Z-Score Calculator
Calculate how many standard deviations a value sits from the mean. Enter the value, mean, and standard deviation directly — or paste a raw dataset and let the tool compute them first. Every result shows the formula worked through with your numbers.
Input mode
Enter a value, mean, and a standard deviation greater than zero to see the z-score.
Frequently Asked Questions
- What is a z-score?
- A z-score (also called a standard score) tells you how many standard deviations a value sits above or below the mean. It is calculated as z = (x − μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. A z-score of 0 means the value equals the mean.
- How do I calculate a z-score from raw data?
- Switch to the dataset mode, paste your numbers, and enter the value you want to standardize. The calculator first computes the mean and the population standard deviation of your data, then applies z = (x − μ) / σ and shows every step of the working.
- What does a negative z-score mean?
- A negative z-score means the value is below the mean. For example, z = −1.5 means the value sits 1.5 standard deviations below the average. Positive z-scores sit above the mean.
- How accurate is the percentile shown?
- The percentile comes from the standard normal cumulative distribution function, evaluated with the Abramowitz-Stegun approximation of the error function. It is accurate to about four decimal places, but it is still an approximation — and it only applies if the underlying data is roughly normally distributed.
- Does the dataset mode use sample or population standard deviation?
- The dataset mode uses the population standard deviation (dividing by n), which is the usual choice when standardizing values within the data you have. If you need to use a sample standard deviation calculated elsewhere, enter it directly in the value/mean/SD mode instead.