Z-Score Calculator - Standard Score & Percentile

Raw value (x)Mean (μ)Standard deviation (σ)

Z-score1.5

Approx. percentile93.3193%

Distance from mean15

PositionAbove the mean

The z-score itself is a standardized distance. The displayed percentile interprets that score using a standard normal distribution.

How to use the Z-Score Calculator

Enter the raw observed value.
Enter the mean of the reference distribution.
Enter a positive standard deviation.
The mean is subtracted from the raw value and the difference is divided by the standard deviation.
A standard-normal cumulative distribution approximation provides the optional percentile interpretation.

Examples

One standard deviation above

For x=80, mean=70 and standard deviation=10, z=1.

Below the mean

A negative z-score means the raw value lies below the supplied mean.

At the mean

When the raw value equals the mean, z=0.

Frequently asked questions

What does a z-score measure?

It expresses the signed distance between a value and the mean in standard-deviation units.

Can standard deviation be zero?

No. The z-score formula divides by standard deviation, so it must be greater than zero.

Does a z-score require normal data?

The standardized z-score itself does not require normality, but interpreting it as a normal-distribution percentile assumes an appropriate normal model.

What does z=0 mean?

It means the observation is exactly equal to the supplied mean.

Related tools