The formula
How to calculate interquartile range
The interquartile range is the spread of the middle half of the data — the distance between the 25th and 75th percentiles. Because it ignores the tails entirely, it is unaffected by extreme values.
The 1.5 × IQR fences are Tukey's rule, and they are what draw the whiskers on a box plot. Points beyond them are flagged as outliers for investigation.
What to enter:
- First quartile (Q1)
- Third quartile (Q3)
Results appear immediately — there is nothing to submit. Changing a field rewrites the link, so you can share the exact scenario you are looking at.
The calculation runs on exactly the numbers currently in the fields above, recomputed in full each time — there is no dependency on the order values are entered in, so adjusting one input to test a scenario and then changing it back leaves the result exactly where it started.
Why interquartile range matters
This kind of calculation comes up in coursework, in a laboratory or field setting, and in professional practice, and the arithmetic is identical in every case — only the numbers being fed into it, and what is riding on getting them right, actually change.
This also functions as a reference implementation of the formula itself: where the exact form of an equation is in question, the one used on this page, stated in the formula section above, is the standard version found in the relevant textbooks and reference material.
It is worth remembering that a formula is only ever as good as the assumptions built into it, and most of the standard equations used across science and statistics carry at least one simplifying assumption — a linear approximation, an idealised gas, a normally distributed error term — that holds well in most ordinary cases and breaks down at the extremes. The result here reflects the standard formula exactly; whether that formula's assumptions are appropriate for your particular situation is a separate judgement worth making deliberately rather than assuming automatically.
In practice, a formula like this one is most often reached for at the exact moment a manual calculation needs checking against a deadline — a lab report due, a problem set to submit — which is precisely the situation where a small arithmetic slip is easiest to miss and most costly to leave uncorrected. Running the same inputs through an independent calculator catches that class of error reliably.
Worked example
Take the figures the calculator starts with:
- First quartile (Q1): 62
- Third quartile (Q3): 84
That gives:
- Interquartile range: 22
- Lower outlier fence: 29
- Upper outlier fence: 117
The figures above are the calculator's own default values, shown purely so the working is visible rather than hidden — the same steps apply exactly to your own numbers, entered in the fields at the top of this page.
Reading the result
The IQR is the robust alternative to standard deviation. For skewed data — incomes, response times, house prices — the median and IQR describe the distribution far better than the mean and standard deviation.
Where this goes wrong. Different software computes quartiles differently — there are nine recognised methods — and they can disagree noticeably on small datasets. State the method when the exact value matters.
A result that is wrong by an exact factor of ten, a hundred or a similar round number is almost always a units error rather than a mistake in the formula itself — checking each input against the unit stated beside it is the fastest way to track it down.
Tukey chose it as a practical compromise. For normally distributed data it flags roughly 0.7% of points, which is rare enough to be worth investigating without drowning you in false alarms.
For skewed data or data with outliers, yes, because it is not distorted by extremes. For roughly normal data the standard deviation uses all the information and is more efficient.
The answer it gives you is interquartile range. With 62 first quartile (Q1) and 84 third quartile (Q3), that comes to 22. Change any field and the figure moves with it.
Generally, no more than the least precise input justifies — a result reported to six decimal places from inputs measured to two significant figures is implying a precision the calculation does not actually have. The calculator shows full precision so you can round appropriately for your own use.
Yes — the equation shown in the formula section above is the standard form used in textbooks and reference material for this calculation, not a simplified or approximate version.
Yes, in the sense that it applies the correct standard formula and returns an accurate result for the inputs given — but check your own course or publication's requirements for how results should be rounded, presented and referenced, since those conventions vary and are not something a calculator can know on your behalf.