This calculator finds the standardized z-score for a provided raw score (**x**), a population mean (𝝻) and a population standard deviation (𝞂).

The z-score (**z**) formula is

**z = (x – 𝝻) / 𝞂**

Enter the raw score, the population mean, and the population standard deviation and then click the `Calculate`

button.

Z score: (**X**– 𝝁) / 𝝈 =

## About the Z-score

The Z-score describes the position of a raw score in terms of its distance from the mean measured in standard deviation units. If the z-score is positive, the raw score lies above the mean, and if it is negative the raw score lies below the mean.

We can use the z-score to calculate the probability of a score occurring within a standard normal distribution. We can also compare two scores from different samples, which may have different means and standard deviations.