Z-Score Calculator
How many standard deviations a value sits from the mean, and the percentile that implies.
The formula
z = (x - μ) / σ
A value of 130 against a mean of 100 and standard deviation of 15 gives z = 2: two standard deviations above average. On a normal curve that beats about 97.7% of values, which is exactly how IQ scores and standardized tests are scaled.
Reading z-scores
z = 0 is dead average; ±1 covers the middle 68% of a normal distribution, ±2 covers 95%, and ±3 covers 99.7% (the 68-95-99.7 rule). The percentile conversion assumes the data is roughly normal; for skewed data the z-score still measures distance from the mean, but the percentile reading no longer holds.