How this normalization calculator works
Enter a score, the group mean, and the standard deviation. The calculator finds a Z-score with Z = (Score − Mean) ÷ Std. deviation. A score of 85 with mean 70 and standard deviation 10 is (85 − 70) ÷ 10 = 1.5000. The result is labelled Z-score and shown to four decimal places.
A Z-score counts how many standard deviations the score sits above or below the mean. Z = 0.0000 means the score equals the mean. Z = 1.0000 means one standard deviation above—for example 75 with mean 70 and standard deviation 5. Z = −1.5000 means one and a half standard deviations below, as with 55, 70, and 10.
Standard deviation must be a finite value greater than 0, because the formula divides by it. All three fields must be filled. An empty box, a zero or negative standard deviation, or a non-finite value leaves the result as “--.”
This page computes a standard score only. It is not min–max scaling into a 0–1 range. Check by hand: subtract the mean from the score, then divide by the standard deviation. For 92, 78, and 8 you get 14 ÷ 8 = 1.7500.