Interquartile Range Calculator
This interquartile range calculator finds the IQR of your data the moment you paste it in, along with Q1, the median, and Q3. Type your numbers separated by commas or spaces, and you'll get the quartiles, the IQR, the minimum and maximum, and any outliers beyond the fences. It draws a live box plot too, so you can see exactly where the middle 50% of your data sits. It's the quick way to measure spread without getting tripped up by extreme values.
- Q1, median, Q3
- IQR = Q3 - Q1
- Outlier detection
- Live box plot
- Tukey method
Last updated June 18, 2026 Method: IQR = Q3 - Q1 (Tukey) Reviewed by the Calcowa math team
Enter at least four numbers to find the quartiles.
Show fences, min, max, and outliers
IQR = Q3 - Q1 = 10 - 4 = 6
What is the interquartile range?
The interquartile range is the spread of the middle half of your data, and it's found with IQR = Q3 - Q1. Q1's the median of the lower half and Q3's the median of the upper half. For 2, 4, 5, 7, 8, 10, 12, the IQR is 6, since Q3's 10 and Q1's 4.
What makes the IQR useful is what it ignores. By focusing on the middle 50% and leaving out the lowest and highest quarters, it shrugs off outliers that'd distort the plain range. That's why it's the spread measure of choice for skewed data, and it's what powers the box plot and the standard outlier test. You won't get fooled by one runaway value the way you would with the range.
How do you calculate the IQR?
It's a tidy five-step routine, and you won't need anything past sorting and finding medians. Here's how the quartiles and the IQR come together:
- 1
Sort the dataPut every value in order from smallest to largest.
- 2
Find the medianTake the middle value. That's Q2, and it splits the set in two.
- 3
Find Q1Take the median of the lower half. The exclusive method leaves the overall median out.
- 4
Find Q3Take the median of the upper half the same way.
- 5
Subtract for the IQRIQR = Q3 - Q1. For outliers, check beyond Q1 - 1.5 IQR and Q3 + 1.5 IQR.
Finding outliers with the 1.5 IQR rule
The IQR doubles as an outlier detector, and that's where it really earns its keep. Build two fences, a lower one at Q1 - 1.5 × IQR and an upper one at Q3 + 1.5 × IQR, and any value past them counts as an outlier. Take 1, 2, 3, 4, 5, 6, 100: the IQR's 4, so the upper fence sits at 12, and that 100 gets flagged right away. The calculator lists every value beyond the fences, which is the same rule that draws the dots on a box plot. If you want a different angle on spread, the Standard Deviation Calculator measures distance from the mean, and the Mean Median Mode Calculator covers the centers.
The quartiles at a glance
Here's what each piece means. The quartiles split the data into four equal parts, and the IQR captures the middle two of them.
| Term | How to find it | Good to know |
|---|---|---|
| Q1 (first quartile) | Median of the lower half | 25% of the data falls below it |
| Q2 (median) | Middle value of the whole set | The center, 50% below it |
| Q3 (third quartile) | Median of the upper half | 75% of the data falls below it |
| IQR | Q3 minus Q1 | The spread of the middle 50% |
| Outlier fences | Q1 - 1.5 IQR and Q3 + 1.5 IQR | Values outside are flagged as outliers |
Frequently asked questions
What does a box plot show?
A box plot is the picture of these numbers. The box runs from Q1 to Q3, so its width is the IQR, and the line inside marks the median. The whiskers stretch to the fences, and any dots beyond them are outliers. The chart above redraws itself as you change the data, so you can watch the spread shift in real time.
The interquartile range, or IQR, is the spread of the middle 50% of a data set. You find it by subtracting the first quartile (Q1) from the third quartile (Q3): IQR = Q3 - Q1. Because it ignores the lowest 25% and the highest 25%, it isn't thrown off by a few extreme values the way the full range is.
Sort the data, find the median, then split the set into a lower half and an upper half. Q1 is the median of the lower half and Q3 is the median of the upper half. Subtract them, and that's the IQR. This calculator uses the exclusive (Tukey) method, which leaves the overall median out of both halves when the count is odd.
Q1, the first quartile, is the value below which 25% of the data sits, and it's the median of the lower half. Q3, the third quartile, is the value below which 75% sits, the median of the upper half. Together with the median (Q2), they split the data into four equal quarters, which is where the name quartile comes from.
The IQR sets up two fences: a lower fence at Q1 - 1.5 × IQR and an upper fence at Q3 + 1.5 × IQR. Any value beyond those fences is flagged as an outlier. It's the standard rule behind box plots, and this calculator lists every value that falls outside the fences for you.
The plain range is just the largest value minus the smallest, so a single extreme value can blow it up. The IQR looks only at the middle half, so it stays steady even when the data has outliers. That makes it a far more reliable measure of spread for skewed data like incomes, prices, or test scores.
Yes, and it's worth knowing. The exclusive (Tukey) method used here drops the median before splitting, while the inclusive method keeps it, and some software interpolates between values. The answers usually land close, but they don't always match exactly, so it helps to say which method you used when you report a result.
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