Z-Score Calculator

What a Z-Score Tells You

A raw number like “scored 80” does not mean much on its own - 80 could be excellent or poor depending on the test. A z-score fixes that by measuring a value in standard deviations from the mean: how far above or below average it sits, on a scale that works for any data set.

• A z-score of 0 means the value is exactly average.
• Positive means above average, negative means below.
• A z-score of 2 means “two standard deviations above the mean” - unusually high.

Because it is on a standard scale, a z-score lets you compare results from completely different tests. The number line by the calculator marks the mean and shows where your value lands.

Z-Score Formula

$$z = \frac{x - \mu}{\sigma}$$

where x is the value, μ is the mean, and σ is the standard deviation.

How to Use It

1. Enter the value, the mean, and the standard deviation.
2. Read the z-score.

Worked Examples

Value	Mean	SD	z-score
80	65	10	1.5
50	65	10	−1.5
65	65	10	0
90	70	8	2.5

FAQ

What is a z-score?

It is how far a value sits from the mean, measured in standard deviations. A z-score of 1.5 means the value is 1.5 standard deviations above the mean.

What does a negative z-score mean?

The value is below the mean. A z-score of 0 means it equals the mean.

How do I get the standard deviation?

Use the standard deviation calculator on your data set, then enter it here.