IQR Calculator — Interquartile Range
Calculate interquartile range, Q1, Q3, and Tukey outlier fences from up to 10 values.
Uses the exclusive quartile method.
Identifies mild and extreme outliers.
The interquartile range is the spread of the middle 50% of a dataset. Compute Q1 (25th percentile) and Q3 (75th percentile), then subtract: IQR = Q3 - Q1. Unlike the full range (max - min), IQR ignores the extremes, so a single rogue value cannot inflate it. That makes it the go-to spread measure for skewed data, income distributions, test scores, and anything where outliers are expected.
The quartile method used here is the exclusive (Tukey) method: split the sorted data at the median position, excluding the median itself from both halves when n is odd. This matches what Excel QUARTILE.EXC and most statistics textbooks return. Note that different software packages define quartiles differently – R, SAS, and Excel all have their own conventions, and they can produce slightly different Q1/Q3 values for small datasets.
Once you have the IQR, outlier fences follow automatically. A mild outlier falls below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR. An extreme outlier is beyond Q1 - 3 x IQR or Q3 + 3 x IQR. These thresholds come from Tukey’s 1977 boxplot paper and are baked into every major stats package – though they are a rule of thumb, not a law.
The IQR only measures spread, not shape. A dataset with IQR = 10 could be symmetric, left-skewed, or bimodal. Always pair it with a quick look at the median and the actual sorted values before drawing conclusions about the distribution.
How to use: enter your values in any order (blanks are skipped). At least 4 values are needed to compute meaningful quartiles. The result shows Q1, Q3, IQR, both Tukey fences, and any detected outliers.