Z Score Calculator

A z-score is the number of standard deviations a data point is from the population mean — enter your values below and the result updates instantly. Two calculators: one for a single raw data point, one for a sample mean (using the standard error). Looking for the reference table instead? Browse the z-tables.

Z Score Using a Data Point

Enter the values below — the result updates automatically.

Data Point (x)

The data point value

Population Mean (μ)

Population Standard Deviation (σ)

Z Score (z)

Essentially, this is how you can express the above computation:

$z equals x minus mu, over sigma$

Z Score Using Sample Mean and Size

Enter the values below — the result updates automatically.

Sample Mean (x̅)

Sample Size (n)

Population Mean (μ)

Population Standard Deviation (σ)

Z Score (z)

Essentially, this is how you can express the above computation:

$z equals x-bar minus mu, over sigma over the square root of n$

About the Z Score

The z-score is the number of standard deviations a data point is from the population mean. You can calculate a z-score for any raw data value on a normal distribution.

Calculating a z-score converts a raw data value into a standardized score on a standard normal distribution. Because z-scores are expressed in standard deviations, they let you compare data from different samples on the same scale.

A positive z-score means the data value is above average; a negative z-score means it's below average. You can also look up the percentage of the population that lies above or below any z-score using a z-score table.