Z-Score Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The z-score is calculated with z = (value − mean) ÷ standard deviation. For a value of 75 in a population with a mean of 70 and a standard deviation of 5, the z-score is 1: the value sits one standard deviation above the mean.
Explanation
The z-score (or standard score) shows how many standard deviations a value sits from the mean of a distribution: a positive z-score means the value is above the mean, a negative one means it's below, and a score of 0 means it exactly equals the mean. Its main use is making values from different scales or distributions comparable (for example, comparing a math test score and a reading test score, on different scales) by putting them on the same standardized unit. For a distribution following a normal curve, about 68% of values fall between a z-score of −1 and +1, and about 95% between −2 and +2 (the 68-95-99.7 rule). This calculator applies the formula directly from an already-known mean and standard deviation; it doesn't calculate them itself from a raw data sample.
Example: value 75, mean 70, standard deviation 5
Inputs
Observed value: 75. Mean: 70. Standard deviation: 5.
Calculation
Z-score = (75 − 70) ÷ 5 = 5 ÷ 5 = 1.
Result
This value sits 1 standard deviation above the mean.
Frequently asked questions
What is a z-score actually used for?
It lets you place an individual value relative to a group (for example, a test score relative to a class's average performance), and compare values measured on different scales by putting them on a common basis. It's also the basis for calculating percentiles in a normal distribution.
What does a negative z-score mean?
A negative z-score simply means the observed value is below the population mean: a score of −2, for example, means the value sits two standard deviations below the mean. It's not necessarily "bad" — that depends entirely on what the measurement represents.
What does the 68-95-99.7 rule mean?
For a distribution that follows a normal (bell-shaped) curve, about 68% of values have a z-score between −1 and +1, about 95% between −2 and +2, and about 99.7% between −3 and +3. This empirical rule helps quickly interpret the scale of a z-score, but it assumes a normal distribution, which isn't always the case in practice.