Percentile Calculator Formula

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

Use the Percentile Calculator

Formulas Used

Estimated Value at Target Percentile

percentile_val = lower_val + frac * (upper_val - lower_val)

Interpolation Fraction

interpolation_fraction = frac

Variables

VariableDescriptionDefault
lower_valValue at Lower Rank70
upper_valValue at Upper Rank80
lower_rankLower Percentile Rank40
upper_rankUpper Percentile Rank60
target_rankTarget Percentile50
fracDerived 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
  1. 01Fraction = (50 - 40) / (60 - 40) = 10 / 20 = 0.5
  2. 02Value at 50th percentile = 70 + 0.5 * (80 - 70)
  3. 03= 70 + 0.5 * 10 = 70 + 5 = 75

Ready to run the numbers?

Open Percentile Calculator