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.

There are more things to explain, so watch this space, but at the moment just play around!

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