Third Quartile (Q3) Calculator

Paste a dataset to find the third quartile (Q3, the 75th percentile), plus Q1, the median, and the interquartile range.

Quick Facts

Method
Q3 = 75th percentile = median of the upper half of the sorted data
Q1, Q2 (median), Q3 split the data into four equal parts; IQR = Q3 − Q1.

Your Results

Calculated
Third quartile (Q3)
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75th percentile
First quartile (Q1)
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25th percentile
Median (Q2)
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50th percentile
Interquartile range
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IQR = Q3 − Q1

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Paste your numbers and press Calculate.

What the third quartile (Q3) is

The third quartile, written Q3, is the value below which 75% of the data in a sorted dataset falls. It is the same thing as the 75th percentile. Quartiles divide an ordered dataset into four equal-sized groups: Q1 (the first quartile, or 25th percentile) marks the boundary of the lowest 25%, Q2 is the median (50th percentile), and Q3 marks the point where the top 25% begins. So a quarter of your values sit above Q3 and three quarters sit at or below it.

Q3 is most useful as part of the five-number summary — minimum, Q1, median, Q3, maximum — which is what a box-and-whisker plot draws. The upper edge of the box in a box plot is exactly Q3, and the distance from Q1 to Q3 is the interquartile range (IQR), the span of the middle 50% of the data.

How Q3 is calculated

The most common textbook method (used by Moore & McCabe and equivalent to Tukey's hinges) is a two-step median split:

  1. Sort the data from smallest to largest.
  2. Find the overall median (Q2). If the dataset has an odd count, the median is the single middle value; if even, it is the average of the two middle values.
  3. Take the upper half of the data — all values above the median position — and Q3 is the median of that upper half.

Worked example on the sorted set 7, 15, 36, 39, 40, 41 (six values): the median is (36 + 39) / 2 = 37.5. The upper half is 39, 40, 41, whose median is 40, so Q3 = 40. The lower half is 7, 15, 36, whose median is 15, so Q1 = 15, and IQR = 40 − 15 = 25.

Because there is no single agreed convention, spreadsheet software may report slightly different values. Excel's QUARTILE.INC uses linear interpolation at position (n − 1) × 0.75 (0-indexed), while QUARTILE.EXC uses position (n + 1) × 0.75. This calculator lets you pick any of the three methods; they agree exactly on large datasets and differ only by small amounts on short or oddly-sized ones.

Why Q3 matters

  • Outlier detection. The standard rule flags a value as an outlier if it lies more than 1.5 × IQR above Q3 (the upper fence, Q3 + 1.5 × IQR) or below Q1 (the lower fence, Q1 − 1.5 × IQR).
  • Robust spread. The IQR (Q3 − Q1) describes dispersion without being distorted by extreme values, unlike the range or standard deviation.
  • Benchmarking and percentiles. "75th percentile" salary bands, test-score cutoffs, and growth charts all rely on Q3-style percentile logic to say where a value ranks against the rest.

Frequently Asked Questions

Is the third quartile the same as the 75th percentile?
Yes. Q3 is by definition the 75th percentile — the value at or below which 75% of the sorted data lies. Q1 is the 25th percentile and the median (Q2) is the 50th percentile.
Why does my textbook get a different Q3 than Excel?
Different quartile conventions place the quartile at slightly different positions. The median-split method (this tool's default) excludes the median when splitting an odd-length dataset, while Excel interpolates between values at a computed rank. For a dataset like 1, 2, 3, 4, 5 the median-split gives Q3 = 4.5 but Excel QUARTILE.INC gives 4. Both are correct under their own definition; pick one and stay consistent.
Do I include the median when finding Q3?
In the median-split method, no. When the dataset has an odd number of values, you drop the single middle value and take the median of the values strictly above it. When the count is even, there is no shared middle value, so the upper half is simply the top n/2 values.

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