Normal Curve Equivalent (NCE)

A Normal Curve Equivalent is a standardized score on a scale of 1-99 that is often used in education. NCEs have several desirable properties, including:

• Scores are on an equal-interval scale (e.g. the distance from 5-10 is the same as the distance from 50-55);
• The 1st, 50th, and 99th NCEs are equivalent to the 1st, 50th, and 99th percentiles for a given set of scores;
• The shape of the distribution of NCEs follows that of a normal distribution

The formula for calculating an NCE is:

$$NCE=70770+\text{qnorm}(.99)\times z$$

or approximately

$$50+21.063\times z$$