Enter the set of numbers in the input field of the Percentile Calculator, specify the percentile to be calculated and choose the calculation method to be used. You can paste the input data copied from a spreadsheet or csv-file or enter manually using comma, space or enter as separators.
Percentile Formula
A percentile is a statistical measure indicating the value in a data set below which a given percentage of the values fall. For example, the 75th percentile is 37 means that 75% of all values in a data set fall below 37 and only 25% of all values exceed 37.
Percentiles have numerous applications in various fields of everyday life.
When ISPs bill “burstable” internet bandwidth at the 95th percentile, that means they cut off the top 5% of bandwidth peaks in each month. The 95th percentile means that 95% of the time the usage is below this amount and the remaining 5% of the time the usage is above that amount. This method allows users to have short bursts in traffic without charges for it.
Pediatricians often use percentiles to assess children’s growth in comparison to average values provided by the WHO or national standards in terms of weight, height, and head circumference. The percentiles show how a child’s growth parameters compare to those of other children. For example, 75th percentile for a boy height measurement means that the boy is taller than 75% of other boys of the same age.
Such percentiles are found in growth charts issued by health institutions. Percentiles are used in our BMI Calculator for Children and Child Height Predictor which utilize the CDC Growth Charts of the US.
Another example is the percentile rank of a test score found on a child’s testing reports. It is the percentage of scores that fall at or below a given score. For example, if a student scores at the 80th percentile (80th percentile rank) that means the student did better than 80% of other students.
Despite percentiles are long being in everyday use, there is no standard definition of percentile. However all definitions yield similar results when the number of values is very large. In our online percentile calculator we use two most widely used methods of percentile calculation.
The nearest-rank method
According to the first often used definition the \(P\)-th percentile \((0 \lt P \le 100)\) of a list of \(N\) ordered values \((v_i\text{, } i=1,2,\ldots,N)\) sorted from least to greatest is the lowest value \(v_n\) in the list such that no more than \(P\) percent of the data is strictly less than the value and at least \(P\) percent of the data is less than or equal to that value. To find this value first one has to calculate the ordinal rank and then take the value from the ordered list that corresponds to that rank. The ordinal rank \(n\) is calculated using this formula:
$$n = \left \lceil \frac{P}{100} \times N \right \rceil, \kern.6em 0 < P \le 100$$
where \(\lceil x\rceil\) denotes the ceiling function that rounds \(x\) upwards to the nearest integer.
It should be noted that a percentile calculated using the nearest-rank method is always a member of the original ordered list. For lists with less than 100 distinct values this method can result in the same value being used for more than one percentile.
The linear interpolation method
To increase accuracy, linear interpolation between adjacent values in the dataset is used instead of rounding the rank calculated according to the first definition. The fractional part is used for calculation of the percentile value \(v(x)\) using the two adjacent values from the list:
$$v(x)=v_{n}+\{x\}(v_{n+1}-v_{n}), \kern.6em P \lt 100,$$ $$v(x)=v_{n}, \kern.6em P=100, $$ $$\forall x\in[1,N] : v(i)=v_i\text{, for } i=1,2,\ldots,N$$
$$x = \left ( \frac{P}{100} \times (N-1) + 1 \right ), \kern.6em n = \left \lfloor x \right \rfloor, \kern.6em 0 \le P \le 100 $$
where \(\lfloor x\rfloor\) denotes the floor function that rounds \(x\) downwards to the nearest integer. It represents the integral part of positive \(x\), whereas \(\{x\}=x-\lfloor x\rfloor\) denotes the fractional part of \(x\).
Related calculators
Check out our other statistics calculators such as Percentile Rank Calculator or Quartile Calculator.