How to use the z-score standardization calculator
Paste a list of values and the calculator works out the mean and standard deviation, then converts every value into a z-score and lays them out in a table. A z-score subtracts the mean and divides by the standard deviation, so the unit disappears and what remains is how many standard deviations a value sits from the centre. That is what lets two exams with different scales, or metrics in different units, be compared on the same ruler.
Check the standard deviation basis before reading anything else. If the values you have are the whole group, divide by n for the population basis; if they are a sample drawn from something larger, divide by n−1. The same data gives a different standard deviation and therefore different z-scores under each basis, so the chosen basis is printed with the result. The list 2, 4, 4, 4, 5, 5, 7, 9 has a mean of 5 and a population standard deviation of exactly 2.
Any value with |z| of 3 or more is counted as an outlier candidate, and an optional field standardizes a value that is not in the list against the same mean and standard deviation. With fewer than two values, or with every value identical so the standard deviation is zero, the division is impossible and the calculator explains that instead. Percentile conversion needs a normality assumption and is not supported.
Frequently asked questions
Divide by n when the values are the entire group of interest, and by n−1 when they are a sample drawn from something larger.
No. Values below the mean are negative, values above it are positive and a value equal to the mean is zero. The sign is direction and the size is distance.
The standard deviation becomes zero and a z-score divides by it, which is a division by zero. The data has to vary before it can be standardized.