Z-Score Calculator
Calculate the Z-score (standard score) for any data value. Find how many standard deviations a value is from the mean of a dataset. Enter your values below to get an instant result with step-by-step explanation.
How to Use
- Enter the data value (x) — the value you want to evaluate.
- Enter the population mean (μ) — the average of the dataset.
- Enter the standard deviation (σ) — a measure of spread in the data.
- Click Calculate to see the Z-score, its interpretation, and the percentile.
Formula
Where:
• x = data value
• μ = population mean
• σ = population standard deviation
Examples
You scored 75 on a test. The class average is 60 with a standard deviation of 10.
Z = (75 − 60) / 10 = 15 / 10 = 1.5
Your score is 1.5 standard deviations above the mean, which is above average.
A person is 160 cm tall. The mean height is 170 cm with a standard deviation of 8 cm.
Z = (160 − 170) / 8 = −10 / 8 = −1.25
The person is 1.25 standard deviations below the mean, below average.
Frequently Asked Questions
What does a Z-score mean?
A Z-score tells you how many standard deviations a data point is from the mean. A Z-score of 0 means the value is exactly at the mean. A positive Z-score indicates the value is above the mean, while a negative Z-score indicates it is below the mean.
How do I interpret Z-scores?
A Z-score between −1 and +1 means the value is within one standard deviation of the mean (about 68% of data). Between −2 and +2 covers about 95% of data. A Z-score beyond ±3 is considered an outlier (only about 0.3% of data).
What is a good Z-score?
There is no universally "good" Z-score — it depends on context. In most cases, a Z-score close to 0 (between −1 and +1) is considered typical or average. Values beyond ±2 or ±3 are unusual and may indicate outliers or exceptional performance.