How to calculate a z-score
Enter the observed value, the mean of the distribution, and the standard deviation. The z-score formula is: z = (x - mean) / standard deviation. The percentile tells you what percentage of the population scores below your value, assuming a normal distribution.
Z-score reference
z = 0 means the value equals the mean. z = 1 means one standard deviation above the mean (84th percentile). z = 2 means two standard deviations above the mean (97.7th percentile). z = -1 is one standard deviation below (15.9th percentile). About 68% of values fall within z = -1 to z = 1.
FAQ
What does a z-score tell you?
A z-score tells you how many standard deviations a value is from the mean. A z-score of 0 means the value is exactly at the mean. Positive z-scores are above the mean; negative z-scores are below.
What is the percentile calculated here?
The percentile is calculated using the cumulative distribution function (CDF) of the standard normal distribution. It tells you what percentage of a normally distributed population scores below your value.