# Z Score Calculator

Enter raw score, population mean, and standard deviation to find the z score using z score calculator.

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Z score calculator is an online tool that find the z score of a normal distribution. It takes population mean, standard deviation, and raw score as input to calculate z-score for a normal distribution.

Let’s find out z score definition, its formula, and how to calculate z score without using z-score calculator.

## Definition - What is z score?

Z score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. It is also known as standard score.

Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores. A z-score can be placed on a normal distribution curve. Z-scores range from -3 standard deviations up to +3 standard deviations.

## Z score formula

The following equation is used to calculate z score.

Z = (x – μ) / σ

## How to find z score?

Z-score can also be calculated using the z value calculator above. In this section, we will find the z score using an example and its formula.

Example

Find the z-score if standard deviation is 10, population mean of a data is 20, and raw score is 15.

Solution:

Step 1: Write down the given values.

x = 15

μ = 20

σ = 10

Step 2: Substitute the values in z-score formula.

Z = (x – μ) / σ

Z = (15 – 20) / 10

Z = -5/10

Z = -0.5