Percentile methods explained
Linear interpolation versus nearest rank, why tools disagree on the same data, and how to read percentile rank the cumulative way.
Two questions, one data set
Percentiles work in both directions, and this calculator answers each. Going one way, you name a percentile and ask which value sits there, which is how you find a median, a quartile or a cutoff. Going the other way, you name a value and ask what percentile rank it holds, which tells you how a single score compares to the group. Both use the same sorted list of numbers, but they run different calculations, so the two results are not simply inverses of each other.
How linear interpolation finds a value
The linear method treats percentiles as positions on the sorted data rather than fixed members of it. For n numbers, the target zero based position is (n minus 1) times the percentile divided by 100. If that position lands between two entries, the result is a weighted blend of them based on the fractional part. On the list 1 to 10, the 90th percentile targets position 8.1, which blends the ninth and tenth values to give 9.1. This matches Excel PERCENTILE.INC and NumPy, which is why spreadsheet users see familiar numbers here.
When to choose nearest rank
Nearest rank never invents a value that is not in your data. It computes the same target position, then rounds to the closest whole index and returns that actual entry. This suits cases where an interpolated number would be meaningless, such as picking a real response time from a log or an actual student score. On the same 1 to 10 list, nearest rank returns 9 for the 90th percentile instead of 9.1. Different software defaults to different methods, so always note which one you used when you report a percentile.
Reading percentile rank correctly
Percentile rank here uses the cumulative, or weak, definition: the share of values at or below your number. It counts every entry that is less than or equal to the value, including exact matches and duplicates, then divides by the total. That is why 85 in the list 55, 60, 70, 80, 85, 90, 95, 100 ranks at 62.5 percent, since five of the eight values are at or below it. Because ties are included, the maximum value always ranks 100 percent.