Z-score calculator
In a normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three. That is why a z-score above 2 is often treated as notable and above 3 as rare — roughly one value in 370 sits beyond three standard deviations in either direction. It only holds for data that is actually normal, which is worth checking before leaning on it.
A z-score is how many standard deviations a value sits from the mean: (x − μ) ÷ σ. A score of 115 against a mean of 100 and a standard deviation of 15 gives z = 1, which is the 84.1st percentile.
How to calculate a z-score
Standardising is what makes different scales comparable. An IQ of 115 and an SAT section score of 600 are both about one standard deviation above their means, so they represent the same relative standing despite being entirely different numbers. That is the whole purpose of a z-score: to strip away the units and the scale so that position within a distribution is all that remains.
Questions
The number of standard deviations a value is from the mean. Positive is above, negative below.