Percentile Calculator
This percentile calculator works on your own data: enter the values, pick the percentage and the result appears at once. For 15 20 35 40 50 55 62 70 85 90 the 90th percentile by the Excel method is 85.5 – along with quartiles, the percentile rank of a single value and the working.
Source: Wikipedia – Quantil (Berechnungsverfahren). Updated: .
How it is calculated
The pth percentile is the value below which p percent of the values in a data set fall. The 50th percentile is the median; the 25th and 75th are the first and third quartiles. “Percentile” and “quantile” mean the same thing, except that a quantile is given as a fraction between 0 and 1.
Methods compared
With a finite data set, rarely does a value sit exactly at p percent, so there are several methods and they give slightly different answers:
- Inclusive (Excel PERCENTILE.INC): position p ÷ 100 × (n − 1) + 1, with linear interpolation in between. The 0th and 100th percentiles are the smallest and largest values.
- Exclusive (PERCENTILE.EXC): position p ÷ 100 × (n + 1). It only works when the position falls inside the data and suits samples better.
- Nearest rank: the rank p ÷ 100 × n is rounded up, so the answer is always a value that actually occurs.
Percentile rank
The reverse question asks what percentage of values lie below a value x. The tool computes (number of smaller values + half the number of equal values) ÷ n × 100. This is used for test scores and salary comparisons. Note: growth percentile charts for children rest on their own reference data and cannot be calculated this way. For the mean, median and standard deviation of the data use the standard deviation calculator.
Frequently asked questions
What is a percentile?
The pth percentile is the value below which p percent of the data lie. The 90th percentile separates the lowest 90% from the top 10%.
How do you calculate the 90th percentile?
Sort the values, work out the position p ÷ 100 × (n − 1) + 1 and interpolate between the neighbouring values. With 10 values the position is 9.1.
How do I calculate a percentile in Excel?
Use =PERCENTILE.INC(range, 0.9) for the 90th percentile. PERCENTILE.EXC works exclusively. The tool reproduces both functions.
What is the difference between percentile and percentile rank?
For a percentile you give the percentage and look for the value; for a percentile rank you give the value and look for the percentage.
How are percentiles, quartiles and the median related?
Median = 50th percentile, first quartile = 25th, third quartile = 75th percentile. The tool shows all three.
Sources and legal basis
- Wikipedia – Quantil (Berechnungsverfahren)
- Wikipedia – Percentile (Nearest-rank, lineare Interpolation, Percentile rank)
- Microsoft – PERCENTILE.INC / PERCENTILE.EXC (Excel)
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