Scaled Score Calculator Formula

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

Use the Scaled Score Calculator

Formulas Used

Scaled Score

scaled = round(scale_min + proportion * (scale_max - scale_min))

Raw Percentage

raw_pct = proportion * 100

Scale Range

scale_range = scale_max - scale_min

Variables

VariableDescriptionDefault
raw_scoreRaw Score45
raw_maxMaximum Raw Score60
scale_minScale Minimum200
scale_maxScale Maximum800
proportionDerived value= raw_score / raw_maxcalculated

How It Works

How to Calculate a Scaled Score

A scaled score converts a raw score to a standardized scale for fair comparison.

Formula

Scaled Score = Scale Min + (Raw Score / Max Raw) x (Scale Max - Scale Min)

This linear mapping preserves relative performance across different test forms.

Worked Example

A student gets a raw score of 45 out of 60, mapped to a 200–800 scale.

raw_score = 45raw_max = 60scale_min = 200scale_max = 800
  1. 01Proportion = 45 / 60 = 0.75
  2. 02Scale range = 800 - 200 = 600
  3. 03Scaled score = round(200 + 0.75 x 600) = round(650) = 650

Ready to run the numbers?

Open Scaled Score Calculator