Percentile and quartile calculator

A percentile is a statistical measure indicating the value below which a given percentage of observations fall. For example, the 90th percentile means that 90% of data points are lower than this value. Percentiles are widely used in test scoring, child growth charts, and data analysis.

Quartiles are special cases of percentiles: Q1 is the 25th percentile, Q2 (the median) is the 50th percentile, and Q3 is the 75th percentile. They divide the dataset into four equal parts and are the basis for box plot visualizations.

The median is the middle value of a sorted dataset — exactly half the observations lie below it and half above. That makes it equivalent to the 50th percentile. Unlike the mean, the median is resistant to outliers, making it a better central tendency measure for skewed distributions.

IQR is the difference between the third quartile (Q3) and the first quartile (Q1): IQR = Q3 − Q1. It describes the range containing the middle 50% of the data. IQR is robust to outliers and is used to detect them: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are typically flagged as outliers.

Multiple methods exist (R-1 through R-9, as described by Hyndman and Fan). This calculator uses the R-7 linear interpolation method: rank = p/100 × (n−1); result = x[lo] + frac × (x[lo+1] − x[lo]). This is the default in Excel (PERCENTILE.INC) and R. Minor differences between software packages stem from different edge-case handling.

Growth charts show the distribution of physical measurements (e.g. height, weight) in a population by age and sex. A child at the 50th percentile has a measurement typical for half of peers. Charts published by pediatricians and the WHO are built from data collected on hundreds of thousands of children.

Standardised tests (e.g. SAT, GRE) often report scores as percentiles. A score at the 80th percentile means the test-taker performed better than 80% of those who sat the test. Percentiles enable fair comparison across different test versions and populations regardless of absolute scores.

A percent describes a proportion of a total (e.g. 80% of questions answered correctly), while a percentile describes position within a dataset relative to other observations (e.g. a score better than 80% of test-takers). You can score 80% of points but be at the 60th percentile if most others also scored well.

Interpretation depends on context. In child growth screening, percentiles 3–97 are within the normal range. In academic tests, above the 90th percentile is considered outstanding. In industrial process quality analysis, engineers focus on extreme percentiles (1st and 99th) as boundary cases. There is no universal "good" percentile — always evaluate in the context of the domain and objective.

Yes. The calculator handles any real numbers, including negative values and decimals. The linear interpolation method works identically regardless of the sign or magnitude of the data. Simply enter the numbers separated by commas or spaces and the calculator will sort them and compute the requested percentile.