Z-Score Calculator
Calculate the z-score (standard score) from a raw value, mean, and standard deviation.
Find how many standard deviations a value is from the mean.
Z-Score Results
Z-Score Formula:
z = (x - μ) / σ
Where:
- x = the raw value
- μ (mu) = the population mean
- σ (sigma) = the population standard deviation
What the Z-Score tells you:
- z = 0 means the value equals the mean
- z = 1 means the value is 1 standard deviation above the mean
- z = -2 means the value is 2 standard deviations below the mean
Common thresholds:
- About 68% of values fall within z = -1 to +1
- About 95% fall within z = -2 to +2
- About 99.7% fall within z = -3 to +3
This is known as the 68-95-99.7 rule (empirical rule).