Z-Score Calculator
Compute standard deviation units from the population or sample mean.
Calculated Z-Score
1.5000
Percentile: 93.32% (Area to the left)
Step-by-Step Calculation:
$$ z = \frac{X - \mu}{\sigma} = \frac{85 - 70}{10} = \frac{15}{10} = 1.5000 $$
Z-Score Formulas & How to Calculate
View All Math Formulas Handbook →Population Z-Score Formula
Standard score using population parameters $\mu$ and $\sigma$:
$$ z = \frac{x - \mu}{\sigma} $$
How to calculate:
$$ \text{Numerator} = x - \mu, \quad z = \frac{\text{Numerator}}{\sigma} $$
Sample Z-Score Formula
Standard score using sample mean $\bar{x}$ and sample standard deviation $s$:
$$ z = \frac{x - \bar{x}}{s} $$
Inverse (converting $z$ back to $x$):
$$ x = \mu + z \times \sigma $$