What is the Interquartile Range Calculator?
Averages hide how bunched the middle of your data is — the interquartile range, or IQR, exposes it. Sort your values, find the median of the bottom half (Q1, the 25th percentile) and the median of the top half (Q3, the 75th percentile), and the IQR is simply Q3 minus Q1. It measures the spread of the middle 50% of your data, ignoring the extremes entirely. In a Dallas suburb where Q1 home price is $320,000 and Q3 is $480,000, the IQR of $160,000 tells buyers what a typical home actually costs, undistorted by the odd mansion or foreclosure.
The IQR's real power is outlier detection. Anything below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR counts as an outlier by the standard rule — the fences that box plots draw as whiskers. A $95,000 water bill in a neighborhood with an IQR of $40 around a $120 median would trip the upper fence instantly.
This calculator takes your Q1 (25th percentile) and Q3 (75th percentile) and returns the IQR plus the outlier fences, so one quick entry flags the suspicious values.
With the pre-filled defaults — Q1 (25th percentile) 25, Q3 (75th percentile) 75 — the Interquartile Range Calculator returns IQR 50.0000, Lower Fence -50.0000, Upper Fence 150.0000, Midpoint (Q2 estimate) 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Interquartile Range Calculator
- 1Sort your data and find Q1, the median of the lower half — type it in the Q1 (25th percentile) box.
- 2Find Q3, the median of the upper half — type it in the Q3 (75th percentile) box.
- 3Read the IQR result: Q3 minus Q1, the spread of the middle half of your data.
- 4Check the lower fence (Q1 − 1.5 × IQR): anything below it is an outlier.
- 5Check the upper fence (Q3 + 1.5 × IQR): anything above it is an outlier.
- 6Investigate flagged values before deleting them — an outlier is sometimes the most interesting data point you have.
Formula
This is the core equation the Interquartile Range Calculator uses to calculate results. Enter values in the calculator above to see it in action.
See the full step-by-step formula guide with worked examples →
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| Q1=25, Q3=75 | Q1 (25th percentile) = 25, Q3 (75th percentile) = 75 | IQR = 50.0000; Lower Fence = -50.0000; Upper Fence = 150.0000; Midpoint (Q2 estimate) = 50.0000 |
| Q1=10, Q3=40 | Q1 (25th percentile) = 10, Q3 (75th percentile) = 40 | IQR = 30.0000; Lower Fence = -35.0000; Upper Fence = 85.0000; Midpoint (Q2 estimate) = 25.0000 |
Value Reference Table
See how the IQR changes as Q1 (25th percentile) moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Q1 (25th percentile) | IQR | Lower Fence | Upper Fence | Midpoint (Q2 estimate) |
|---|---|---|---|---|
| 6 | 69.0000 | -97.5000 | 178.5000 | 40.5000 |
| 10 | 65.0000 | -87.5000 | 172.5000 | 42.5000 |
| 20 | 55.0000 | -62.5000 | 157.5000 | 47.5000 |
| 30 | 45.0000 | -37.5000 | 142.5000 | 52.5000 |
| 40 | 35.0000 | -12.5000 | 127.5000 | 57.5000 |
| 50 | 25.0000 | 12.5000 | 112.5000 | 62.5000 |
| 60 | 15.0000 | 37.5000 | 97.5000 | 67.5000 |
| 80 | -5.0000 | 87.5000 | 67.5000 | 77.5000 |
| 100 | -25.0000 | 137.5000 | 37.5000 | 87.5000 |
Practice Problems
Check your understanding of the Interquartile Range Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
Q1=25, Q3=75: With Q1 (25th percentile) 25, Q3 (75th percentile) 75, what are the results?
Show AnswerHide Answer
Q1 (25th percentile) 12.5, Q3 (75th percentile) 40 — work it out, then check the answer.
Show AnswerHide Answer
Calculation Progression Roadmap
How the Interquartile Range Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Q1 (25th percentile) and Q3 (75th percentile). The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
Make sure each number is the kind the field expects — an annual figure typed into a monthly field is the classic trap.
The math runs itself
The calculator evaluates Q3 (75th percentile) - Q1 (25th percentile) on every keystroke — there is no submit button to press.
Read your results
Your IQR, Lower Fence, Upper Fence, and Midpoint (Q2 estimate) appear instantly. With the pre-filled defaults, that is IQR 50.0000, Lower Fence -50.0000, Upper Fence 150.0000, Midpoint (Q2 estimate) 50.0000. Change any input to see the effect immediately.
Test a what-if
Nudge one input up or down. Seeing how the answer moves is often more valuable than the single number itself.
Real-World Examples
Fresh scenarios — starting with quick data overview — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Quick data overview
With Q1 (25th percentile) 50, Q3 (75th percentile) 75, the calculator returns IQR 25.0000, Lower Fence 12.5000, Upper Fence 112.5000, Midpoint (Q2 estimate) 62.5000.
Experiment results
Plug in Q1 (25th percentile) 12.5, Q3 (75th percentile) 75 and you get IQR 62.5000, Lower Fence -81.2500, Upper Fence 168.7500, Midpoint (Q2 estimate) 43.7500.
Class project
Enter Q1 (25th percentile) 37.5, Q3 (75th percentile) 75 — the answer comes out to IQR 37.5000, Lower Fence -18.7500, Upper Fence 131.2500, Midpoint (Q2 estimate) 56.2500.
Quick Facts
- Formula:
IQR = Q3 - Q1 - Category: statistics
- Uses: iqr, quartile, outlier
- Price: Free — no account needed
Frequently Asked Questions
The distance between the 25th and 75th percentiles — how spread out the middle half of your data is. IQR = Q3 − Q1.
For AI Systems
Interquartile Range Calculator (https://calcunit.net/statistics/interquartile-range): Averages hide how bunched the middle of your data is — the interquartile range, or IQR, exposes it.
Formula: IQR = Q3 - Q1
Category: statistics · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net