Many properties of real-world world phenomena can be modelled with a normal distribution. In clinical psychology, many different scales are commonly used to describe values of normally distributed variables. This is a tool to help convert between these scales, and to discover their relationships. You can also define your own scales.

Each scale has one of three different types:

Normal

A scale of the "Normal" type is defined with a mean value (M) and a standard deviation (SD). It is a continuous variable, that in theory can take on any value from the set of real numbers.

Discrete

A scale of the "Discrete" type is also defined with a mean value and a standard deviation. It however only includes values from a finite set of integer values.

Percentile

A value on a scale of the "Percentile" type tells you how many percent of the total distribution lies "to the left of" – is smaller than or equal to – the current value. It is also called the cumulative distribution function of the normal distribution.

This tool is free, open source, software. You may freely use, copy, modify and re-publish the source according to the terms of the MIT license. The code is managed at Github.

It was originally built in 2013 and hosted on helgo.net/simon/normalscore/, then moved to this site in 2023. A little blog series about that was published if you're into tech details.

Please feel free to contact me if you have anything to say about the Normal Score Converter!