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Quartile Calculator

Calculate Q1, Q2, Q3 and the interquartile range from any numerical data set. Get accurate quartile values with a clear step-by-step result.

Calculate Quartiles

Enter your data values to calculate Q1, Q2, Q3 and IQR.

Separate values with commas, spaces, or line breaks. Decimal and negative values are supported.
Try Example Data
Quartile Results
Q2 = 0
Q1 0
Q2 / Median 0
Q3 0
IQR 0

What Are Quartiles?

Quartiles are statistical values that divide an ordered data set into four approximately equal parts. They are useful for understanding how values are distributed and how widely the data is spread.

The three main quartiles are Q1, Q2, and Q3. Q1 represents the 25th percentile, Q2 represents the median or 50th percentile, and Q3 represents the 75th percentile.

Q1 = 25th Percentile   |   Q2 = 50th Percentile   |   Q3 = 75th Percentile

How Does the Quartile Calculator Work?

The calculator first sorts your values from smallest to largest. It then determines Q1, Q2, and Q3 using percentile-style linear interpolation. Finally, it subtracts Q1 from Q3 to calculate the interquartile range.

  1. Enter all values from your data set.
  2. The calculator automatically sorts the values in ascending order.
  3. Q1 is calculated at the 25th percentile.
  4. Q2 is calculated at the 50th percentile, which is the median.
  5. Q3 is calculated at the 75th percentile.
  6. The interquartile range is calculated as Q3 − Q1.

Quartile Formulas

When using the linear interpolation method, the percentile position can be calculated using:

Position = (P ÷ 100) × (n − 1)

Here, P is the desired percentile and n is the number of values in the sorted data set.

First Quartile — Q1

Q1 is the 25th percentile and represents the point below which approximately 25% of the data falls.

Q1 = P25

Second Quartile — Q2

Q2 is the 50th percentile and is also called the median.

Q2 = P50 = Median

Third Quartile — Q3

Q3 is the 75th percentile and represents the point below which approximately 75% of the data falls.

Q3 = P75

Interquartile Range — IQR

The interquartile range measures the spread of the middle 50% of the data.

IQR = Q3 − Q1

Quartile Calculation Example

Consider this data set:

10, 20, 30, 40, 50, 60, 70

The values are already arranged from smallest to largest. Using the linear interpolation method:

Q1 = P25 = 25
Q2 = P50 = 40
Q3 = P75 = 55

Therefore, the interquartile range is:

IQR = Q3 − Q1
IQR = 55 − 25
IQR = 30

Why Are Quartiles Important?

Quartiles provide a useful summary of the distribution of a data set. Instead of looking only at the minimum and maximum values, quartiles show where the lower, middle, and upper portions of the data are located.

Understanding Data Distribution

Q1, Q2, and Q3 can help identify whether values are concentrated in certain parts of a distribution.

Detecting Outliers

The interquartile range is frequently used when identifying potential outliers. A common rule considers values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR as potential outliers.

Comparing Data Sets

Quartiles can make it easier to compare distributions, especially when data sets contain extreme values that could strongly affect the mean.

Frequently Asked Questions

Q1 is the 25th percentile, Q2 is the 50th percentile or median, and Q3 is the 75th percentile.
The interquartile range, or IQR, is the difference between Q3 and Q1. The formula is IQR = Q3 − Q1.
Yes. Q2 is the 50th percentile and is equal to the median of the data set.
Yes. Quartile values can be decimal numbers when interpolation is required between two data values.
No. You can enter your values in any order. The calculator automatically sorts them from smallest to largest before calculating the quartiles.
Q1 is the 25th percentile. This calculator determines its position using linear interpolation when the position falls between two data values.
Q3 is the 75th percentile and is calculated using the same linear interpolation approach.