Z-Score Calculator

Z-Score Calculator converts a value into the number of standard deviations it sits from the mean, which is what makes values from different distributions comparable. A mark of 85 where the mean is 75 and the standard deviation 8 is a z-score of 1.25, and that 1.25 means the same thing whatever the test was out of.

The percentile follows from the z-score if the data is normally distributed. A z of 1.25 puts a value at about the 89th percentile, so roughly eleven per cent of values are higher. The calculator also gives the two-tailed probability, which is the share of values at least that far from the mean in either direction -- the figure that matters when the direction of the difference is not specified in advance.

That normality assumption is a real limitation and worth stating. The z-score itself is just arithmetic and always valid; the percentile attached to it is only as good as the assumption that the distribution is bell-shaped. For strongly skewed data, use the actual percentile from the data instead.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

• Shows z-score, percentile, probability below, probability above and beyond this far either way together, so you are not running it twice
• A results table you can read across
• Updates as you type, with no button to press and no page reload
• Copy the result in one click
• Free, no sign-up, and it runs entirely in your browser

The z-score calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

• Comparing results from tests with different scales
• Finding the percentile a score corresponds to
• Identifying outliers by how many standard deviations out they are
• Converting a z-score back into a raw value