Percentile vs Percentile Rank

The kth percentile is the value at or below which about $k$ percent of the observations lie. For example, if your test score is at the 85th percentile, roughly 85 percent of test-takers scored at or below you. Quartiles are percentiles too: the first quartile is the 25th percentile and the median is the 50th. Percentiles let you compare a single value to a whole distribution without knowing its shape.

Percentile rank turns a raw value into a position, which is why score reports quote it. You compute it as $\frac{\text{number of values at or below } x}{n} \times 100$, where $n$ is the number of observations. If 170 of 200 test takers scored at or below your score, your percentile rank is $\frac{170}{200} \times 100 = 85$, so you are at the 85th percentile. The two terms run in opposite directions: a percentile is a data value, while a percentile rank is the percentage attached to a value you already have.