To find the 25th percentile of a data set, you sort all values from smallest to largest, then identify the point below which 25% of the data falls. The 25th percentile is also called the first quartile (Q1), and the exact calculation depends on whether your rank lands on a whole number or a decimal.
What the 25th Percentile Means
The 25th percentile is the value in your data set where one quarter of all observations fall at or below it. It’s one of three quartiles that divide data into four equal groups: the 25th percentile (Q1), the 50th percentile (the median), and the 75th percentile (Q3). If you’ve ever seen a child’s growth chart at the doctor, you’ve seen percentiles in action. A 24-month-old boy whose weight falls at the 25th percentile weighs more than 25% of boys that age and less than 75% of them, and that’s considered perfectly healthy.
The Step-by-Step Calculation
Start by sorting your data from smallest to largest. This is essential, and skipping it is the most common mistake. Once your values are in order, use this formula to find the rank (position) of the 25th percentile:
Rank = (25 / 100) × (n + 1)
Here, n is the total number of data points. Say you have these 8 test scores: 35, 42, 43, 46, 52, 61, 71, 83. Plugging in:
Rank = 0.25 × (8 + 1) = 0.25 × 9 = 2.25
That rank of 2.25 tells you the 25th percentile sits between the 2nd and 3rd values in your sorted list. What you do next depends on whether you round or interpolate.
When the Rank Is a Whole Number
If your formula produces a clean integer, like a rank of 3 in a data set of 11 values, the 25th percentile is simply the value sitting at that position. No extra math needed. Sort the data, count to that position, and you have your answer.
When the Rank Falls Between Two Values
Most of the time, the formula gives you a decimal like 2.25 or 4.75. You have two options.
The simpler approach, common in introductory courses, is to round up to the next whole number. In the example above, a rank of 2.25 rounds up to 3, so you’d take the 3rd value in the sorted list: 43. This follows the definition that the 25th percentile is the lowest score greater than 25% of the data.
The more precise approach is linear interpolation. Take the rank of 2.25: the integer part is 2, and the fractional part is 0.25. Find the values at positions 2 and 3 in your sorted data (42 and 43). Multiply the difference between those two values by the fractional part, then add that to the lower value:
42 + 0.25 × (43 − 42) = 42 + 0.25 = 42.25
So the 25th percentile by interpolation is 42.25. This method gives you a more precise estimate, especially with small data sets where rounding can shift the result significantly.
Why Different Tools Give Slightly Different Answers
If you’ve ever calculated a percentile by hand and then checked it in Excel or a statistics program, you may have noticed the numbers don’t match exactly. That’s because there are multiple valid formulas for computing percentile rank, and different tools use different ones.
The formula above, Rank = p × (n + 1), is the one recommended by the National Institute of Standards and Technology and used by many statistics textbooks. Excel’s default PERCENTILE.INC function uses a different formula: Rank = p × (n − 1) + 1. For the same 8-value data set at the 25th percentile, NIST’s formula gives a rank of 2.25, while Excel’s gives 2.75. Both are mathematically defensible, and for larger data sets the results converge closely.
Excel also offers PERCENTILE.EXC, which uses the (n + 1) formula and aligns more closely with the textbook method. The trade-off is that PERCENTILE.EXC can’t compute percentiles at the very extremes of small data sets, returning an error if you ask for a percentile below 1/(n+1) or above n/(n+1). For most purposes, either function works. Just be consistent with whichever method your class or project requires.
Calculating Q1 in Excel or Google Sheets
If your data is in cells A1 through A20, type this into any empty cell:
=PERCENTILE.INC(A1:A20, 0.25)
The 0.25 tells the function you want the 25th percentile. You can also use the QUARTILE.INC function with a quartile number instead:
=QUARTILE.INC(A1:A20, 1)
Both return the same result. Google Sheets supports the same syntax. In R, the default quantile() function uses Excel’s interpolation method, while Python’s NumPy library uses it as well by default, though both let you switch between methods if needed.
A Full Worked Example
Suppose you have 12 monthly electricity bills in dollars: 95, 110, 88, 134, 102, 78, 121, 145, 99, 112, 87, 108.
First, sort them: 78, 87, 88, 95, 99, 102, 108, 110, 112, 121, 134, 145.
Calculate the rank: 0.25 × (12 + 1) = 3.25. The integer part is 3, the fractional part is 0.25. The 3rd value is 88 and the 4th value is 95.
Interpolate: 88 + 0.25 × (95 − 88) = 88 + 1.75 = 89.75.
The 25th percentile of your electricity bills is $89.75. That means roughly one quarter of your monthly bills came in below this amount.
How Q1 Is Used Beyond the Classroom
The 25th percentile plays a key role in identifying outliers through the interquartile range, or IQR. The IQR is the distance between Q3 and Q1. Any data point that falls more than 1.5 times the IQR below Q1 is flagged as an unusually low outlier. For example, if Q1 is 80 and Q3 is 90, the IQR is 10. The lower fence sits at 80 − (1.5 × 10) = 65, so anything below 65 would be considered an outlier.
Percentiles also appear frequently in health contexts. Pediatric growth charts plot children’s height and weight against national percentile curves. Standardized test scores are often reported as percentile ranks. In salary data, knowing the 25th percentile for your job title tells you the threshold below which only one quarter of workers are paid, giving you a concrete benchmark for negotiation. In every case, the underlying math is the same: sort the values, find the position, and interpolate if needed.