Z-Score Calculator

Find the z-score, or standard score, of a value: how many standard deviations it sits above or below the mean, with the formula and every step shown.

Z-score —

How to Calculate a Z-Score

A z-score tells you how many standard deviations a value lies from the mean.

1

Enter the value, mean and standard deviation

Type the raw value x, the mean μ of the distribution, and the standard deviation σ. The standard deviation must be greater than zero.

2

The calculator applies the formula

It computes z = (x − μ) / σ, subtracting the mean from the value and dividing by the standard deviation.

3

Read the z-score and interpretation

A positive z-score is above the mean, a negative one is below it, and zero is exactly at the mean. Not sure of your mean or standard deviation? Find them with the Standard Deviation Calculator.

Frequently Asked Questions

What is a z-score?
A z-score, or standard score, tells you how many standard deviations a value is above or below the mean of its distribution. A z-score of 2 means the value is two standard deviations above the mean; a z-score of −1.5 means it is one and a half standard deviations below. Z-scores let you compare values from different distributions on a common scale.
What is the z-score formula?
The z-score is z = (x − μ) / σ, where x is the raw value, μ is the mean, and σ is the standard deviation. You subtract the mean from the value and divide by the standard deviation. This calculator applies that formula and shows each step.
What does a negative z-score mean?
A negative z-score simply means the value is below the mean. For example, a z-score of −1 is one standard deviation below the average. The sign shows the direction (below the mean) and the magnitude shows the distance in standard deviations.
Can the standard deviation be zero?
No. The z-score formula divides by the standard deviation, so it must be greater than zero. A standard deviation of zero would mean every value is identical, in which case there is no spread and a z-score is undefined.

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