# Quartile Calculator

Free quartile calculator. Find Q1, Q2 (median), Q3, interquartile range (IQR), and outlier fences from a normal distribution.

## What this calculates

Calculate the three quartiles (Q1, Q2, Q3), the interquartile range (IQR), and outlier fences for a normal distribution based on the mean and standard deviation.

## Inputs

- **Mean (μ)** — The mean of the distribution.
- **Standard Deviation (σ)** — min 0.0001 — The standard deviation of the distribution.

## Outputs

- **Q1 (25th Percentile)** — The first quartile. 25% of data falls below this value.
- **Q2 (Median / 50th Percentile)** — The second quartile (median). 50% of data falls below this value.
- **Q3 (75th Percentile)** — The third quartile. 75% of data falls below this value.
- **Interquartile Range (IQR)** — The range between Q1 and Q3 (Q3 - Q1).
- **Lower Fence** — Q1 - 1.5 × IQR. Values below this may be outliers.
- **Upper Fence** — Q3 + 1.5 × IQR. Values above this may be outliers.

## Details

Quartiles divide a data set into four equal parts.

For a Normal Distribution

- Q1 = μ - 0.6745σ (25th percentile)

- Q2 = μ (50th percentile / median)

- Q3 = μ + 0.6745σ (75th percentile)

- IQR = Q3 - Q1 = 1.349σ

Outlier Detection

- Lower fence = Q1 - 1.5 × IQR

- Upper fence = Q3 + 1.5 × IQR

- Values outside the fences are potential outliers.

## Frequently Asked Questions

**Q: What is the interquartile range (IQR)?**

A: The IQR is the difference between Q3 and Q1 (IQR = Q3 - Q1). It represents the middle 50% of the data and is a robust measure of spread that is not affected by outliers, unlike the range or standard deviation.

**Q: How are quartiles used in box plots?**

A: A box plot displays Q1 (left edge of box), Q2/median (line inside box), and Q3 (right edge of box). The whiskers extend to the fences or the most extreme non-outlier values. Points beyond the fences are plotted individually as outliers.

**Q: Why does this calculator assume a normal distribution?**

A: Since this calculator works with summary statistics (mean and standard deviation) rather than raw data, it uses the normal distribution to estimate quartile positions. For raw data, quartiles should be calculated by sorting the data directly.

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Source: https://vastcalc.com/calculators/statistics/quartile
Category: Statistics
Last updated: 2026-04-21