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Interquartile Range (IQR) Calculator

Calculate the interquartile range and identify outlier boundaries using the 1.5*IQR rule. The IQR measures the spread of the middle 50% of data and is robust to extreme values.

Reviewed by Chase FloiedUpdated

This free online interquartile range (iqr) calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

The 25th percentile of your data.

The 75th percentile of your data.

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Interquartile Range (IQR) Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Interquartile Range (IQR) Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Interquartile Range (IQR) Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • Use the Interquartile Range (IQR) Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

About This Calculator

The Interquartile Range (IQR) Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the interquartile range and identify outlier boundaries using the 1.5*IQR rule. The IQR measures the spread of the middle 50% of data and is robust to extreme values. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.

About Interquartile Range (IQR) Calculator

The interquartile range (IQR) calculator computes the spread of the middle 50% of your data and identifies potential outliers using the 1.5*IQR rule. Unlike standard deviation, the IQR is resistant to extreme values because it depends only on the 25th and 75th percentiles, not on every data point. This makes it the preferred measure of spread for skewed distributions and datasets with outliers. The IQR is the foundation of the box-and-whisker plot, one of the most informative graphical summaries in exploratory data analysis. It is widely used in data science, epidemiology, environmental monitoring, and finance to characterize data distributions and flag unusual observations.

The Math Behind It

The IQR is defined as Q3 - Q1, where Q1 is the first quartile (25th percentile) and Q3 is the third quartile (75th percentile). It captures the range of the central half of the data. The 1.5*IQR rule, developed by John Tukey, defines outlier fences: any data point below Q1 - 1.5*IQR or above Q3 + 1.5*IQR is considered a potential outlier, and points beyond Q1 - 3*IQR or Q3 + 3*IQR are extreme outliers. For a normal distribution, the IQR equals approximately 1.35 standard deviations, and the 1.5*IQR rule identifies about 0.7% of data as outliers. The IQR is part of the five-number summary (minimum, Q1, median, Q3, maximum) and is displayed in box plots. Quartiles can be computed in several ways (inclusive, exclusive, interpolated), and different statistical software may produce slightly different values. The semi-interquartile range (SIQR = IQR/2) is sometimes used as a robust measure of dispersion, and the median absolute deviation (MAD) is another robust alternative.

Formula Reference

Interquartile Range

IQR = Q3 - Q1

Variables: Q1 = 25th percentile; Q3 = 75th percentile

Outlier Fences

Lower = Q1 - 1.5*IQR; Upper = Q3 + 1.5*IQR

Variables: Values outside fences are potential outliers

Worked Examples

Example 1: Employee salary analysis

Q1 = $45,000, Q3 = $75,000. Find the IQR and outlier boundaries.

Step 1:IQR = 75000 - 45000 = $30,000.
Step 2:Lower fence = 45000 - 1.5*30000 = 45000 - 45000 = $0.
Step 3:Upper fence = 75000 + 1.5*30000 = 75000 + 45000 = $120,000.

Salaries above $120,000 would be flagged as potential outliers. The IQR of $30,000 captures the middle 50% of salaries.

Example 2: Test score distribution

Q1 = 65, Q3 = 85.

Step 1:IQR = 85 - 65 = 20.
Step 2:Lower fence = 65 - 30 = 35.
Step 3:Upper fence = 85 + 30 = 115.

Scores below 35 or above 115 are potential outliers.

Common Mistakes & Tips

  • !Confusing IQR with the full range (max - min). The IQR only covers the middle 50%.
  • !Automatically removing flagged outliers without investigating whether they are genuine extreme values or data errors.
  • !Using IQR for very small datasets where quartile estimates are unreliable.

Related Concepts

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Frequently Asked Questions

Why is 1.5 used as the multiplier for outlier detection?

Tukey chose 1.5 as a practical compromise: it flags about 0.7% of normally distributed data as outliers, which aligns well with real-world expectations. A multiplier of 3 identifies extreme outliers.

Can the IQR be zero?

Yes, if more than half the data values are identical, Q1 and Q3 can be equal, giving IQR = 0. This indicates very little variability in the central portion of the data.

How does IQR compare to standard deviation?

For a normal distribution, IQR is approximately 1.35 times the standard deviation. The IQR is more robust to outliers, while the standard deviation uses all data points and is needed for many parametric tests.