Outlier Detection with Tukey Fences [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lower-fence-calculator
TG we-Calculate Editorial Team. "Lower Fence Calculator — Outlier Detection with Tukey Fences." TG we-Calculate. 2026. https://we-calculate.com/calculator/lower-fence-calculator.
TG we-Calculate Editorial Team, "Lower Fence Calculator — Outlier Detection with Tukey Fences," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lower-fence-calculator
@misc{wecalculate_lower_fence_calculator, title = {Lower Fence Calculator — Outlier Detection with Tukey Fences}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lower-fence-calculator}}, year = {2026}, note = {TG we-Calculate} }
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