Percentile Calculator Formula

Understand the math behind the percentile calculator. Each variable explained with a worked example.

Formulas Used

Estimated Value at Target Percentile

percentile_val = lower_val + frac * (upper_val - lower_val)

Interpolation Fraction

interpolation_fraction = frac

Variables

Variable	Description	Default
`lower_val`	Value at Lower Rank	70
`upper_val`	Value at Upper Rank	80
`lower_rank`	Lower Percentile Rank	40
`upper_rank`	Upper Percentile Rank	60
`target_rank`	Target Percentile	50
`frac`	Derived value`= (target_rank - lower_rank) / (upper_rank - lower_rank)`	calculated

How It Works

How to Estimate a Percentile by Interpolation

Formula

Value at P = Lower Value + Fraction * (Upper Value - Lower Value)

where Fraction = (Target Percentile - Lower Rank) / (Upper Rank - Lower Rank)

This linearly interpolates between two known ranked values. The kth percentile is the value below which k% of observations fall.

Worked Example

The 40th percentile is 70 and the 60th percentile is 80. Estimate the 50th percentile.

lower_val = 70upper_val = 80lower_rank = 40upper_rank = 60target_rank = 50

01Fraction = (50 - 40) / (60 - 40) = 10 / 20 = 0.5
02Value at 50th percentile = 70 + 0.5 * (80 - 70)
03= 70 + 0.5 * 10 = 70 + 5 = 75

Frequently Asked Questions

What is a percentile?

The kth percentile is the value below which k percent of the data falls. The 90th percentile means 90% of observations are at or below that value.

How does this differ from a percentile rank?

A percentile value is the data value at a given rank. A percentile rank is the percentage of values at or below a given data value. They are inverse operations.

Is the 50th percentile the same as the median?

Yes. The 50th percentile and the median are the same concept: the value that splits the data into two equal halves.

Learn More

Guide

How to Calculate Percentiles and Quartiles

Learn how to calculate percentiles and quartiles from a dataset. This guide explains the percentile rank formula, the interquartile range, and how these measures describe data distribution.

Ready to run the numbers?

Open Percentile Calculator