Third Quartile Calculator — Q3 (75th Percentile)
Enter a list of numbers to find Q3 — the third quartile (75th percentile) — plus Q1, Q2, the IQR and the upper Tukey fence. Q3 is the value below which 75% of your data falls.
75th percentile — median of the upper half of the data
- 1
Count (n)
11 - 2
Median (Q2)
19The data is split at this median; for odd n the median itself is excluded from both halves (Tukey hinges). - 3
Upper half size
5Values above Q2 — Q3 is the median of these 5 values. - 4
Third quartile (Q3)
median of upper 5 values = 30
How does this calculator work?
Q3 is the 75th percentile: sort the data, split at the median, then take the median of the upper half (Tukey hinges). It marks the boundary below which three-quarters of the data falls and anchors the IQR (Q3 − Q1). The upper fence Q3 + 1.5 × IQR flags potential outliers. Needs ≥ 4 data points.
Formula
How this is calculated
The third quartile (Q3) is found by first sorting all values in ascending order and locating Q2 (the overall median). The data is then split into two halves: when the count is odd, the median value itself is excluded from both halves (Tukey hinges method, the default in R and Excel's QUARTILE.EXC). Q3 is the median of the upper half — the values above Q2.
Q3 marks the 75th percentile: roughly three-quarters of your data falls at or below this value. Together with Q1 it defines the interquartile range IQR = Q3 − Q1, which measures the spread of the central 50% of the data without distortion from extreme values. The upper Tukey fence (Q3 + 1.5 × IQR) is the standard box-plot threshold above which values are flagged as potential outliers.
Different software may return slightly different Q3 values because there are at least nine recognised interpolation methods. The Tukey hinges method used here works directly on data values without interpolation, making it the most transparent and widely taught approach. For large samples all methods converge to the same result.
Frequently asked questions
Q3 is the value below which approximately 75% of the data falls. It marks the right edge of the box in a box-and-whisker plot and anchors the upper end of the interquartile range. A very high Q3 relative to the mean suggests a right skew or upper outliers in the distribution.
There are nine standard methods for computing quartiles. This calculator uses Tukey hinges (R type 2 / Excel QUARTILE.EXC), which excludes the median from both halves. R's default (type 7) uses linear interpolation and may return a slightly different value, especially for small samples. Differences shrink as sample size grows.
You need at least 4 values to split the data into meaningful halves and compute both Q1 and Q3. With very small samples (4–6 values) the quartiles can be sensitive to individual values — interpret Q3 with caution for tiny data sets.
Also known as
TG we-Calculate Editorial Team. (2026). Third Quartile Calculator — Q3 (75th Percentile) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/third-quartile-calculator
TG we-Calculate Editorial Team. "Third Quartile Calculator — Q3 (75th Percentile)." TG we-Calculate. 2026. https://we-calculate.com/calculator/third-quartile-calculator.
TG we-Calculate Editorial Team, "Third Quartile Calculator — Q3 (75th Percentile)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/third-quartile-calculator
@misc{wecalculate_third_quartile_calculator, title = {Third Quartile Calculator — Q3 (75th Percentile)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/third-quartile-calculator}}, year = {2026}, note = {TG we-Calculate} }
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