First Quartile Calculator — Q1 (25th Percentile)
Enter a list of numbers to find Q1 — the first quartile (25th percentile) — plus Q2, Q3, the IQR and the lower Tukey fence. Q1 is the value below which 25% of your data falls.
25th percentile — median of the lower half of the data
How does this calculator work?
Q1 is the 25th percentile: sort the data, split at the median, then take the median of the lower half (Tukey hinges). It marks the boundary below which one quarter of the data falls and anchors the IQR (Q3 − Q1). Needs ≥ 4 data points.
Formula
How this is calculated
The first quartile (Q1) is calculated by first sorting all values in ascending order and finding Q2 (the overall median). The data is then split: all values below the median form the lower half. When the count is odd, the median value itself is excluded from both halves (this is the Tukey hinges method, used by most textbooks, R, and Excel's QUARTILE.EXC function). Q1 is the median of that lower half.
Q1 marks the 25th percentile: roughly one quarter of your data falls at or below this value. Together with Q3 (the 75th percentile) it defines the interquartile range (IQR = Q3 − Q1), which measures the spread of the central 50% of the data without being distorted by extreme values. The lower Tukey fence (Q1 − 1.5 × IQR) is the standard box-plot threshold below which values are considered potential outliers.
Different software may give slightly different Q1 values because there are at least nine recognised interpolation methods. The Tukey hinges method used here avoids interpolation and works exactly on data values, making it the most transparent and widely taught approach.
Frequently asked questions
Q1 is the value below which approximately 25% of the data falls. It anchors the lower end of the interquartile range (IQR) and is the left edge of a box plot. A very low Q1 relative to the mean can signal a left skew or lower outliers in the data.
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. Other tools use linear interpolation (R type 7, the R default) and may return a slightly different value — differences are small for large samples.
You need at least 4 values to split the data into meaningful halves and compute Q1 and Q3. For very small samples (4–6 values) the quartiles may be sensitive to individual values — use caution when interpreting Q1 for tiny data sets.
Also known as
TG we-Calculate Editorial Team. (2026). First Quartile Calculator — Q1 (25th Percentile) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/first-quartile-calculator
TG we-Calculate Editorial Team. "First Quartile Calculator — Q1 (25th Percentile)." TG we-Calculate. 2026. https://we-calculate.com/calculator/first-quartile-calculator.
TG we-Calculate Editorial Team, "First Quartile Calculator — Q1 (25th Percentile)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/first-quartile-calculator
@misc{wecalculate_first_quartile_calculator, title = {First Quartile Calculator — Q1 (25th Percentile)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/first-quartile-calculator}}, year = {2026}, note = {TG we-Calculate} }
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